Abstract: The fractionalization of global symmetry charges is a striking hallmark of topological quantum order. Here, we discuss the fractionalization of subsystem symmetries in two-dimensional topological phases. In line with previous no-go arguments, we show that subsystem symmetry fractionalization is not possible in many cases due to the additional rigid geometric structure of the symmetries. However, we identify a mechanism that allows fractionalization, involving global relations between macroscopically many symmetry generators. We find that anyons can fractionalize such relations, meaning that the total charge carried under all generators involved in the global relation is nontrivial, despite the fact that these generators multiply to the identity. We first discuss the general algebraic framework needed to characterize this type of fractionalization, and then explore this framework using a number of exactly solvable models with Z₂ topological order, including models having line and fractal symmetries. These models all showcase another necessary property of subsystem symmetry fractionalization: Fractionalized anyons must have restricted mobility when the symmetry is enforced, such that they are confined to a single line or point in the case of line and fractal symmetries, respectively. Looking forward, we expect that our identification of the importance of global relations in fractionalization will hold significance for the classification of phases with subsystem symmetries in all dimensions.

Publication: Physical Review B Vol.: 106 No.: 8 ISSN: 2469-9950

ID: CaltechAUTHORS:20220803-536016000

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Abstract: We consider quantum error-correcting subsystem codes whose gauge generators realize a translation-invariant, free-fermion-solvable spin model. In this setting, errors are suppressed by a Hamiltonian whose terms are the gauge generators of the code and whose exact spectrum and eigenstates can be found via a generalized Jordan-Wigner transformation. Such solutions are characterized by the frustration graph of the Hamiltonian: the graph whose vertices are Hamiltonian terms, which are neighboring if the terms anticommute. We provide methods for embedding a given frustration graph in the anticommutation relations of a spin model and present the first known example of an exactly solvable spin model with a two-dimensional free-fermion description and exact topological qubits. This model can be viewed as a free-fermionized version of the two-dimensional Bacon-Shor code. Using graph-theoretic tools to study the unit cell, we give an efficient algorithm for deciding if a given translation-invariant spin model is solvable, and explicitly construct the solution. Further, we examine the energetics of these exactly solvable models from the graph-theoretic perspective and show that the relevant gaps of the spin model correspond to known graph-theoretic quantities: the skew energy and the median eigenvalue of an oriented graph. Finally, we numerically search for models that have large spectral gaps above the ground-state spin configuration and thus exhibit particularly robust thermal suppression of errors. These results suggest that optimal models will have low dimensionality and odd coordination numbers, and that the primary limit to energetic error suppression is the skew energy difference between different symmetry sectors rather than single-particle excitations of the free fermions.

Publication: PRX Quantum Vol.: 3 No.: 3 ISSN: 2691-3399

ID: CaltechAUTHORS:20220811-457365000

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Abstract: The dynamics of open quantum systems is generally described by a master equation, which describes the loss of information into the environment. By using a simple model of uncoupled emitters, we illustrate how the recovery of this information depends on the monitoring scheme applied to register the decay clicks. The dissipative dynamics, in this case, is described by pure-state stochastic trajectories, and we examine different unravelings of the same master equation. More precisely, we demonstrate how registering the sequence of clicks from spontaneously emitted photons through a linear optical interferometer induces entanglement in the trajectory states. Since this model consists of an array of single-photon emitters, we show a direct equivalence with Fock-state boson sampling and link the hardness of sampling the outcomes of the quantum jumps with the scaling of trajectory entanglement.

Publication: Physical Review Research Vol.: 4 No.: 3 ISSN: 2643-1564

ID: CaltechAUTHORS:20220809-495520000

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Abstract: Entanglement is one of the most important concepts in quantum physics. We review recent progress in understanding the quantum entanglement in many-body systems using large-N solvable models: the Sachdev—Ye—Kitaev (SYK) model and its generalizations. We present the study of entanglement entropy in the original SYK model using three different approaches: the exact diagonalization, the eigenstate thermalization hypothesis, and the path-integral representation. For coupled SYK models, the entanglement entropy shows linear growth and saturation at the thermal value. The saturation is related to replica wormholes in gravity. Finally, we consider the steady-state entanglement entropy of quantum many-body systems under repeated measurements. The traditional symmetry breaking in the enlarged replica space leads to the measurement-induced entanglement phase transition.

Publication: Frontiers of Physics Vol.: 17 No.: 4 ISSN: 2095-0462

ID: CaltechAUTHORS:20220329-173622413

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Abstract: The discovery of quantum many-body scars (QMBS) both in Rydberg atom simulators and in the Affleck–Kennedy–Lieb–Tasaki spin-1 chain model, have shown that a weak violation of ergodicity can still lead to rich experimental and theoretical physics. In this review, we provide a pedagogical introduction to and an overview of the exact results on weak ergodicity breaking via QMBS in isolated quantum systems with the help of simple examples such as the fermionic Hubbard model. We also discuss various mechanisms and unifying formalisms that have been proposed to encompass the plethora of systems exhibiting QMBS. We cover examples of equally-spaced towers that lead to exact revivals for particular initial states, as well as isolated examples of QMBS. Finally, we review Hilbert space fragmentation, a related phenomenon where systems exhibit a richer variety of ergodic and non-ergodic behaviors, and discuss its connections to QMBS.

Publication: Reports on Progress in Physics Vol.: 85 No.: 8 ISSN: 0034-4885

ID: CaltechAUTHORS:20211213-225027530

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Abstract: Twisted bilayer graphene (TBG) exhibits extremely low Fermi velocities for electrons, with the speed of sound surpassing the Fermi velocity. This regime enables the use of TBG for amplifying vibrational waves of the lattice through stimulated emission, following the same principles of operation of free-electron lasers. Our work proposes a lasing mechanism relying on the slow-electron bands to produce a coherent beam of acoustic phonons. We propose a device based on undulated electrons in TBG, which we dub the phaser. The device generates phonon beams in a terahertz (THz) frequency range, which can then be used to produce THz electromagnetic radiation. The ability to generate coherent phonons in solids breaks new ground in controlling quantum memories, probing quantum states, realizing non-equilibrium phases of matter, and designing new types of THz optical devices.

Publication: arXiv
ID: CaltechAUTHORS:20220816-183030641

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Abstract: Quantum Hall-superconductor heterostructures provide possible platforms for intrinsically fault-tolerant quantum computing. Motivated by several recent experiments that successfully integrated these phases, we investigate transport through a proximitized integer quantum Hall edge--paying particular attention to the impact of vortices in the superconductor. By examining the downstream conductance, we identify regimes in which sub-gap vortex levels mediate Andreev processes that would otherwise be frozen out in a vortex-free setup. Moreover, we show that at finite temperature, and in the limit of a large number of vortices, the downstream conductance can average to zero, indicating that the superconductor effectively behaves like a normal contact. Our results highlight the importance of considering vortices when using transport measurements to study superconducting correlations in quantum Hall-superconductor hybrids.

Publication: arXiv
ID: CaltechAUTHORS:20220816-192424755

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Abstract: Motivated by recent experiments on low-carrier-density superconductors, including twisted multilayer graphene, we study signatures of the BCS to BEC evolution in Andreev reflection spectroscopy. We establish that in a standard quantum point contact geometry, Andreev reflection in a BEC superconductor is unable to mediate a zero-bias conductance beyond e²/h per lead channel. This bound is shown to result from a duality that links the sub-gap conductance of BCS and BEC superconductors. We then demonstrate that sharp signatures of BEC superconductivity, including perfect Andreev reflection, can be recovered by tunneling through a suitably designed potential well. We propose various tunneling spectroscopy setups to experimentally probe this recovery.

Publication: arXiv
ID: CaltechAUTHORS:20220816-183023896

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Abstract: Relativistic Mott insulators known as “Kitaev materials” potentially realize spin liquids hosting non-Abelian anyons. Motivated by fault-tolerant quantum-computing applications in this setting, we introduce a dynamical anyon-generation protocol that exploits universal edge physics. The setup features holes in the spin liquid, which define energetically cheap locations for non-Abelian anyons, connected by a narrow bridge that can be tuned between spin liquid and topologically trivial phases. We show that modulating the bridge from trivial to spin liquid over intermediate time scales—quantified by analytics and extensive simulations—deposits non-Abelian anyons into the holes with O(1) probability. The required bridge manipulations can be implemented by integrating the Kitaev material into magnetic tunnel junction arrays that engender locally tunable exchange fields. Combined with existing readout strategies, our protocol reveals a path to topological qubit experiments in Kitaev materials at zero applied magnetic field.

Publication: Physical Review Letters Vol.: 129 No.: 3 ISSN: 0031-9007

ID: CaltechAUTHORS:20211214-190046323

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Abstract: Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyze a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent of the number of terms L in the Hamiltonian. Second, unlike previous L-independent approaches, such as those based on qDRIFT, all algorithmic errors in our method can be suppressed by collecting more data samples, without increasing the circuit depth.

Publication: Physical Review Letters Vol.: 129 No.: 3 ISSN: 0031-9007

ID: CaltechAUTHORS:20220714-369333000

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Abstract: Van der Waals (vdW) materials at their two-dimensional limit are diverse, flexible, and unique laboratories to study fundamental quantum phenomena and their future applications. Their novel properties rely on their pronounced Coulomb interactions, variety of crystal symmetries and spin-physics, and the ease of incorporation of different vdW materials to form sophisticated heterostructures. In particular, the excited state properties of many two-dimensional semiconductors and semi-metals are relevant for their technological applications, particularly those that can be induced by light. In this paper, we review the recent advances made in studying out-of-equilibrium, light-induced, phenomena in these materials using powerful, surface-sensitive, time-resolved photoemission-based techniques, with a particular emphasis on the emerging multi-dimensional photoemission spectroscopy technique of time-resolved momentum microscopy. We discuss the advances this technique has enabled in studying the nature and dynamics of occupied excited states in these materials. Then, we project for the future research directions opened by these scientific and instrumental advancements, studying the physics of two-dimensional materials and the opportunities to engineer their band-structure and band-topology by laser fields.

Publication: Advanced MaterialsISSN: 0935-9648

ID: CaltechAUTHORS:20220714-369415000

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Abstract: The transition metal monopnictide family of Weyl semimetals recently has been shown to exhibit anomalously strong second-order optical nonlinearity, which is theoretically attributed to a highly asymmetric polarization distribution induced by their polar structure. We experimentally test this hypothesis by measuring optical second harmonic generation (SHG) from TaAs across a pressure-tuned polar-to-nonpolar structural phase transition. Despite the high-pressure structure remaining noncentrosymmetric, the SHG yield is reduced by more than 60% by 20 GPa as compared to the ambient pressure value. By examining the pressure dependence of distinct groups of SHG susceptibility tensor elements, we find that the yield is primarily controlled by a single element that governs the response along the polar axis. Our results confirm a connection between the polar axis and the giant optical nonlinearity of Weyl semimetals and demonstrate pressure as a means to tune this effect in situ.

Publication: Physical Review B Vol.: 106 No.: 1 ISSN: 2469-9950

ID: CaltechAUTHORS:20220705-671865000

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Abstract: Twisted bilayers of nodal superconductors were recently proposed as a promising platform to host superconducting phases that spontaneously break time-reversal symmetry. Here we extend this analysis to twisted multilayers, focusing on two high-symmetry stackings with alternating (±θ) and constant (θ) twist angles. In analogy to alternating-twist multilayer graphene, the former can be mapped to twisted bilayers with renormalized interlayer couplings, along with a remnant gapless monolayer when the number of layers L is odd. In contrast, the latter exhibits physics beyond twisted bilayers, including the occurrence of “magic angles” characterized by cubic band crossings when L mod 4 = 3. Due to their power-law divergent density of states, such multilayers are highly susceptible to secondary instabilities. Within a BCS mean-field theory, defined in the continuum and on a lattice, we find that both stackings host chiral topological superconductivity in extended regions of their phase diagrams.

Publication: Physical Review B Vol.: 106 No.: 1 ISSN: 2469-9950

ID: CaltechAUTHORS:20220728-729493000

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Abstract: Triorthogonal codes are a class of quantum error-correcting codes used in magic state distillation protocols. We classify all triorthogonal codes with n+k≤38, where n is the number of physical qubits and k is the number of logical qubits of the code. We find 38 distinguished triorthogonal subspaces, and we show that every triorthogonal code with n+k≤38 descends from one of these subspaces through elementary operations such as puncturing and deleting qubits. Specifically, we associate each triorthogonal code with a Reed-Muller polynomial of weight n+k, and we classify the Reed-Muller polynomials of low weight using the results of Kasami, Tokura, and Azumi [IEEE Trans. Inf. Theory 16, 752 (1970); Inf. Contr. 30, 380 (1976)] and an extensive computerized search. In an Appendix independent of the main text, we improve a magic state distillation protocol by reducing the time variance due to stochastic Clifford corrections.

Publication: Physical Review A Vol.: 106 No.: 1 ISSN: 2469-9926

ID: CaltechAUTHORS:20220729-722022000

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Abstract: Universal fault-tolerant quantum computers will require the use of efficient protocols to implement encoded operations necessary in the execution of algorithms. In this work, we show how SMT solvers can be used to automate the construction of Clifford circuits with certain fault-tolerance properties and we apply our techniques to a fault-tolerant magic-state-preparation protocol. Part of the protocol requires converting magic states encoded in the color code to magic states encoded in the surface code. Since the teleportation step involves decoding a color code merged with a surface code, we develop a decoding algorithm that is applicable to such codes.

Publication: Physical Review Applied Vol.: 18 No.: 1 ISSN: 2331-7019

ID: CaltechAUTHORS:20220729-722274000

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Abstract: Synthesis of many-body quantum systems in the laboratory can provide further insight into the emergent behavior of quantum materials. While the majority of engineerable many-body systems, or quantum simulators, consist of particles on a lattice with local interactions, quantum systems featuring long-range interactions are particularly difficult to model and interesting to study due to the rapid spatio-temporal growth of entanglement in such systems. Here we present a scalable quantum simulator architecture based on superconducting transmon qubits on a lattice, with interactions mediated by the exchange of photons via a metamaterial waveguide quantum bus. The metamaterial waveguide enables extensible scaling of the system and multiplexed qubit read-out, while simultaneously protecting the qubits from radiative decay. As an initial demonstration of this platform, we realize a 10-qubit simulator of the one-dimensional Bose-Hubbard model, with in situ tunability of both the hopping range and the on-site interaction. We characterize the Hamiltonian of the system using a measurement-efficient protocol based on quantum many-body chaos, uncovering the remnant phase of Bloch waves of the metamaterial bus in the long-range hopping terms. We further study the many-body quench dynamics of the system, revealing through global bit-string statistics the predicted crossover from integrability to ergodicity as the hopping range is extended beyond nearest-neighbor. Looking forward, the metamaterial quantum bus may be extended to a two-dimensional lattice of qubits, and used to generate other spin-like lattice interactions or tailored lattice connectivity, expanding the accessible Hamiltonians for analog quantum simulation using superconducting quantum circuits.

Publication: arXiv
ID: CaltechAUTHORS:20220628-234305742

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Abstract: We study the problem of one-shot channel simulation of DMCs with unlimited shared randomness. For any fixed tolerance measured in total variational distance, we propose an achievability bound and a converse bound on the size of the code to simulate the channel. The achievability bound utilizes the convex split lemma, whereas the converse bound is the result of the relationships between smoothed max-divergences and the max-mutual information. The achievability proof does not rely on a "universal state" (compared with some previous related works), and provides a tighter bound. Using the two bounds, we also provide an alternative proof to the reverse Shannon theorem.

ID: CaltechAUTHORS:20220804-765722000

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Abstract: Light is a powerful tool for controlling mechanical motion, as shown by numerous applications in the field of cavity optomechanics. Recently, small scale optomechanical circuits, connecting a few optical and mechanical modes, have been demonstrated in an ongoing push towards multi-mode on-chip optomechanical systems. An ambitious goal driving this trend is to produce topologically protected phonon transport. Once realized, this will unlock the full toolbox of optomechanics for investigations of topological phononics. Here, we report the realization of topological phonon transport in an optomechanical device. Our experiment is based on an innovative multiscale optomechanical crystal design and allows for site-resolved measurements in an array of more than 800 cavities. The sensitivity inherent in our optomechanical read-out allowed us to detect thermal fluctuations traveling along topological edge channels. This represents a major step forward in an ongoing effort to downscale mechanical topological systems.

Publication: Nature Communications Vol.: 13ISSN: 2041-1723

ID: CaltechAUTHORS:20220622-390529700

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Abstract: Magic-angle twisted trilayer graphene (MATTG) has emerged as a moiré material that exhibits strong electronic correlations and unconventional superconductivity. However, local spectroscopic studies of this system are still lacking. Here we perform high-resolution scanning tunnelling microscopy and spectroscopy of MATTG that reveal extensive regions of atomic reconstruction favouring mirror-symmetric stacking. In these regions, we observe symmetry-breaking electronic transitions and doping-dependent band-structure deformations similar to those in magic-angle bilayers, as expected theoretically given the commonality of flat bands. Most notably in a density window spanning two to three holes per moiré unit cell, the spectroscopic signatures of superconductivity are manifest as pronounced dips in the tunnelling conductance at the Fermi level accompanied by coherence peaks that become gradually suppressed at elevated temperatures and magnetic fields. The observed evolution of the conductance with doping is consistent with a gate-tunable transition from a gapped superconductor to a nodal superconductor, which is theoretically compatible with a sharp transition from a Bardeen–Cooper–Schrieffer superconductor to a Bose–Einstein-condensation superconductor with a nodal order parameter. Within this doping window, we also detect peak–dip–hump structures that suggest that superconductivity is driven by strong coupling to bosonic modes of MATTG. Our results will enable further understanding of superconductivity and correlated states in graphene-based moiré structures beyond twisted bilayers.

Publication: Nature Vol.: 606 No.: 7914 ISSN: 0028-0836

ID: CaltechAUTHORS:20220621-285198100

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Abstract: Kramers' theorem ensures double degeneracy in the energy spectrum of a time-reversal symmetric fermionic system with half-integer total spin. Here, we are trying to go beyond the closed system and discuss Kramers' degeneracy in open systems out of equilibrium. A natural way to extend the Kramers' degeneracy in open quantum systems is by the degeneracy of different spins' spectra together with the vanishing interspin spectrum. We find the violation of Kramers' degeneracy in time-reversal symmetric open quantum systems is locked with whether the system reaches thermal equilibrium. After a general coupling to an environment in a time-reversal symmetry-preserving way, the Kramers doublet experiences an energy splitting at a short time and then a recovery process. We verified the violation and revival of Kramers' degeneracy in a concrete model of interacting fermions and we find Kramers' degeneracy is restored after the local thermalization time. By contrast, for time-reversal symmetry ˜T with ˜T²=1, we find that although there is a violation and revival of spectral degeneracy for different spins, the inter-spin spectral function is always nonzero. We also prove that the degeneracy in spectral function protected by unitary symmetry can always be maintained.

Publication: Physical Review B Vol.: 105 No.: 24 ISSN: 2469-9950

ID: CaltechAUTHORS:20211018-185259557

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Abstract: Quantum technology promises to revolutionize how we learn about the physical world. An experiment that processes quantum data with a quantum computer could have substantial advantages over conventional experiments in which quantum states are measured and outcomes are processed with a classical computer. We proved that quantum machines could learn from exponentially fewer experiments than the number required by conventional experiments. This exponential advantage is shown for predicting properties of physical systems, performing quantum principal component analysis, and learning about physical dynamics. Furthermore, the quantum resources needed for achieving an exponential advantage are quite modest in some cases. Conducting experiments with 40 superconducting qubits and 1300 quantum gates, we demonstrated that a substantial quantum advantage is possible with today’s quantum processors.

Publication: Science Vol.: 376 No.: 6598 ISSN: 0036-8075

ID: CaltechAUTHORS:20220113-234532429

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Abstract: We show that the universal Lindblad equation (ULE) captures steady-state expectation values of observables up to rigorously bounded corrections that scale linearly with the system-bath coupling, Γ. We moreover identify a simple quasilocal transformation, whose application guarantees a relative deviation generically scaling to zero with Γ, even for observables such as currents whose steady-state values themselves vanish in the weak coupling limit. This result provides a solution to recently identified limitations on the accuracy of Lindblad-form master equations, which imply significan't relative errors for observables whose steady-state values vanish with Γ, while most generic observables are otherwise captured faithfully. The transformation allows for high-fidelity computation of sensitive observables while retaining the stability and physicality of a Lindblad-form master equation.

Publication: arXiv
ID: CaltechAUTHORS:20220707-204116791

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Abstract: The Petz recovery channel plays an important role in quantum information science as an operation that approximately reverses the effect of a quantum channel. The pretty good measurement is a special case of the Petz recovery channel, and it allows for near-optimal state discrimination. A hurdle to the experimental realization of these vaunted theoretical tools is the lack of a systematic and efficient method to implement them. This Letter sets out to rectify this lack: Using the recently developed tools of quantum singular value transformation and oblivious amplitude amplification, we provide a quantum algorithm to implement the Petz recovery channel when given the ability to perform the channel that one wishes to reverse. Moreover, we prove that, in some sense, our quantum algorithm’s usage of the channel implementation cannot be improved by more than a quadratic factor. Our quantum algorithm also provides a procedure to perform pretty good measurements when given multiple copies of the states that one is trying to distinguish.

Publication: Physical Review Letters Vol.: 128 No.: 22 ISSN: 0031-9007

ID: CaltechAUTHORS:20220608-849402000

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Abstract: Advances in isolating, controlling and entangling quantum systems are transforming what was once a curious feature of quantum mechanics into a vehicle for disruptive scientific and technological progress. Pursuing the vision articulated by Feynman, a concerted effort across many areas of research and development is introducing prototypical digital quantum devices into the computing ecosystem available to domain scientists. Through interactions with these early quantum devices, the abstract vision of exploring classically-intractable quantum systems is evolving toward becoming a tangible reality. Beyond catalyzing these technological advances, entanglement is enabling parallel progress as a diagnostic for quantum correlations and as an organizational tool, both guiding improved understanding of quantum many-body systems and quantum field theories defining and emerging from the standard model. From the perspective of three domain science theorists, this article compiles thoughts about the interface on entanglement, complexity, and quantum simulation in an effort to contextualize recent NISQ-era progress with the scientific objectives of nuclear and high-energy physics.

Publication: Reports on Progress in Physics Vol.: 85 No.: 6 ISSN: 0034-4885

ID: CaltechAUTHORS:20210825-184704845

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Abstract: Non-unitary evolution can give rise to novel steady states classified by their entanglement properties. In this work, we aim to understand the effect of long-range hopping that decays with r^(−α) in non-Hermitian free-fermion systems. We first study two solvable Brownian models with long-range non-unitary dynamics: a large-N SYK₂ chain and a single-flavor fermion chain and we show that they share the same phase diagram. When α > 0.5, we observe two critical phases with subvolume entanglement scaling: (i) α > 1.5, a logarithmic phase with dynamical exponent z = 1 and logarithmic subsystem entanglement, and (ii) 0.5 < α < 1.5, a fractal phase with z = 2α−1/2 and subsystem entanglement S_A∝L^(1−z)/A, where L_A is the length of the subsystem A. These two phases cannot be distinguished by the purification dynamics, in which the entropy always decays as L/T. We then confirm that the results are also valid for the static SYK₂ chain, indicating the phase diagram is universal for general free-fermion systems. We also discuss phase diagrams in higher dimensions and the implication in measurement-induced phase transitions.

Publication: Quantum Vol.: 6ISSN: 2521-327X

ID: CaltechAUTHORS:20210629-200841842

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Abstract: Strange metal behavior appears across a variety of condensed matter settings and beyond, and achieving a universal understanding is an exciting prospect. The beyond-Landau quantum criticality of Kondo destruction has had considerable success in describing the behavior of strange metal heavy fermion compounds, and there is some evidence that the associated partial localization-delocalization nature can be generalized to diverse materials classes. Other potential overarching principles at play are also being explored. An intriguing proposal is that Planckian scattering, with a rate of k_BT/ℏ, captures the linear temperature dependence of the (dc) electrical resistivity, which is a hallmark of strange metal behavior. Here we extend a previously introduced analysis scheme based of the Drude description of the dc resistivity to optical conductivity data. When they are well described by a simple (ac) Drude model, the scattering rate can be directly extracted. This avoids the need to determine the ratio of charge carrier concentration to effective mass, which has complicated previous analyses based on the dc resistivity. However, we point out that strange metals may exhibit strong deviations from Drude behavior, as exemplified by the "extreme" strange metal YbRh₂Si₂. This calls for alternative approaches, and we point to the power of scaling relationships in terms of temperature and energy (or frequency).

Publication: arXiv
ID: CaltechAUTHORS:20220707-204118082

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Abstract: Optical control of polyatomic molecules promises new opportunities in precision metrology, fundamental chemistry, quantum information, and many-body science. Contemporary experimental and theoretical efforts have mostly focused on cycling photons via excitation of a single electron localized to an alkaline earth (group 2)-like metal center. In this manuscript, we consider pathways towards optical cycling in polyatomic molecules with multi-electron degrees of freedom, which arise from two or more cycling electrons localized to p-block post-transition metal and metalloid (group 13, 14, and 15) centers. We characterize the electronic structure and rovibrational branching of several prototypical candidates using ab initio quantum chemical methods. Despite increased internal complexity and challenging design parameters, we find several molecules possessing quasi-closed photon cycling schemes with highly diagonal, visible and near-infrared transitions. Furthermore, we identify new heuristics for engineering optically controllable and laser-coolable polyatomic molecules with multi-electron cycling centers. Our results help elucidate the interplay between hybridization, repulsion, and ionicity in optically active species and provide a first step towards using polyatomic molecules with complex electronic structure as a resource for quantum science and measurement.

Publication: arXiv
ID: CaltechAUTHORS:20220707-204114065

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Abstract: Numerical codes that require arbitrary precision floating point (APFP) numbers for their core computation are dominated by elementary arithmetic operations due to the super-linear complexity of multiplication in the number of mantissa bits. APFP computations on conventional software-based architectures are made exceedingly expensive by the lack of native hardware support, requiring elementary operations to be emulated using instructions operating on machine-word-sized blocks. In this work, we show how APFP multiplication on compile-time fixed-precision operands can be implemented as deep FPGA pipelines with a recursively defined Karatsuba decomposition on top of native DSP multiplication. When comparing our design implemented on an Alveo U250 accelerator to a dual-socket 36-core Xeon node running the GNU Multiple Precision Floating-Point Reliable (MPFR) library, we achieve a 9.8× speedup at 4.8 GOp/s for 512-bit multiplication, and a 5.3× speedup at 1.2 GOp/s for 1024-bit multiplication, corresponding to the throughput of more than 351× and 191× CPU cores, respectively. We apply this architecture to general matrix-matrix multiplication, yielding a 10× speedup at 2.0 GOp/s over the Xeon node, equivalent to more than 375× CPU cores, effectively allowing a single FPGA to replace a small CPU cluster. Due to the significant dependence of some numerical codes on APFP, such as semidefinite program solvers, we expect these gains to translate into real-world speedups. Our configurable and flexible HLS-based code provides as high-level software interface for plug-and-play acceleration, published as an open source project.

ID: CaltechAUTHORS:20220614-222241000

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Abstract: Fracton order features point excitations that either cannot move at all or are only allowed to move in a lower-dimensional submanifold of the whole system. In this paper, we generalize the (2+1)-dimensional [(2+1)D] U(1) Chern-Simons (CS) theory, a powerful tool in the study of (2+1)D topological orders, to include infinite gauge field components and find that they can describe interesting types of (3+1)-dimensional fracton order beyond what is known from exactly solvable models and tensor gauge theories. On the one hand, they can describe foliated fractonic systems for which increasing the system size requires insertion of nontrivial (2+1)D topological states. The CS formulation provides an easier approach to study the phase relation among foliated models. More interestingly, we find simple examples that lie beyond the foliation framework, characterized by 2D excitations of infinite order and irrational braiding statistics. This finding extends our realm of understanding of possible fracton phenomena.

Publication: Physical Review B Vol.: 105 No.: 19 ISSN: 2469-9950

ID: CaltechAUTHORS:20210106-102305508

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Abstract: Twisted bilayer graphene (TBG) near the magic twist angle of ∼1.1° exhibits a rich phase diagram. However, the interplay between different phases and their dependence on twist angle is still elusive. Here, we explore the stability of various TBG phases and demonstrate that superconductivity near filling of two electrons per moiré unit cell alongside Fermi surface reconstructions, as well as entropy-driven high-temperature phase transitions and linear-in-T resistance occur over a range of twist angles which extends far beyond those exhibiting correlated insulating phases. In the vicinity of the magic angle, we also find a metallic phase that displays a hysteretic anomalous Hall effect and incipient Chern insulating behaviour. Such a metallic phase can be rationalized in terms of the interplay between interaction-driven deformations of TBG bands leading to Berry curvature redistribution and Fermi surface reconstruction. Our results provide an extensive perspective on the hierarchy of correlated phases in TBG as classified by their robustness against deviations from the magic angle or, equivalently, their electronic interaction requirements.

Publication: arXiv
ID: CaltechAUTHORS:20220524-180258498

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Abstract: In the presence of a large perpendicular electric field, Bernal-stacked bilayer graphene (BLG) features several broken-symmetry metallic phases as well as magnetic-field-induced superconductivity. The superconducting state is quite fragile, however, appearing only in a narrow window of density and with a maximum critical temperature T꜀ ≈ 30~mK. Here, we show that placing monolayer tungsten diselenide (WSe₂) on BLG promotes Cooper pairing to an extraordinary degree: superconductivity appears at zero magnetic field, exhibits an order of magnitude enhancement in T꜀, and occurs over a density range that is wider by a factor of eight. By mapping quantum oscillations in BLG-WSe₂ as a function of electric field and doping, we establish that superconductivity emerges throughout a region whose normal state is polarized, with two out of four spin-valley flavours predominantly populated. In-plane magnetic field measurements further reveal a striking dependence of the critical field on doping, with the Chandrasekhar-Clogston (Pauli) limit roughly obeyed on one end of the superconducting dome yet sharply violated on the other. Moreover, the superconductivity arises only for perpendicular electric fields that push BLG hole wavefunctions towards WSe₂ -- suggesting that proximity-induced (Ising) spin-orbit coupling plays a key role in enhancing the pairing. Our results pave the way for engineering robust, highly tunable, and ultra-clean graphene-based superconductors.

Publication: arXiv
ID: CaltechAUTHORS:20220524-180301852

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Abstract: The fate of a Mott insulator under strong low frequency optical driving conditions is a fundamental problem in quantum many-body dynamics. Using ultrafast broadband optical spectroscopy, we measured the transient electronic structure and charge dynamics of an off-resonantly pumped Mott insulator Ca₂RuO₄. We observe coherent bandwidth renormalization and nonlinear doublon-holon pair production occurring in rapid succession within a sub-100-fs pump pulse duration. By sweeping the electric field amplitude, we demonstrate continuous bandwidth tuning and a Keldysh crossover from a multiphoton absorption to quantum tunneling dominated pair production regime. Our results provide a procedure to control coherent and nonlinear heating processes in Mott insulators, facilitating the discovery of novel out-of-equilibrium phenomena in strongly correlated systems.

Publication: Physical Review Letters Vol.: 128 No.: 18 ISSN: 0031-9007

ID: CaltechAUTHORS:20220525-286273000

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Abstract: We show that the proof of the generalised quantum Stein's lemma [Brandão & Plenio, Commun. Math. Phys. 295, 791 (2010)] is not correct due to a gap in the argument leading to Lemma III.9. Hence, the main achievability result of Brandão & Plenio is not known to hold. This puts into question a number of established results in the literature, in particular the reversibility of quantum entanglement [Brandão & Plenio, Commun. Math. Phys. 295, 829 (2010); Nat. Phys. 4, 873 (2008)] and of general quantum resources [Brandão & Gour, Phys. Rev. Lett. 115, 070503 (2015)] under asymptotically resource non-generating operations. We discuss potential ways to recover variants of the newly unsettled results using other approaches.

Publication: arXiv
ID: CaltechAUTHORS:20220804-201336824

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Abstract: Contribution: A roadmap is provided for building a quantum engineering education program to satisfy U.S. national and international workforce needs. Background: The rapidly growing quantum information science and engineering (QISE) industry will require both quantum-aware and quantum-proficient engineers at the bachelor's level. Research Question: What is the best way to provide a flexible framework that can be tailored for the full academic ecosystem? Methodology: A workshop of 480 QISE researchers from across academia, government, industry, and national laboratories was convened to draw on best practices; representative authors developed this roadmap. Findings: 1) For quantum-aware engineers, design of a first quantum engineering course, accessible to all STEM students, is described; 2) for the education and training of quantum-proficient engineers, both a quantum engineering minor accessible to all STEM majors, and a quantum track directly integrated into individual engineering majors are detailed, requiring only three to four newly developed courses complementing existing STEM classes; 3) a conceptual QISE course for implementation at any postsecondary institution, including community colleges and military schools, is delineated; 4) QISE presents extraordinary opportunities to work toward rectifying issues of inclusivity and equity that continue to be pervasive within engineering. A plan to do so is presented, as well as how quantum engineering education offers an excellent set of education research opportunities; and 5) a hands-on training plan on quantum hardware is outlined, a key component of any quantum engineering program, with a variety of technologies, including optics, atoms and ions, cryogenic and solid-state technologies, nanofabrication, and control and readout electronics.

Publication: IEEE Transactions on Education Vol.: 65 No.: 2 ISSN: 0018-9359

ID: CaltechAUTHORS:20220210-721846000

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Abstract: Lattice surgery is a measurement-based technique for performing fault-tolerant quantum computation in two dimensions. When using the surface code, the most general lattice surgery operations require lattice irregularities called twist defects. However, implementing twist-based lattice surgery may require additional resources, such as extra device connectivity, and could lower the threshold and overall performance for the surface code. Here we provide an explicit twist-based lattice surgery protocol and its requisite connectivity layout. We also provide new stabilizer measurement circuits for measuring twist defects which are compatible with our chosen gate scheduling. We undertake the first circuit-level error correction simulations during twist-based lattice surgery using a biased depolarizing noise model. Our results indicate a slight decrease in the threshold for timelike logical failures compared to lattice surgery protocols with no twist defects in the bulk. However, comfortably below threshold (i.e., with CNOT infidelities below 5 × 10⁻³), the performance degradation is mild and in fact preferable over proposed alternative twist-free schemes. Lastly, we provide an efficient scheme for measuring Y operators along boundaries of surface codes, which bypasses certain steps that were required in previous schemes.

Publication: Physical Review Research Vol.: 4 No.: 2 ISSN: 2643-1564

ID: CaltechAUTHORS:20220601-257648000

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Abstract: Quantum chaos in Hermitian systems concerns the sensitivity of long-time dynamical evolution to initial conditions. The skin effect discovered recently in non-Hermitian systems reveals the sensitivity to the spatial boundary condition even deep in the bulk. In this Letter, we show that these two seemingly different phenomena can be unified through the space-time duality. The intuition is that the space-time duality maps unitary dynamics to nonunitary dynamics and exchanges the temporal direction and spatial direction. Therefore, the space-time duality can establish the connection between the sensitivity to the initial condition in the temporal direction and the sensitivity to the boundary condition in the spatial direction. Here, we demonstrate this connection by studying the space-time duality of the out-of-time-ordered correlator in a concrete chaotic Hermitian model. We show that the out-of-time-ordered correlator is mapped to a special two-point correlator of a non-Hermitian system in the dual picture. For comparison, we show that the sensitivity disappears when the non-Hermiticity is removed in the dual picture.

Publication: Physical Review Research Vol.: 4 No.: 2 ISSN: 2643-1564

ID: CaltechAUTHORS:20220629-796883600

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Abstract: Optomechanical crystals provide coupling between phonons and photons by confining them to commensurate wavelength-scale dimensions. We present a new concept for designing optomechanical crystals capable of achieving unprecedented coupling rates by confining optical and mechanical waves to deep sub-wavelength dimensions. Our design is based on a dielectric bowtie unit cell with an effective optical/mechanical mode volume of 7.6 × 10⁻³ (λ/n_(Si))³/1.2 × 10⁻³ λ_(mech)³. We present results from numerical modeling, indicating a single-photon optomechanical coupling of 2.2 MHz with experimentally viable parameters. Monte Carlo simulations are used to demonstrate the design’s robustness against fabrication disorder.

Publication: Optics Express Vol.: 30 No.: 8 ISSN: 1094-4087

ID: CaltechAUTHORS:20220223-214609456

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Abstract: Controlling the density of exciton and trion quasiparticles in monolayer two-dimensional (2D) materials at room temperature by nondestructive techniques is highly desired for the development of future optoelectronic devices. Here, the effects of different orbital angular momentum (OAM) lights on monolayer tungsten disulfide at both room temperature and low temperatures are investigated, which reveal simultaneously enhanced exciton intensity and suppressed trion intensity in the photoluminescence spectra with increasing topological charge of the OAM light. In addition, the trion-to-exciton conversion efficiency is found to increase rapidly with the OAM light at low laser power and decrease with increasing power. Moreover, the trion binding energy and the concentration of unbound electrons are estimated, which shed light on how these quantities depend on OAM. A phenomenological model is proposed to account for the experimental data. These findings pave a way toward manipulating the exciton emission in 2D materials with OAM light for optoelectronic applications.

Publication: Science Advances Vol.: 8 No.: 13 ISSN: 2375-2548

ID: CaltechAUTHORS:20220413-746783000

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Abstract: It is well established that linear dispersive modes in a flowing quantum fluid behave as though they are coupled to an Einstein-Hilbert metric and exhibit a host of phenomena coming from quantum field theory in curved space, including Hawking radiation. We extend this analogy to any nonrelativistic Goldstone mode in a flowing spinor Bose-Einstein condensate. In addition to showing the linear dispersive result for all such modes, we show that the quadratically dispersive modes couple to a special nonrelativistic spacetime called a Newton-Cartan geometry. The kind of spacetime (Einstein-Hilbert or Newton-Cartan) is intimately linked to the mean-field phase of the condensate. To illustrate the general result, we further provide the specific theory in the context of a pseudospin-1/2 condensate where we can tune between relativistic and nonrelativistic geometries. We uncover the fate of Hawking radiation upon such a transition: it vanishes and remains absent in the Newton-Cartan geometry despite the fact that any fluid flow creates a horizon for certain wave numbers. Finally, we use the coupling to different spacetimes to compute and relate various energy and momentum currents in these analog systems. While this result is general, present-day experiments can realize these different spacetimes including the magnon modes for spin-1 condensates such as ⁸⁷Rb, ⁷Li, ⁴¹K (Newton-Cartan), and ²³Na (Einstein-Hilbert).

Publication: Physical Review A Vol.: 105 No.: 4 ISSN: 2469-9926

ID: CaltechAUTHORS:20220601-257657000

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Abstract: Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states whose site-averaged ground state properties match the translation-invariant critical Ising model. In this work, we substantially sharpen this relationship by deriving disordered local Hamiltonians generalizing the critical Ising model whose ground and low-energy excited states are accurately represented by the matchgate ansatz without any averaging. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model based on layers of the hyperbolic lattice, breaking the conformal symmetries of the critical Ising model in a controlled manner. We provide a direct identification of correlation functions of ground and low-energy excited states between the disordered and translation-invariant models and give numerical evidence that the former approaches the latter in the large bond dimension limit. This establishes tensor networks on regular hyperbolic tilings as an effective tool for the study of conformal field theories. Furthermore, our numerical probes of the bulk parameters corresponding to boundary excited states constitute a first step towards a tensor network bulk-boundary dictionary between regular hyperbolic geometries and critical boundary states.

Publication: Journal of High Energy Physics Vol.: 2022 No.: 4 ISSN: 1029-8479

ID: CaltechAUTHORS:20220603-310946700

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Abstract: We simulate, using nonperturbative methods, the real-time dynamics of small bubbles of “false vacuum” in a quantum spin chain near criticality, where the low-energy physics is described by a relativistic (1+1)-dimensional quantum field theory. We consider bubbles whose walls are kink and antikink quasiparticle excitations, so that wall collisions are kink-antikink scattering events. To construct these bubbles in the presence of strong correlations, we extend a recently proposed matrix product state (MPS) ansatz for quasiparticle wavepackets. We simulate dynamics within a window of about 1000 spins embedded in an infinite chain at energies of up to about 5 times the mass gap. By choosing the wavepacket width and the bubble size appropriately, we avoid strong lattice effects and observe relativistic kink-antikink collisions. We use the MPS quasiparticle ansatz to detect scattering outcomes. (i) In the Ising model, with transverse and longitudinal fields, we do not observe particle production despite nonintegrability (supporting recent observations of nonthermalizing states in this model). (ii) Switching on an additional interaction, we see production of confined and unconfined particle pairs. We characterize the amount of entanglement generated as a function of energy and time and conclude that our classical simulation methods will ultimately fail as these increase. We anticipate that kink-antikink scattering in 1+1 dimensions will be an instructive benchmark problem for future quantum computers and analog quantum simulators.

Publication: PRX Quantum Vol.: 3 No.: 2 ISSN: 2691-3399

ID: CaltechAUTHORS:20210512-104051553

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Abstract: A central question of quantum computing is determining the source of the advantage of quantum computation over classical computation. Even though simulating quantum dynamics on a classical computer is thought to require exponential overhead in the worst case, efficient simulations are known to exist in several special cases. It was widely assumed that these easy-to-simulate cases as well as any yet-undiscovered ones could be avoided by choosing a quantum circuit at random. We prove that this intuition is false by showing that certain families of constant-depth, 2D random circuits can be approximately simulated on a classical computer in time only linear in the number of qubits and gates, even though the same families are capable of universal quantum computation and are hard to exactly simulate in the worst case (under standard hardness assumptions). While our proof applies to specific random circuit families, we demonstrate numerically that typical instances of more general families of sufficiently shallow constant-depth 2D random circuits are also efficiently simulable. We propose two classical simulation algorithms. One is based on first simulating spatially local regions which are then “stitched” together via recovery maps. The other reduces the 2D simulation problem to a problem of simulating a form of 1D dynamics consisting of alternating rounds of random local unitaries and weak measurements. Similar processes have recently been the subject of an intensive research focus, which has observed that the dynamics generally undergo a phase transition from a low-entanglement (and efficient-to-simulate) regime to a high-entanglement (and inefficient-to-simulate) regime as measurement strength is varied. Via a mapping from random quantum circuits to classical statistical mechanical models, we give analytical evidence that a similar computational phase transition occurs for both of our algorithms as parameters of the circuit architecture like the local Hilbert space dimension and circuit depth are varied and, additionally, that the effective 1D dynamics corresponding to sufficiently shallow random quantum circuits falls within the efficient-to-simulate regime. Implementing the latter algorithm for the depth-3 “brickwork” architecture, for which exact simulation is hard, we find that a laptop could simulate typical instances on a 409×409 grid with a total variation distance error less than 0.01 in approximately one minute per sample, a task intractable for previously known circuit simulation algorithms. Numerical results support our analytic evidence that the algorithm is asymptotically efficient.

Publication: Physical Review X Vol.: 12 No.: 2 ISSN: 2160-3308

ID: CaltechAUTHORS:20210512-104029585

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Abstract: Moiré materials, and in particular twisted bilayer graphene (TBG), exhibit a range of fascinating phenomena that emerge from the interplay of band topology and interactions. We show that the nonlinear second-order photoresponse is an appealing probe of this rich interplay. A dominant part of the photoresponse is the shift current, which is determined by the geometry of the electronic wave functions and carrier properties and thus becomes strongly modified by electron-electron interactions. We analyze its dependence on the twist angle and doping and investigate the role of interactions. In the absence of interactions, the response of the system is dictated by two energy scales: (i) the mean energy of direct transitions between the hole and electron flat bands and (ii) the gap between flat and dispersive bands. Including electron-electron interactions both enhances the response at the noninteracting characteristic frequencies and produces new resonances. We attribute these changes to the filling-dependent band renormalization in TBG. Our results highlight the connection between nontrivial geometric properties of TBG and its optical response, as well as demonstrate how optical probes can access the role of interactions in moiré materials.

Publication: Physical Review Research Vol.: 4 No.: 1 ISSN: 2643-1564

ID: CaltechAUTHORS:20210825-184647720

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Abstract: Arrays of Rydberg atoms constitute a highly tunable, strongly interacting venue for the pursuit of exotic states of matter. We develop a new strategy for accessing a family of fractionalized phases known as quantum spin liquids in two-dimensional Rydberg arrays. We specifically use effective field theory methods to study arrays assembled from Rydberg chains tuned to an Ising phase transition that famously hosts emergent fermions propagating within each chain. This highly entangled starting point allows us to naturally access spin liquids familiar from Kitaev's honeycomb model, albeit from an entirely different framework. In particular, we argue that finite-range repulsive Rydberg interactions, which frustrate nearby symmetry-breaking orders, can enable coherent propagation of emergent fermions between the chains in which they were born. Delocalization of emergent fermions across the full two-dimensional Rydberg array yields a gapless Z2 spin liquid with a single massless Dirac cone. Here, the Rydberg occupation numbers exhibit universal power-law correlations that provide a straightforward experimental diagnostic of this phase. We further show that explicitly breaking symmetries perturbs the gapless spin liquid into gapped, topologically ordered descendants: Breaking lattice symmetries generates toric-code topological order, whereas introducing chirality generates non-Abelian Ising topological order. In the toric-code phase, we analytically construct microscopic incarnations of non-Abelian defects, which can be created and transported by dynamically controlling the atom positions in the array. Our work suggests that appropriately tuned Rydberg arrays provide a cold-atoms counterpart of solid-state 'Kitaev materials' and, more generally, spotlights a new angle for pursuing experimental platforms for Abelian and non-Abelian fractionalization.

Publication: arXiv
ID: CaltechAUTHORS:20220428-212235605

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Abstract: We show how to apply the recursive quantum approximate optimization algorithm (RQAOA) to MAX-k-CUT, the problem of finding an approximate k-vertex coloring of a graph. We compare this proposal to the best known classical and hybrid classical-quantum algorithms. First, we show that the standard (non-recursive) QAOA fails to solve this optimization problem for most regular bipartite graphs at any constant level p: the approximation ratio achieved by QAOA is hardly better than assigning colors to vertices at random. Second, we construct an efficient classical simulation algorithm which simulates level-1 QAOA and level-1 RQAOA for arbitrary graphs. In particular, these hybrid algorithms give rise to efficient classical algorithms, and no benefit arising from the use of quantum mechanics is to be expected. Nevertheless, they provide a suitable testbed for assessing the potential benefit of hybrid algorithm: We use the simulation algorithm to perform large-scale simulation of level-1 QAOA and RQAOA with up to 300 qutrits applied to ensembles of randomly generated 3-colorable constant-degree graphs. We find that level-1 RQAOA is surprisingly competitive: for the ensembles considered, its approximation ratios are often higher than those achieved by the best known generic classical algorithm based on rounding an SDP relaxation. This suggests the intriguing possibility that higher-level RQAOA may be a potentially useful algorithm for NISQ devices.

Publication: Quantum Vol.: 6ISSN: 2521-327X

ID: CaltechAUTHORS:20220622-433041200

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Abstract: Protected qubits such as the 0−π qubit, and bosonic qubits including cat qubits and Gottesman-Kitaev-Preskill (GKP) qubits offer advantages for fault tolerance. Some of these protected qubits (e.g., 0−π qubit and Kerr-cat qubit) are stabilized by Hamiltonians which have (near-)degenerate ground state manifolds with large energy gaps to the excited state manifolds. Without dissipative stabilization mechanisms the performance of such energy-gap-protected qubits can be limited by leakage to excited states. Here, we propose a scheme for dissipatively stabilizing an energy-gap-protected qubit using colored (i.e., frequency-selective) dissipation without inducing errors in the ground state manifold. Concretely we apply our colored dissipation technique to Kerr-cat qubits and propose colored Kerr-cat qubits which are protected by an engineered colored single-photon loss. When applied to the Kerr-cat qubits our scheme significantly suppresses leakage-induced bit-flip errors (which we show are a limiting error mechanism) while only using linear interactions. Beyond the benefits to the Kerr-cat qubit we also show that our frequency-selective loss technique can be applied to a broader class of protected qubits.

Publication: Physical Review Letters Vol.: 128 No.: 11 ISSN: 0031-9007

ID: CaltechAUTHORS:20210922-210830647

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Abstract: Protected qubits such as the 0−π qubit, and bosonic qubits including cat qubits and Gottesman-Kitaev-Preskill (GKP) qubits offer advantages for fault tolerance. Some of these protected qubits (e.g., 0−π qubit and Kerr-cat qubit) are stabilized by Hamiltonians which have (near-)degenerate ground state manifolds with large energy gaps to the excited state manifolds. Without dissipative stabilization mechanisms the performance of such energy-gap-protected qubits can be limited by leakage to excited states. Here, we propose a scheme for dissipatively stabilizing an energy-gap-protected qubit using colored (i.e., frequency-selective) dissipation without inducing errors in the ground state manifold. Concretely we apply our colored dissipation technique to Kerr-cat qubits and propose colored Kerr-cat qubits which are protected by an engineered colored single-photon loss. When applied to the Kerr-cat qubits our scheme significantly suppresses leakage-induced bit-flip errors (which we show are a limiting error mechanism) while only using linear interactions. Beyond the benefits to the Kerr-cat qubit we also show that our frequency-selective loss technique can be applied to a broader class of protected qubits.

Publication: Physical Review Letters Vol.: 128 No.: 11 ISSN: 0031-9007

ID: CaltechAUTHORS:20220315-626393000

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Abstract: Moiré materials such as magic angle twisted bilayer graphene (MATBG) exhibit remarkable phenomenology, but present significant challenges for certain experimental methods, particularly scanning probes such as scanning tunneling microscopy (STM). Typical STM studies that can image tens of thousands of atomic unit cells can image roughly ten moiré cells, making data analysis statistically fraught. Here, we propose a method to mitigate this problem by aggregating STM conductance data from several bias voltages, and then using the unsupervised machine learning method of gaussian mixture model clustering to draw maximal insight from the resulting dataset. We apply this method, using as input coarse-grained bond variables respecting the point group symmetry, to investigate nematic ordering tendencies in MATBG for both charge neutral and hole-doped samples. For the charge-neutral dataset, the clustering reveals the surprising coexistence of multiple types of nematicity that are unrelated by symmetry, and therefore generically nondegenerate. By contrast, the clustering in the hole doped data is consistent with long range order of a single type. Beyond its value in analyzing nematicity in MATBG, our method has the potential to enhance understanding of symmetry breaking and its spatial variation in a variety of moiré materials.

Publication: arXiv
ID: CaltechAUTHORS:20220524-180254587

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Abstract: Magnetic monopoles play a central role in areas of physics that range from electromagnetism to topological matter. String theory promotes conventional vector gauge fields of electrodynamics to tensor gauge fields and predicts the existence of more exotic tensor monopoles. Here, we report the synthesis of a tensor monopole in a four-dimensional parameter space defined by the spin degrees of freedom of a single solid-state defect in diamond. Using two complementary methods, we characterized the tensor monopole by measuring its quantized topological charge and its emanating Kalb-Ramond field. By introducing a fictitious external field that breaks chiral symmetry, we further observed an intriguing spectral transition, characterized by spectral rings protected by mirror symmetries. Our work demonstrates the possibility of emulating exotic topological structures inspired by string theory.

Publication: Science Vol.: 375 No.: 6584 ISSN: 0036-8075

ID: CaltechAUTHORS:20220512-105365100

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Abstract: Stabilized cat qubits that possess biased noise channel with bit-flip errors exponentially smaller than phase-flip errors. Together with a set of bias-preserving (BP) gates, cat qubits are a promising candidate for realizing hardware efficient quantum error correction and fault-tolerant quantum computing. Compared to dissipatively stabilized cat qubits, the Kerr cat qubits can in principle support faster gate operations with higher gate fidelity, benefiting from the large energy gap that protects the code space. However, the leakage of the Kerr cats can increase the minor type of errors and compromise the noise bias. Both the fast implementation of gates and the interaction with environment can lead to such detrimental leakage if no sophisticated controls are applied. In this work, we introduce new fine-control techniques to overcome the above obstacles for Kerr cat qubits. To suppress the gate leakage, we use the derivative-based transition suppression technique to design derivative-based controls for the Kerr BP gates. We show that the fine-controlled gates can simultaneously have high gate fidelity and high noise bias and when applied to concatenated quantum error correction, can not only improve the logical error rate but also reduce resource overhead. To suppress the environment-induced leakage, we introduce colored single-photon dissipation, which can continuously cool the Kerr cats and suppress the minor errors while not enhancing the major errors.

No.: 12015
ID: CaltechAUTHORS:20220307-189714000

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Abstract: Out-of-time-order correlators (OTOCs) are a standard measure of quantum chaos. Of the four operators involved, one pair may be regarded as a source and the other as a probe. A usual approach, applicable to large-N systems such as the SYK model, is to replace the actual source with some mean-field perturbation and solve for the probe correlation function on the double Keldysh contour. We show how to obtain the OTOC by combining two such solutions for perturbations propagating forward and backward in time. These dynamical perturbations, or scrambling modes, are considered on the thermofield double background and decomposed into a coherent and an incoherent part. For the large-q SYK, we obtain the OTOC in a closed form. We also prove a previously conjectured relation between the Lyapunov exponent and high-frequency behavior of the spectral function.

Publication: Journal of High Energy Physics Vol.: 2022 No.: 3 ISSN: 1029-8479

ID: CaltechAUTHORS:20220323-545297000

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Abstract: The competition between kinetic energy and Coulomb interactions in electronic systems leads to complex many-body ground states with competing orders. Here we present zinc oxide-based two-dimensional electron systems as a high-mobility system to study the low-temperature phases of strongly interacting electrons. An analysis of the electronic transport provides evidence for competing correlated metallic and insulating states with varying degrees of spin polarization. Some features bear quantitative resemblance to quantum Monte Carlo simulation results, including the transition point from the paramagnetic Fermi liquid to Wigner crystal and the absence of a Stoner transition. At very low temperatures, we resolve a non-monotonic spin polarizability of electrons across the phase transition, pointing towards a low spin phase of electrons, and a two-order-of-magnitude positive magnetoresistance that is challenging to understand within traditional metallic transport paradigms. This work establishes zinc oxide as a platform for studying strongly correlated electrons in two dimensions.

Publication: Nature Materials Vol.: 21 No.: 3 ISSN: 1476-1122

ID: CaltechAUTHORS:20210409-151541040

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Abstract: We study the phenomenon of Hilbert space fragmentation in isolated Hamiltonian and Floquet quantum systems using the language of commutant algebras, the algebra of all operators that commute with each local term that appears in the Hamiltonian or each local gate of the circuit. We provide a precise definition of Hilbert space fragmentation in this formalism as the case where the dimension of the commutant algebra grows exponentially with the system size. Fragmentation can, hence, be distinguished from systems with conventional symmetries such as U(1) or SU(2), where the dimension of the commutant algebra grows polynomially with the system size. Furthermore, the commutant algebra language also helps distinguish between “classical” and “quantum” Hilbert space fragmentation, where the former refers to fragmentation in the product state basis. We explicitly construct the commutant algebra in several systems exhibiting classical fragmentation, including the t−J_z model and the spin-1 dipole-conserving model, and we illustrate the connection to previously studied “statistically localized integrals of motion.” We also revisit the Temperley-Lieb spin chains, including the spin-1 biquadratic chain widely studied in the literature, and show that they exhibit quantum Hilbert space fragmentation. Finally, we study the contribution of the full commutant algebra to the Mazur bounds in various cases. In fragmented systems, we use expressions for the commutant to analytically obtain new or improved Mazur bounds for autocorrelation functions of local operators that agree with previous numerical results. In addition, we are able to rigorously show the localization of the on-site spin operator in the spin-1 dipole-conserving model.

Publication: Physical Review X Vol.: 12 No.: 1 ISSN: 2160-3308

ID: CaltechAUTHORS:20220113-182211896

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Abstract: We construct a Pauli stabilizer model for every two-dimensional Abelian topological order that admits a gapped boundary. Our primary example is a Pauli stabilizer model on four-dimensional qudits that belongs to the double semion (DS) phase of matter. The DS stabilizer Hamiltonian is constructed by condensing an emergent boson in a Z₄ toric code, where the condensation is implemented at the level of the ground states by two-body measurements. We rigorously verify the topological order of the DS stabilizer model by identifying an explicit finite-depth quantum circuit (with ancillary qubits) that maps its ground-state subspace to that of a DS string-net model. We show that the construction of the DS stabilizer Hamiltonian generalizes to all twisted quantum doubles (TQDs) with Abelian anyons. This yields a Pauli stabilizer code on composite-dimensional qudits for each such TQD, implying that the classification of topological Pauli stabilizer codes extends well beyond stacks of toric codes—in fact, exhausting all Abelian anyon theories that admit a gapped boundary. We also demonstrate that symmetry-protected topological phases of matter characterized by type-I and type-II cocycles can be modeled by Pauli stabilizer Hamiltonians by gauging certain 1-form symmetries of the TQD stabilizer models.

Publication: PRX Quantum Vol.: 3 No.: 1 ISSN: 2691-3399

ID: CaltechAUTHORS:20220427-804972400

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Abstract: We show that entangled measurements provide an exponential advantage in sample complexity for Pauli channel estimation, which is both a fundamental problem and a practically important subroutine for benchmarking near-term quantum devices. The specific task we consider is to simultaneously learn all the eigenvalues of an n-qubit Pauli channel to ±ε precision. We give an estimation protocol with an n-qubit ancilla that succeeds with high probability using only O(n/ε²) copies of the Pauli channel, while prove that any ancilla-free protocol (possibly with adaptive control and channel concatenation) would need at least Ω(2^(n/3)) rounds of measurement. We further study the advantages provided by a small number of ancillas. For the case that a k-qubit ancilla (k≤n) is available, we obtain a sample complexity lower bound of Ω(2^((n−k)/3)) for any non-concatenating protocol, and a stronger lower bound of Ω(n^(2n−k)) for any non-adaptive, non-concatenating protocol, which is shown to be tight. We also show how to apply the ancilla-assisted estimation protocol to a practical quantum benchmarking task in a noise-resilient and sample-efficient manner, given reasonable noise assumptions. Our results provide a practically-interesting example for quantum advantages in learning and also bring new insight for quantum benchmarking.

Publication: Physical Review A Vol.: 105 No.: 3 ISSN: 2469-9926

ID: CaltechAUTHORS:20220325-509656125

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Abstract: We consider quantum circuits consisting of randomly chosen two-local gates and study the number of gates needed for the distribution over measurement outcomes for typical circuit instances to be anticoncentrated, roughly meaning that the probability mass is not too concentrated on a small number of measurement outcomes. An understanding of the conditions for anticoncentration is important for determining which quantum circuits are difficult to simulate classically, as anticoncentration has been in some cases an ingredient of mathematical arguments that simulation is hard and in other cases a necessary condition for easy simulation. Our definition of anticoncentration is that the expected collision probability of the distribution—that is, the probability that two independently drawn outcomes will agree—is only a constant factor larger than the collision probability for the uniform distribution. We show that when the two-local gates are each drawn from the Haar measure (or any 2-design), at least Ω(n log(n)) gates (and thus Ω(log(n)) circuit depth) are needed for this condition to be met on an n-qudit circuit. In both the case where the gates are nearest neighbor on a one-dimensional ring and the case where gates are long range, we show that O(n log(n)) gates are also sufficient and we precisely compute the optimal constant prefactor for the n log(n). The technique we employ relies upon a mapping from the expected collision probability to the partition function of an Ising-like classical statistical-mechanical model, which we manage to bound using stochastic and combinatorial techniques.

Publication: PRX Quantum Vol.: 3 No.: 1 ISSN: 2691-3399

ID: CaltechAUTHORS:20210511-131126866

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Abstract: We propose a method to reliably and efficiently extract the fidelity of many-qubit quantum circuits composed of continuously parametrized two-qubit gates called matchgates. This method, which we call matchgate benchmarking, relies on advanced techniques from randomized benchmarking as well as insights from the representation theory of matchgate circuits. We argue the formal correctness and scalability of the protocol, and moreover deploy it to estimate the performance of matchgate circuits generated by two-qubit XY spin interactions on a quantum processor.

Publication: Quantum Vol.: 6ISSN: 2521-327X

ID: CaltechAUTHORS:20220420-536258700

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Abstract: Solid-state nuclear spins surrounding individual, optically addressable qubits are a crucial resource for quantum networks, computation and simulation. Although hosts with sparse nuclear spin baths are typically chosen to mitigate qubit decoherence, developing coherent quantum systems in nuclear-spin-rich hosts enables exploration of a much broader range of materials for quantum information applications. The collective modes of these dense nuclear spin ensembles provide a natural basis for quantum storage; however, using them as a resource for single-spin qubits has thus far remained elusive. Here, by using a highly coherent, optically addressed ¹⁷¹Yb³⁺ qubit doped into a nuclear-spin-rich yttrium orthovanadate crystal, we develop a robust quantum control protocol to manipulate the multi-level nuclear spin states of neighbouring ⁵¹V⁵⁺ lattice ions. Via a dynamically engineered spin-exchange interaction, we polarize this nuclear spin ensemble, generate collective spin excitations, and subsequently use them to implement a quantum memory. We additionally demonstrate preparation and measurement of maximally entangled ¹⁷¹Yb–⁵¹V Bell states. Unlike conventional, disordered nuclear-spin-based quantum memories, our platform is deterministic and reproducible, ensuring identical quantum registers for all ¹⁷¹Yb³⁺ qubits. Our approach provides a framework for utilizing the complex structure of dense nuclear spin baths, paving the way towards building large-scale quantum networks using single rare-earth ion qubits.

Publication: Nature Vol.: 602 No.: 7897 ISSN: 0028-0836

ID: CaltechAUTHORS:20210917-222630119

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Abstract: The breaking of time-reversal symmetry is a crucial ingredient to topological bands. It can occur intrinsically in materials with magnetic order, or be induced by external fields, such as magnetic fields in quantum Hall systems or circularly polarized light fields in Floquet Chern insulators. Apart from polarization, photons can carry another degree of freedom, orbital angular momentum, through which time-reversal symmetry can be broken. In this Letter we pose the question of whether this property allows for inducing topological bands via a linearly polarized but twisted light beam. To this end we study a graphenelike model of electrons on a honeycomb lattice interacting with a twisted light field. To identify the topological behavior of the electrons, we calculate their local markers of Chern number and monitor the presence of in-gap edge states. Our results are shown to be fully analogous to the behavior found in paradigmatic models for static and driven Chern insulators, and realizing the state is experimentally straightforward. With this, our work establishes a mechanism for generating fermionic topological phases of matter that can harness the central phase singularity of an optical vortex beam.

Publication: Physical Review B Vol.: 105 No.: 8 ISSN: 2469-9950

ID: CaltechAUTHORS:20220209-266105000

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Abstract: Twisted bilayer graphene (TBG) realizes a highly tunable, strongly interacting system featuring superconductivity and various correlated insulating states. We establish gate-defined wires in TBG with proximity-induced spin-orbit coupling as (i) a tool for revealing the nature of correlated insulators and (ii) a platform for Majorana-based topological qubits. We show that the band structure of a gate-defined wire immersed in an intervalley coherent correlated insulator inherits electrically detectable fingerprints of symmetry breaking native to the latter. Surrounding the wire by a superconducting TBG region on one side and an intervalley coherent correlated insulator on the other further enables the formation of Majorana zero modes—possibly even at zero magnetic field depending on the precise symmetry-breaking order present. Our proposal not only introduces a highly gate-tunable topological qubit medium relying on internally generated proximity effects but can also shed light on the Cooper-pairing mechanism in TBG.

Publication: Physical Review B Vol.: 105 No.: 8 ISSN: 2469-9950

ID: CaltechAUTHORS:20220104-233136449

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Abstract: A locally testable code is an error-correcting code that admits very efficient probabilistic tests of membership. Tensor codes provide a simple family of combinatorial constructions of locally testable codes that generalize the family of Reed-Muller codes. The natural test for tensor codes, the axis-parallel line vs. point test, plays an essential role in constructions of probabilistically checkable proofs. We analyze the axis-parallel line vs. point test as a two-prover game and show that the test is sound against quantum provers sharing entanglement. Our result implies the quantum-soundness of the low individual degree test, which is an essential component of the MIP* = RE theorem. Our proof also generalizes to the infinite-dimensional commuting-operator model of quantum provers.

Publication: arXiv
ID: CaltechAUTHORS:20220202-191902193

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Abstract: Strongly driven antiferromagnetic Mott insulators have the potential to exhibit exotic transient phenomena that are forbidden in thermal equilibrium. However, such far-from-equilibrium regimes, where conventional time-dependent Ginzburg-Landau descriptions fail, are experimentally challenging to prepare and to probe especially in solid state systems. Here we use a combination of time-resolved second harmonic optical polarimetry and coherent magnon spectroscopy to interrogate n-type photo-doping induced ultrafast magnetic order parameter dynamics in the antiferromagnetic Mott insulator Sr₂IrO₄. We find signatures of an unusual far-from-equilibrium critical regime in which the divergences of the magnetic correlation length and relaxation time are decoupled. This violation of conventional thermal critical behavior arises from the interplay of photo-doping and non-thermal magnon population induced demagnetization effects. Our findings, embodied in a non-equilibrium phase diagram, provide a blueprint for engineering the out-of-equilibrium properties of quantum matter, with potential applications to terahertz spintronics technologies.

Publication: Communications Physics Vol.: 5ISSN: 2399-3650

ID: CaltechAUTHORS:20220113-234606083

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Abstract: The study of critical quantum many-body systems through conformal field theory (CFT) is one of the pillars of modern quantum physics. Certain CFTs are also understood to be dual to higher-dimensional theories of gravity via the anti-de Sitter/conformal field theory (AdS/CFT) correspondence. To reproduce various features of AdS/CFT, a large number of discrete models based on tensor networks have been proposed. Some recent models, most notably including toy models of holographic quantum error correction, are constructed on regular time-slice discretizations of AdS. In this work, we show that the symmetries of these models are well suited for approximating CFT states, as their geometry enforces a discrete subgroup of conformal symmetries. Based on these symmetries, we introduce the notion of a quasiperiodic conformal field theory (qCFT), a critical theory less restrictive than a full CFT and with characteristic multi-scale quasiperiodicity. We discuss holographic code states and their renormalization group flow as specific implementations of a qCFT with fractional central charges and argue that their behavior generalizes to a large class of existing and future models. Beyond approximating CFT properties, we show that these can be best understood as belonging to a paradigm of discrete holography.

Publication: Quantum Vol.: 6ISSN: 2521-327X

ID: CaltechAUTHORS:20220414-470744800

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Abstract: The study of quantum correlation sets initiated by Tsirelson in the 1980s and originally motivated by questions in the foundations of quantum mechanics has more recently been tied to questions in quantum cryptography, complexity theory, operator space theory, group theory, and more. Synchronous correlation sets introduced by Paulsen et al. [J. Funct. Anal. 270, 2188–2222 (2016)] are a subclass of correlations that has proven particularly useful to study and arises naturally in applications. We show that any correlation that is almost synchronous, in a natural ℓ1 sense, arises from a state and measurement operators that are well-approximated by a convex combination of projective measurements on a maximally entangled state. This extends a result of Paulsen et al. [J. Funct. Anal. 270, 2188–2222 (2016)] that applies to exactly synchronous correlations. Crucially, the quality of approximation is independent of the dimension of the Hilbert spaces or of the size of the correlation. Our result allows one to reduce the analysis of many classes of nonlocal games, including rigidity properties, to the case of strategies using maximally entangled states that are generally easier to manipulate.

Publication: Journal of Mathematical Physics Vol.: 63 No.: 2 ISSN: 0022-2488

ID: CaltechAUTHORS:20211006-163212999

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Abstract: We present a comprehensive architectural analysis for a proposed fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware, we propose a system of acoustic resonators coupled to superconducting circuits with a two-dimensional layout. Using estimated physical parameters for the hardware, we perform a detailed error analysis of measurements and gates, including cnot and Toffoli gates. Having built a realistic noise model, we numerically simulate quantum error correction when the outer code is either a repetition code or a thin rectangular surface code. Our next step toward universal fault-tolerant quantum computation is a protocol for fault-tolerant Toffoli magic state preparation that significantly improves upon the fidelity of physical Toffoli gates at very low qubit cost. To achieve even lower overheads, we devise a new magic state distillation protocol for Toffoli states. Combining these results together, we obtain realistic full-resource estimates of the physical error rates and overheads needed to run useful fault-tolerant quantum algorithms. We find that with around 1000 superconducting circuit components, one could construct a fault-tolerant quantum computer that can run circuits, which are currently intractable for classical computers. Hardware with 18 000 superconducting circuit components, in turn, could simulate the Hubbard model in a regime beyond the reach of classical computing.

Publication: PRX Quantum Vol.: 3 No.: 1 ISSN: 2691-3399

ID: CaltechAUTHORS:20201209-172305164

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Abstract: Stabilized cat codes can provide a biased noise channel with a set of bias-preserving (BP) gates, which can significantly reduce the resource overhead for fault-tolerant quantum computing. All existing schemes of BP gates, however, require adiabatic quantum evolution, with performance limited by excitation loss and nonadiabatic errors during the adiabatic gates. In this paper, we apply a derivative-based leakage-suppression technique to overcome nonadiabatic errors, so that we can implement fast BP gates on Kerr-cat qubits with improved gate fidelity while maintaining high noise bias. When applied to concatenated quantum error correction, the fast BP gates not only can improve the logical error rate but also can reduce resource overhead, which enables more efficient implementation of fault-tolerant quantum computing.

Publication: Physical Review Research Vol.: 4 No.: 1 ISSN: 2643-1564

ID: CaltechAUTHORS:20211217-233248077

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Abstract: In quantum mechanics, a quantum many-body system is represented by a large complex matrix whose size scales exponentially with the number of particles. This intrinsic exponential complexity empowers quantum technologies but, at the same time, it makes it practically impossible to completely characterize, or learn, a quantum many-body system even of moderate size (the current limit of quantum tomography being 40–50 qubits). This is an issue given that learning quantum systems is central to the development of quantum technologies.

Publication: Nature Reviews Physics Vol.: 4 No.: 2 ISSN: 2522-5820

ID: CaltechAUTHORS:20220111-643841600

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Abstract: Information scrambling, which is the spread of local information through a system’s many-body degrees of freedom, is an intrinsic feature of many-body dynamics. In quantum systems, the out-of-time-ordered correlator (OTOC) quantifies information scrambling. Motivated by experiments that have measured the OTOC at infinite temperature and a theory proposal to measure the OTOC at finite temperature using the thermofield double state, we describe a protocol to measure the OTOC in a finite temperature spin chain that is realized approximately as one half of the ground state of two moderately-sized coupled spin chains. We consider a spin Hamiltonian with particle–hole symmetry, for which we show that the OTOC can be measured without needing sign-reversal of the Hamiltonian. We describe a protocol to mitigate errors in the estimated OTOC, arising from the finite approximation of the system to the thermofield double state. We show that our protocol is also robust to main sources of decoherence in experiments.

Publication: New Journal of Physics Vol.: 24 No.: 2 ISSN: 1367-2630

ID: CaltechAUTHORS:20220225-724707000

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Abstract: We study the connections between three quantities that can be used as diagnostics for quantum chaos, i.e., the out-of-time-order correlator (OTOC), Loschmidt echo (LE), and complexity. We generalize the connection between OTOC and LE for infinite dimensions and extend it for higher-order OTOCs and multi-fold LEs. Novel applications of this intrinsic relation are proposed. We also investigated the relationship between a specific circuit complexity and LE by using the inverted oscillator model and made a conjecture about their relationship. These relationships signal a deeper connection between these three probes of quantum chaos.

Publication: European Physical Journal C Vol.: 82 No.: 1 ISSN: 1434-6044

ID: CaltechAUTHORS:20190910-112124494

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Abstract: Lattice-surgery protocols allow for the efficient implementation of universal gate sets with two-dimensional topological codes where qubits are constrained to interact with one another locally. In this work, we first introduce a decoder capable of correcting spacelike and timelike errors during lattice-surgery protocols. Subsequently, we compute the logical failure rates of a lattice-surgery protocol for a biased circuit-level noise model. We then provide a protocol for performing twist-free lattice surgery, where we avoid twist defects in the bulk of the lattice. Our twist-free protocol eliminates the extra circuit components and gate-scheduling complexities associated with the measurement of higher weight stabilizers when using twist defects. We also provide a protocol for temporally encoded lattice surgery that can be used to reduce both the run times and the total space-time costs of quantum algorithms. Lastly, we propose a layout for a quantum processor that is more efficient for rectangular surface codes exploiting noise bias and that is compatible with the other techniques mentioned above.

Publication: PRX Quantum Vol.: 3 No.: 1 ISSN: 2691-3399

ID: CaltechAUTHORS:20220404-121646000

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Abstract: Monolayer transition metal dichalcogenides (TMDs) have intrinsic valley degrees of freedom, making them appealing for exploiting valleytronic applications in information storage and processing. WS₂ monolayer possesses two inequivalent valleys in the Brillouin zone, each valley coupling selectively with a circular polarization of light. The degree of valley polarization (DVP) under the excitation of circularly polarized light (CPL) is a parameter that determines the purity of valley polarized photoluminescence (PL) of monolayer WS₂. Here efficient tailoring of valley-polarized PL from monolayer WS₂ at room temperature (RT) through surface plasmon–exciton interactions with plasmonic Archimedes spiral (PAS) nanostructures is reported. The DVP of WS₂ at RT can be enhanced from <5% to 40% and 50% by using 2 turns (2T) and 4 turns (4T) of PAS, respectively. Further enhancement and control of excitonic valley polarization is demonstrated by electrostatically doping monolayer WS₂. For CPL on WS₂–2TPAS heterostructures, the 40% valley polarization is enhanced to 70% by modulating the carrier doping via a backgate, which may be attributed to the screening of momentum-dependent long-range electron–hole exchange interactions. The manifestation of electrically tunable valley-polarized emission from WS₂–PAS heterostructures presents a new strategy toward harnessing valley excitons for application in ultrathin valleytronic devices.

Publication: Advanced Materials Vol.: 34 No.: 3 ISSN: 0935-9648

ID: CaltechAUTHORS:20211201-182130100

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Abstract: We give a quantum speedup for solving the canonical semidefinite programming relaxation for binary quadratic optimization. This class of relaxations for combinatorial optimization has so far eluded quantum speedups. Our methods combine ideas from quantum Gibbs sampling and matrix exponent updates. A de-quantization of the algorithm also leads to a faster classical solver. For generic instances, our quantum solver gives a nearly quadratic speedup over state-of-the-art algorithms. Such instances include approximating the ground state of spin glasses and MaxCut on Erdös-Rényi graphs. We also provide an efficient randomized rounding procedure that converts approximately optimal SDP solutions into approximations of the original quadratic optimization problem.

Publication: Quantum Vol.: 6ISSN: 2521-327X

ID: CaltechAUTHORS:20190912-075203295

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Abstract: We show that a Weyl semimetal irradiated at two distinct frequencies can convert energy between the frequencies at a potentially large rate. The phenomenon is a realization of topological frequency conversion from [Martin et al, PRX 7 041008 (2017)]. When the effect is realized, each electron near a Weyl point acts as a topological frequency converter, and converts energy at a universal rate given by Planck's constant multiplied by the product of the two frequencies. Our results indicate that Weyl points in TaAs support topological frequency conversion in the THz regime at achievable intensities of order 100 W/mm2. When the topological energy conversion rate exceeds the dissipation rate, the effect can be used for optical amplification. This amplification regime can be achieved when the relaxation rate of the system is larger than the characteristic driving period. This phenomenon further amplifies Weyl semimetals' promise for optical amplification and terahertz (THz) generation.

Publication: arXiv
ID: CaltechAUTHORS:20220224-200907852

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Abstract: The Rabi model describes the simplest nontrivial interaction between a few-level system and a bosonic mode, featuring in multiple seemingly unrelated systems of importance to quantum science and technology. While exact expressions for the energies of this model and its few-mode extensions have been obtained, they involve roots of transcendental functions and are thus cumbersome and unintuitive. Utilizing the symmetric generalized rotating wave approximation (S-GRWA), we develop a family of approximations to the energies of the two-mode two-photon Rabi model. The simplest elements of the family are analytically tractable, providing better approximations in regimes of interest than the RWA such as in the ultra- and deep-strong coupling regimes of the system. Higher-order approximate energies can be used if more accuracy is required.

Publication: Physics Letters A Vol.: 422ISSN: 0375-9601

ID: CaltechAUTHORS:20211202-191330464

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Abstract: Photonics is a promising platform for demonstrating a quantum computational advantage (QCA) by outperforming the most powerful classical supercomputers on a well-defined computational task. Despite this promise, existing proposals and demonstrations face challenges. Experimentally, current implementations of Gaussian boson sampling (GBS) lack programmability or have prohibitive loss rates. Theoretically, there is a comparative lack of rigorous evidence for the classical hardness of GBS. In this work, we make progress in improving both the theoretical evidence and experimental prospects. We provide evidence for the hardness of GBS, comparable to the strongest theoretical proposals for QCA. We also propose a QCA architecture we call high-dimensional GBS, which is programmable and can be implemented with low loss using few optical components. We show that particular algorithms for simulating GBS are outperformed by high-dimensional GBS experiments at modest system sizes. This work thus opens the path to demonstrating QCA with programmable photonic processors.

Publication: Science Advances Vol.: 8 No.: 1 ISSN: 2375-2548

ID: CaltechAUTHORS:20220111-884895300

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Abstract: Achieving an accurate description of fermionic systems typically requires considerably many more orbitals than fermions. Previous resource analyses of quantum chemistry simulation often failed to exploit this low fermionic number information in the implementation of Trotter-based approaches and overestimated the quantum-computer runtime as a result. They also depended on numerical procedures that are computationally too expensive to scale up to large systems of practical interest. Here we propose techniques that solve both problems by using various factorized decompositions of the electronic structure Hamiltonian. We showcase our techniques for the uniform electron gas, finding substantial (over 100×) improvements in Trotter error for low-filling fraction and pushing to much higher numbers of orbitals than is possible with existing methods. Finally, we calculate the T-count to perform phase estimation on Jellium. In the low-filling regime, we observe improvements in gate complexity of over 10× compared to the best Trotter-based approach reported to date. We also report gate counts competitive with qubitization-based approaches for Wigner-Seitz values of physical interest.

Publication: Physical Review A Vol.: 105 No.: 1 ISSN: 2469-9926

ID: CaltechAUTHORS:20220118-839577000

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Abstract: Fault-tolerant quantum error correction is essential for implementing quantum algorithms of significant practical importance. In this work, we propose a highly effective use of the surface Gottesman-Kitaev-Preskill (GKP) code, i.e., the surface code consisting of bosonic GKP qubits instead of bare two-level qubits. In our proposal, we use error-corrected two-qubit gates between GKP qubits and introduce a maximum-likelihood decoding strategy for correcting shift errors in the two-GKP-qubit gates. Our proposed decoding reduces the total CNOT failure rate of the GKP qubits, e.g., from 0.87% to 0.36% at a GKP squeezing of 12 dB, compared to the case where the simple closest-integer decoding is used. Then, by concatenating the GKP code with the surface code, we find that the threshold GKP squeezing is given by 9.9 dB under the the assumption that finite squeezing of the GKP states is the dominant noise source. More importantly, we show that a low logical failure rate p_L < 10⁻⁷ can be achieved with moderate hardware requirements, e.g., 291 modes and 97 qubits at a GKP squeezing of 12 dB as opposed to 1457 bare qubits for the standard rotated surface code at an equivalent noise level (i.e., p=0.36%). Such a low failure rate of our surface-GKP code is possible through the use of space-time correlated edges in the matching graphs of the surface-code decoder. Further, all edge weights in the matching graphs are computed dynamically based on analog information from the GKP error correction using the full history of all syndrome measurement rounds. We also show that a highly squeezed GKP state of GKP squeezing ≳12 dB can be experimentally realized by using a dissipative stabilization method, namely, the big-small-big method, with fairly conservative experimental parameters. Lastly, we introduce a three-level ancilla scheme to mitigate ancilla decay errors during a GKP state preparation.

Publication: PRX Quantum Vol.: 3 No.: 1 ISSN: 2691-3399

ID: CaltechAUTHORS:20210511-130157842

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Abstract: The spectral form factor (SFF), characterizing statistics of energy eigenvalues, is a key diagnostic of many-body quantum chaos. In addition, partial spectral form factors (PSFFs) can be defined which refer to subsystems of the many-body system. They provide unique insights into energy eigenstate statistics of many-body systems, as we show in an analysis on the basis of random matrix theory and of the eigenstate thermalization hypothesis. We propose a protocol that allows the measurement of the SFF and PSFFs in quantum many-body spin models, within the framework of randomized measurements. Aimed to probe dynamical properties of quantum many-body systems, our scheme employs statistical correlations of local random operations which are applied at different times in a single experiment. Our protocol provides a unified test bed to probe many-body quantum chaotic behavior, thermalization, and many-body localization in closed quantum systems which we illustrate with numerical simulations for Hamiltonian and Floquet many-body spin systems.

Publication: Physical Review X Vol.: 12 No.: 1 ISSN: 2160-3308

ID: CaltechAUTHORS:20220207-90373000

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Abstract: Recent theoretical studies inspired by experiments on the Kitaev magnet α − RuCl₃ highlight the nontrivial impact of phonons on the thermal Hall conductivity of chiral topological phases. Here, we introduce mixed mesoscopic-macroscopic devices that allow refined thermal-transport probes of non-Abelian spin liquids with Ising topological order. These devices feature a quantum-coherent region with quantized or negligible phonon conductance, flanked by macroscopic lobes that facilitate efficient thermalization between chiral Majorana edge modes and bulk phonons. We show that our devices enable (i) accurate determination of the quantized thermal Hall conductivity, (ii) identification of non-Abelian Ising anyons via the temperature dependence of the thermal conductance, and, most interestingly, (iii) single-anyon detection through heat-based anyon interferometry. Analogous results apply broadly to phonon-coupled chiral topological orders.

Publication: Physical Review X Vol.: 12 No.: 1 ISSN: 2160-3308

ID: CaltechAUTHORS:20220222-706490000

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Abstract: AbstractWe study the connections between three quantities that can be used as diagnostics for quantum chaos, i.e., the out-of-time-order correlator (OTOC), Loschmidt echo (LE), and complexity. We generalize the connection between OTOC and LE for infinite dimensions and extend it for higher-order OTOCs and multi-fold LEs. Novel applications of this intrinsic relation are proposed. We also investigated the relationship between a specific circuit complexity and LE by using the inverted oscillator model and made a conjecture about their relationship. These relationships signal a deeper connection between these three probes of quantum chaos.

Publication: European Physical Journal. C, Particles and Fields Vol.: 82 No.: 1 ISSN: 1434-6044

ID: CaltechAUTHORS:20220204-679192000

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Abstract: We introduce the concepts of a symmetry-protected sign problem and symmetry-protected magic to study the complexity of symmetry-protected topological (SPT) phases of matter. In particular, we say a state has a symmetry-protected sign problem or symmetry-protected magic, if finite-depth quantum circuits composed of symmetric gates are unable to transform the state into a non-negative real wave function or stabilizer state, respectively. We prove that states belonging to certain SPT phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, we find that one-dimensional ℤ₂× ℤ₂ SPT states (e.g. cluster state) have a symmetry-protected sign problem, and two-dimensional ℤ₂ SPT states (e.g. Levin-Gu state) have symmetry-protected magic. Furthermore, we comment on the relation between a symmetry-protected sign problem and the computational wire property of one-dimensional SPT states. In an appendix, we also introduce explicit decorated domain wall models of SPT phases, which may be of independent interest.

Publication: Quantum Vol.: 5ISSN: 2521-327X

ID: CaltechAUTHORS:20220202-382557100

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Abstract: Graphene moire superlattices have emerged as a platform hosting and abundance of correlated insulating, topological, and superconducting phases. While the origins of strong correlations and non-trivial topology are shown to be directly linked to flat moire bands, the nature and mechanism of superconductivity remain enigmatic. In particular, only alternating twisted stacking geometries of bilayer and trilayer graphene are found to exhibit robust superconductivity manifesting as zero resistance and Fraunhofer interference patterns. Here we demonstrate that magic-angle twisted tri-, quadri-, and pentalayers placed on monolayer tungsten diselenide exhibit flavour polarization and superconductivity. We also observe insulating states in the trilayer and quadrilayer arising at finite electric displacement fields, despite the presence of dispersive bands introduced by additional graphene layers. Moreover, the three multilayer geometries allow us to identify universal features in the family of graphene moire structures arising from the intricate relations between superconducting states, symmetry-breaking transitions, and van Hove singularities. Remarkably, as the number of layers increases, superconductivity emerges over a dramatically enhanced filling-factor range. In particular, in twisted pentalayers, superconductivity extends well beyond the filling of four electrons per moire unit cell, demonstrating the non-trivial role of the additional bands. Our results highlight the importance of the interplay between flat and dispersive bands in extending superconducting regions in graphene moire superlattices and open new frontiers for developing graphene-based superconductors.

Publication: arXiv
ID: CaltechAUTHORS:20220113-234609742

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Abstract: Interactions in quantum systems can spread initially localized quantum information into the exponentially many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is key to resolving several open questions in physics. Here, by measuring the time-dependent evolution and fluctuation of out-of-time-order correlators, we experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We engineer quantum circuits that distinguish operator spreading and operator entanglement and experimentally observe their respective signatures. We show that whereas operator spreading is captured by an efficient classical model, operator entanglement in idealized circuits requires exponentially scaled computational resources to simulate. These results open the path to studying complex and practically relevant physical observables with near-term quantum processors.

Publication: Science Vol.: 374 No.: 6574 ISSN: 0036-8075

ID: CaltechAUTHORS:20211028-210102101

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Abstract: Rydberg chains provide an appealing platform for probing conformal field theories (CFTs) that capture universal behavior in a myriad of physical settings. Focusing on a Rydberg chain at the Ising transition separating charge density wave and disordered phases, we establish a detailed link between microscopics and low-energy physics emerging at criticality. We first construct lattice incarnations of primary fields in the underlying Ising CFT including chiral fermions, a nontrivial task given that the Rydberg chain Hamiltonian does not admit an exact fermionization. With this dictionary in hand, we compute correlations of microscopic Rydberg operators, paying special attention to finite, open chains of immediate experimental relevance. We further develop a method to quantify how second-neighbor Rydberg interactions tune the sign and strength of four-fermion couplings in the Ising CFT. Finally, we determine how the Ising fields evolve when four-fermion couplings drive an instability to Ising tricriticality. Our results pave the way to a thorough experimental characterization of Ising criticality in Rydberg arrays, and can inform the design of novel higher-dimensional phases based on coupled critical chains.

Publication: Physical Review B Vol.: 104 No.: 23 ISSN: 2469-9950

ID: CaltechAUTHORS:20211207-393208000

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Abstract: The Eigenstate Thermalization Hypothesis (ETH) has played a major role in explaining thermodynamic phenomena in quantum systems. However, so far, no connection has been known between ETH and the timescale of thermalization. In this paper, we rigorously show that ETH indeed implies fast thermalization to the global Gibbs state. We show fast convergence for two models of thermalization. In the first, the system is weakly coupled to a bath of (quasi)-free Fermions that we control. We derive a finitely-resolved version of Davies' generator, with explicit error bounds and resource estimates, that describes the joint evolution at finite times. The second is Quantum Metropolis Sampling, a quantum algorithm for preparing Gibbs states on a quantum computer. In both cases, no guarantee for fast convergence was previously known for non-commuting Hamiltonians, partly due to technical issues with a finite energy resolution. The critical feature of ETH we exploit is that the Hamiltonian can be modeled by random matrix theory below a sufficiently small energy scale. We show this gives quantum expander at nearby eigenstates of the Hamiltonian. This then implies fast convergence to the global Gibbs state by mapping the problem to a one-dimensional classical random walk on the spectrum of the Hamiltonian. Our results explain finite-time thermalization in chaotic open quantum systems and suggest an alternative formulation of ETH in terms of quantum expanders, which we confirm numerically for small systems.

Publication: arXiv
ID: CaltechAUTHORS:20220202-191908990

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Abstract: For quantum spin systems in any spatial dimension with a local, translation-invariant Hamiltonian, we prove that asymptotic state convertibility from a quantum state to another one by a thermodynamically feasible class of quantum dynamics, called thermal operations, is completely characterized by the Kullback–Leibler (KL) divergence rate, if the state is translation-invariant and spatially ergodic. Our proof consists of two parts and is phrased in terms of a branch of the quantum information theory called the resource theory. First, we prove that any states, for which the min and max Rényi divergences collapse approximately to a single value, can be approximately reversibly converted into one another by thermal operations with the aid of a small source of quantum coherence. Second, we prove that these divergences collapse asymptotically to the KL divergence rate for any translation-invariant ergodic state. We show this via a generalization of the quantum Stein’s lemma for quantum hypothesis testing beyond independent and identically distributed situations. Our result implies that the KL divergence rate serves as a thermodynamic potential that provides a complete characterization of thermodynamic convertibility of ergodic states of quantum many-body systems in the thermodynamic limit, including out-of-equilibrium and fully quantum situations.

Publication: Journal of Physics A: Mathematical and Theoretical Vol.: 54 No.: 49 ISSN: 1751-8113

ID: CaltechAUTHORS:20190801-134551728

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Abstract: Ising-type pairing in atomically thin superconducting materials has emerged as a novel means of generating devices with resilience to a magnetic field applied parallel to the two-dimensional (2D) plane. In this mini-review, we canvas the state of the field by giving a historical account of 2D superconductors with strongly enhanced in-plane upper critical fields, together with the type-I and type-II Ising pairing mechanisms. We highlight the vital role of spin–orbit coupling in these superconductors and discuss other effects such as symmetry breaking, atomic thicknesses, etc. Finally, we summarize the recent theoretical proposals and highlight the open questions, such as exploring topological superconductivity in these systems and looking for more materials with Ising pairing.

Publication: Nanotechnology Vol.: 32 No.: 50 ISSN: 0957-4484

ID: CaltechAUTHORS:20211001-212811372

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Abstract: Strong periodic driving with light offers the potential to coherently manipulate the properties of quantum materials on ultrafast timescales. Recently, strategies have emerged to drastically alter electronic and magnetic properties by optically inducing non-trivial band topologies, emergent spin interactions and even superconductivity. However, the prospects and methods of coherently engineering optical properties on demand are far less understood. Here we demonstrate coherent control and giant modulation of optical nonlinearity in a van der Waals layered magnetic insulator, manganese phosphorus trisulfide (MnPS₃). By driving far off-resonance from the lowest on-site manganese d–d transition, we observe a coherent on–off switching of its optical second harmonic generation efficiency on the timescale of 100 femtoseconds with no measurable dissipation. At driving electric fields of the order of 10⁹ volts per metre, the on–off ratio exceeds 10, which is limited only by the sample damage threshold. Floquet theory calculations based on a single-ion model of MnPS₃ are able to reproduce the measured driving field amplitude and polarization dependence of the effect. Our approach can be applied to a broad range of insulating materials and could lead to dynamically designed nonlinear optical elements.

Publication: Nature Vol.: 600 No.: 7888 ISSN: 0028-0836

ID: CaltechAUTHORS:20211209-456366000

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Abstract: Achieving quantum computational advantage requires solving a classically intractable problem on a quantum device. Natural proposals rely upon the intrinsic hardness of classically simulating quantum mechanics; however, verifying the output is itself classically intractable. On the other hand, certain quantum algorithms (e.g. prime factorization via Shor's algorithm) are efficiently verifiable, but require more resources than what is available on near-term devices. One way to bridge the gap between verifiability and implementation is to use "interactions" between a prover and a verifier. By leveraging cryptographic functions, such protocols enable the classical verifier to enforce consistency in a quantum prover's responses across multiple rounds of interaction. In this work, we demonstrate the first implementation of an interactive quantum advantage protocol, using an ion trap quantum computer. We execute two complementary protocols -- one based upon the learning with errors problem and another where the cryptographic construction implements a computational Bell test. To perform multiple rounds of interaction, we implement mid-circuit measurements on a subset of trapped ion qubits, with subsequent coherent evolution. For both protocols, the performance exceeds the asymptotic bound for classical behavior; maintaining this fidelity at scale would conclusively demonstrate verifiable quantum advantage.

Publication: arXiv
ID: CaltechAUTHORS:20220202-191905591

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Abstract: 2+1d topological phases are well characterized by the fusion rules and braiding/exchange statistics of fractional point excitations. In 4+1d, some topological phases contain only fractional loop excitations. What kind of loop statistics exist? We study the 4+1d gauge theory with 2-form ℤ₂ gauge field (the loop only toric code) and find that while braiding statistics between two different types of loops can be nontrivial, the self `exchange' statistics are all trivial. In particular, we show that the electric, magnetic, and dyonic loop excitations in the 4+1d toric code are not distinguished by their self-statistics. They tunnel into each other across 3+1d invertible domain walls which in turn give explicit unitary circuits that map the loop excitations into each other. The SL(2,ℤ₂) symmetry that permutes the loops, however, cannot be consistently gauged and we discuss the associated obstruction in the process. Moreover, we discuss a gapless boundary condition dubbed the 'fractional Maxwell theory' and show how it can be Higgsed into gapped boundary conditions. We also discuss the generalization of these results from the ℤ₂ gauge group to ℤ_N.

Publication: arXiv
ID: CaltechAUTHORS:20220113-234540268

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Abstract: The discovery of topological order has revised the understanding of quantum matter and provided the theoretical foundation for many quantum error–correcting codes. Realizing topologically ordered states has proven to be challenging in both condensed matter and synthetic quantum systems. We prepared the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measured a topological entanglement entropy near the expected value of –ln2 and simulated anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigated key aspects of the surface code, including logical state injection and the decay of the nonlocal order parameter. Our results demonstrate the potential for quantum processors to provide insights into topological quantum matter and quantum error correction.

Publication: Science Vol.: 374 No.: 6572 ISSN: 0036-8075

ID: CaltechAUTHORS:20211203-174950058

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Abstract: In order to build a large scale quantum computer, one must be able to correct errors extremely fast. We design a fast decoding algorithm for topological codes to correct for Pauli errors and erasure and combination of both errors and erasure. Our algorithm has a worst case complexity of O(nα(n)), where n is the number of physical qubits and αα is the inverse of Ackermann's function, which is very slowly growing. For all practical purposes, α(n) ≤ 3. We prove that our algorithm performs optimally for errors of weight up to (d−1)/2 and for loss of up to d−1 qubits, where d is the minimum distance of the code. Numerically, we obtain a threshold of 9.9% for the 2d-toric code with perfect syndrome measurements and 2.6% with faulty measurements.

Publication: Quantum Vol.: 5ISSN: 2521-327X

ID: CaltechAUTHORS:20220107-10356300

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Abstract: We study the antiferromagnetic XYZ spin chain with quenched bond randomness, focusing on a critical line between localized Ising magnetic phases. A previous calculation using the spectrum-bifurcation renormalization group, and assuming marginal many-body localization, proposed that critical indices vary continuously. In this work, we solve the low-energy physics using an unbiased numerically exact tensor network method named the “rigorous renormalization group.” We find a line of fixed points consistent with infinite-randomness phenomenology, with indeed continuously varying critical exponents for average spin correlations. A self-consistent Hartree–Fock-type treatment of the z couplings as interactions added to the free-fermion random XY model captures much of the important physics including the varying exponents; we provide an understanding of this as a result of local correlation induced between the mean-field couplings. We solve the problem of the locally correlated XY spin chain with an arbitrary degree of correlation and provide analytical strong-disorder renormalization group proofs of continuously varying exponents based on an associated classical random walk problem. This is also an example of a line of fixed points with continuously varying exponents in the equivalent disordered free-fermion chain. We argue that this line of fixed points also controls an extended region of the critical interacting XYZ spin chain.

Publication: Physical Review B Vol.: 104 No.: 21 ISSN: 2469-9950

ID: CaltechAUTHORS:20210831-203949345

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Abstract: The paradigm of Floquet engineering of topological states of matter can be generalized into the time-quasiperiodic scenario, where a lower-dimensional time-dependent system maps onto a higher-dimensional one by combining the physical dimensions with additional synthetic dimensions generated by multiple incommensurate driving frequencies. Differently from most previous works in which gapped topological phases were considered, we propose an experimentally realizable, one-dimensional chain driven by two frequencies, which maps onto a gapless Weyl semimetal in a synthetic dimension. Based on analytical reasoning and numerical simulations, we find that the nonadiabatic quantum dynamics of this system exhibit energy pumping behaviors characterized by universal functions. We also numerically find that such behaviors are robust against a considerable amount of spatial disorder.

Publication: Physical Review B Vol.: 104 No.: 22 ISSN: 2469-9950

ID: CaltechAUTHORS:20211202-233649522

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Abstract: We consider hierarchically implemented quantum error correction (HI-QEC), in which the fidelities of logical qubits are differentially optimized to enhance the capabilities of quantum devices in scientific applications. By employing qubit representations that propagate hierarchies in simulated systems to those in logical qubit noise sensitivities, heterogeneity in the distribution of physical-to-logical qubits can be systematically structured. For concreteness, we estimate HI-QEC's impact on surface code resources in computing low-energy observables to fixed precision, finding up to approximately 60% reductions in qubit requirements plausible in early error-corrected simulations. Hierarchical qubit maps are also possible without error correction in qubit and qudit systems where fidelities are nonuniform, either unintentionally or by design. Hierarchical optimizations are another element in the codesign process of quantum computations, including quantum simulations for nuclear and particle physics.

Publication: Physical Review A Vol.: 104 No.: 6 ISSN: 2469-9926

ID: CaltechAUTHORS:20220106-173252132

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Abstract: Flat electronic bands, characteristic of ‘magic-angle’ twisted bilayer graphene, host many correlated phenomena. Nevertheless, many properties of these bands and emerging symmetry-broken phases are still poorly understood. Here we use scanning tunnelling spectroscopy to examine the evolution of the twisted bilayer graphene bands and related gapped phases as the twist angle between the two graphene layers changes. We detect filling-dependent flattening of the bands that is appreciable even when the angle is well above the magic angle value and so the material is nominally in a weakly correlated regime. Upon approaching the magic angle, we further show that the most prominent correlated gaps begin to emerge when band flattening is maximized around certain integer fillings of electrons per moiré unit cell. Our observations are consistent with a model that suggests that a significant enhancement of the density of states caused by the band flattening triggers a cascade of symmetry-breaking transitions. Finally, we explore the temperature dependence of the cascade and identify gapped features that develop in a broad range of band fillings where superconductivity is expected. Our results highlight the role of interaction-driven band flattening in defining the electronic properties of twisted bilayer graphene.

Publication: Nature Physics Vol.: 17 No.: 12 ISSN: 1745-2473

ID: CaltechAUTHORS:20210302-094400352

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Abstract: We investigate the photon pumping effect in a topological model consisting of a periodically driven spin-1/2 coupled to a quantum cavity mode out of the adiabatic limit. In the strong-drive adiabatic limit, a quantized frequency conversion of photons is expected as the temporal analog of the Hall current. We numerically establish a novel photon pumping phenomenon in the experimentally accessible nonadiabatic driving regime for a broad region of the parameter space. The photon frequency conversion efficiency exhibits strong fluctuations and high efficiency that can reach up 80% of the quantized value for commensurate frequency combinations. We link the pumping properties to the delocalization of the corresponding Floquet states which display multifractal behavior as the result of hybridization between localized and delocalized sectors. Finally we demonstrate that the quantum coherence properties of the initial state are preserved during the frequency conversion process in both the strong and ultra-weak-drive limit.

Publication: Annals of Physics Vol.: 435ISSN: 0003-4916

ID: CaltechAUTHORS:20210511-095252246

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Abstract: We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. We show that, for local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy benchmark) between the output distribution p_(noisy) of a generic noisy circuit instance and the output distribution pideal of the corresponding noiseless instance shrink exponentially with the expected number of gate-level errors, as F = exp(−2sϵ ± O(sϵ²)), where ϵ is the probability of error per circuit location and s is the number of two-qubit gates. Furthermore, if the noise is incoherent, the output distribution approaches the uniform distribution p_(unif) at precisely the same rate and can be approximated as p_(noisy) ≈ F_(p_(ideal)) + (1−F)p_(unif), that is, local errors are scrambled by the random quantum circuit and contribute only white noise (uniform output). Importantly, we upper bound the total variation error (averaged over random circuit instance) in this approximation as O(Fϵ√s), so the "white-noise approximation" is meaningful when ϵ√s ≪ 1, a quadratically weaker condition than the ϵs≪1 requirement to maintain high fidelity. The bound applies when the circuit size satisfies s ≥ Ω(nlog(n)) and the inverse error rate satisfies ϵ⁻¹ ≥ Ω̃ (n). The white-noise approximation is useful for salvaging the signal from a noisy quantum computation; it was an underlying assumption in complexity-theoretic arguments that low-fidelity random quantum circuits cannot be efficiently sampled classically. Our method is based on a map from second-moment quantities in random quantum circuits to expectation values of certain stochastic processes for which we compute upper and lower bounds.

Publication: arXiv
ID: CaltechAUTHORS:20211213-224949608

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Abstract: Non-Abelian defects that bind Majorana or parafermion zero modes are prominent in several topological quantum computation schemes. Underpinning their established understanding is the quantum Ising spin chain, which can be recast as a fermionic model or viewed as a standalone effective theory for the surface-code edge -- both of which harbor non-Abelian defects. We generalize these notions by deriving an effective Ising-like spin chain describing the edge of quantum-double topological order. Relating Majorana and parafermion modes to anyonic strings, we introduce quantum-double generalizations of non-Abelian defects. We develop a way to embed finite-group valued qunits into those valued in continuous groups. Using this embedding, we provide a continuum description of the spin chain and recast its non-interacting part as a quantum wire via addition of a Wess-Zumino-Novikov-Witten term and non-Abelian bosonization.

Publication: arXiv
ID: CaltechAUTHORS:20220113-182244311

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Abstract: We show that long-distance quantum correlations probe short-distance physics. Two disjoint regions of the latticized, massless scalar field vacuum are numerically demonstrated to become separable at distances beyond the negativity sphere, which extends to infinity in the continuum limit. The size of this quantum coherent volume is determined by the highest momentum mode supported in the identical regions, each of diameter d. More generally, effective field theories (EFTs), describing a system up to a given momentum scale Λ, are expected to share this feature—entanglement between regions of the vacuum depends upon the UV completion beyond a separation proportional to Λ. Through calculations extended to three dimensions, the magnitude of the negativity at which entanglement becomes sensitive to UV physics in an EFT (lattice or otherwise) is conjectured to scale as ∼e^(−Λd), independent of the number of spatial dimensions. It is concluded that two-region vacuum entanglement at increasing separations depends upon the structure of the theory at increasing momentum scales. This phenomenon may be manifest in perturbative QCD processes.

Publication: Physical Review Letters Vol.: 127 No.: 21 ISSN: 0031-9007

ID: CaltechAUTHORS:20210408-123011098

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Abstract: Recently, the steady states of non-unitary free fermion dynamics are found to exhibit novel critical phases with power-law squared correlations and a logarithmic subsystem entanglement. In this work, we theoretically understand the underlying physics by constructing solvable static/Brownian quadratic Sachdev-Ye-Kitaev chains with non-Hermitian dynamics. We find the action of the replicated system generally shows (one or infinite copies of) O(2)×O(2) symmetries, which is broken to O(2) by the saddle-point solution. This leads to an emergent conformal field theory of the Goldstone modes. We derive the effective action and obtain the universal critical behaviors of squared correlators. Furthermore, the entanglement entropy of a subsystem A with length L_A corresponds to the energy of the half-vortex pair S∼ρ_s log L_A, where ρ_s is the total stiffness of the Goldstone modes. We also discuss special limits with more than one branch of Goldstone modes and comment on interaction effects.

Publication: Quantum Vol.: 5ISSN: 2521-327X

ID: CaltechAUTHORS:20210413-083455122

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Abstract: We investigate the problem of fast-forwarding quantum evolution, whereby the dynamics of certain quantum systems can be simulated with gate complexity that is sublinear in the evolution time. We provide a definition of fast-forwarding that considers the model of quantum computation, the Hamiltonians that induce the evolution, and the properties of the initial states. Our definition accounts for any asymptotic complexity improvement of the general case and we use it to demonstrate fast-forwarding in several quantum systems. In particular, we show that some local spin systems whose Hamiltonians can be taken into block diagonal form using an efficient quantum circuit, such as those that are permutation-invariant, can be exponentially fast-forwarded. We also show that certain classes of positive semidefinite local spin systems, also known as frustration-free, can be polynomially fast-forwarded, provided the initial state is supported on a subspace of sufficiently low energies. Last, we show that all quadratic fermionic systems and number-conserving quadratic bosonic systems can be exponentially fast-forwarded in a model where quantum gates are exponentials of specific fermionic or bosonic operators, respectively. Our results extend the classes of physical Hamiltonians that were previously known to be fast-forwarded, while not necessarily requiring methods that diagonalize the Hamiltonians efficiently. We further develop a connection between fast-forwarding and precise energy measurements that also accounts for polynomial improvements.

Publication: Quantum Vol.: 5ISSN: 2521-327X

ID: CaltechAUTHORS:20211222-638987300

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Abstract: Quantum simulation is expected to be one of the key applications of future quantum computers. Product formulas, or Trotterization, are the oldest and, still today, an appealing method for quantum simulation. For an accurate product formula approximation in the spectral norm, the state-of-the-art gate complexity depends on the number of Hamiltonian terms and a certain 1-norm of its local terms. This work studies the concentration aspects of Trotter error: we prove that, typically, the Trotter error exhibits 2-norm (i.e., incoherent) scaling; the current estimate with 1-norm (i.e., coherent) scaling is for the worst cases. For k-local Hamiltonians and higher-order product formulas, we obtain gate count estimates for input states drawn from a 1-design ensemble (e.g., computational basis states). Our gate count depends on the number of Hamiltonian terms but replaces the 1-norm quantity by its analog in 2-norm, giving significant speedup for systems with large connectivity. Our results generalize to Hamiltonians with Fermionic terms and when the input state is drawn from a low-particle number subspace. Further, when the Hamiltonian itself has Gaussian coefficients (e.g., the SYK models), we show the stronger result that the 2-norm behavior persists even for the worst input state. Our main technical tool is a family of simple but versatile inequalities from non-commutative martingales called uniform smoothness. We use them to derive Hypercontractivity, namely p-norm estimates for low-degree polynomials, which implies concentration via Markov's inequality. In terms of optimality, we give examples that simultaneously match our p-norm bounds and the spectral norm bounds. Therefore, our improvement is due to asking a qualitatively different question from the spectral norm bounds. Our results give evidence that product formulas in practice may generically work much better than expected.

Publication: arXiv
ID: CaltechAUTHORS:20211130-215806841

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Abstract: Quantum simulations of chemistry in first quantization offer some important advantages over approaches in second quantization including faster convergence to the continuum limit and the opportunity for practical simulations outside of the Born-Oppenheimer approximation. However, since all prior work on quantum simulation of chemistry in first quantization has been limited to asymptotic analysis, it has been impossible to directly compare the resources required for these approaches to those required for the more commonly studied algorithms in second quantization. Here, we compile, optimize, and analyze the finite resources required to implement two first quantized quantum algorithms for chemistry from Babbush et al. [Npj Quantum Inf. 5, 92 (2019)] that realize block encodings for the qubitization and interaction-picture frameworks of Low et al. [Quantum 3, 163 (2019), arXiv:1805.00675 (2018)]. The two algorithms we study enable simulation with gate complexities of ˜O(η^(8/3)N^(1/3)t+η^(4/3)N^(2/3)t) and ˜O(η^(8/3)N^(1/3)t) where η is the number of electrons, N is the number of plane-wave basis functions, and t is the duration of time evolution (t is linearly inverse to target precision when the goal is to estimate energies). In addition to providing the first explicit circuits and constant factors for any first quantized simulation, and then introducing improvements, which reduce circuit complexity by about a thousandfold over naive implementations for modest sized systems, we also describe new algorithms that asymptotically achieve the same scaling in a real-space representation. Finally, we assess the resources required to simulate various molecules and materials and conclude that the qubitized algorithm will often be more practical than the interaction-picture algorithm. We demonstrate that our qubitization algorithm often requires much less surface-code space-time volume for simulating millions of plane waves than the best second quantized algorithms require for simulating hundreds of Gaussian orbitals.

Publication: PRX Quantum Vol.: 2 No.: 4 ISSN: 2691-3399

ID: CaltechAUTHORS:20211117-230943225

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Abstract: The complexity class NP characterizes the collection of computational problems that have efficiently verifiable solutions. With the goal of classifying computational problems that seem to lie beyond NP, starting in the 1980s complexity theorists have considered extensions of the notion of efficient verification that allow for the use of randomness (the class MA), interaction (the class IP), and the possibility to interact with multiple proofs, or provers (the class MIP). The study of these extensions led to the celebrated PCP theorem and its applications to hardness of approximation and the design of cryptographic protocols. In this work, we study a fourth modification to the notion of efficient verification that originates in the study of quantum entanglement. We prove the surprising result that every problem that is recursively enumerable, including the Halting problem, can be efficiently verified by a classical probabilistic polynomial-time verifier interacting with two all-powerful but noncommunicating provers sharing entanglement. The result resolves long-standing open problems in the foundations of quantum mechanics (Tsirelson's problem) and operator algebras (Connes' embedding problem).

Publication: Communications of the ACM Vol.: 64 No.: 11 ISSN: 0001-0782

ID: CaltechAUTHORS:20200417-131646685

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Abstract: Solving linear systems of equations is essential for many problems in science and technology, including problems in machine learning. Existing quantum algorithms have demonstrated the potential for large speedups, but the required quantum resources are not immediately available on near-term quantum devices. In this work, we study near-term quantum algorithms for linear systems of equations, with a focus on the two-norm and Tikhonov regression settings. We investigate the use of variational algorithms and analyze their optimization landscapes. There exist types of linear systems for which variational algorithms designed to avoid barren plateaus, such as properly-initialized imaginary time evolution and adiabatic-inspired optimization, suffer from a different plateau problem. To circumvent this issue, we design near-term algorithms based on a core idea: the classical combination of variational quantum states (CQS). We exhibit several provable guarantees for these algorithms, supported by the representation of the linear system on a so-called ansatz tree. The CQS approach and the ansatz tree also admit the systematic application of heuristic approaches, including a gradient-based search. We have conducted numerical experiments solving linear systems as large as 2³⁰⁰ × 2³⁰⁰ by considering cases where we can simulate the quantum algorithm efficiently on a classical computer. Our methods may provide benefits for solving linear systems within the reach of near-term quantum devices.

Publication: New Journal of Physics Vol.: 23 No.: 11 ISSN: 1367-2630

ID: CaltechAUTHORS:20211203-204703162

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Abstract: We study the representational power of Boltzmann machines (a type of neural network) in quantum many-body systems. We prove that any (local) tensor network state has a (local) neural network representation. The construction is almost optimal in the sense that the number of parameters in the neural network representation is almost linear in the number of nonzero parameters in the tensor network representation. Despite the difficulty of representing (gapped) chiral topological states with local tensor networks, we construct a quasilocal neural network representation for a chiral p-wave superconductor. These results demonstrate the power of Boltzmann machines.

Publication: Physical Review Letters Vol.: 127 No.: 17 ISSN: 0031-9007

ID: CaltechAUTHORS:20170605-084735797

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Abstract: Learning the structure of the entanglement Hamiltonian (EH) is central to characterizing quantum many-body states in analog quantum simulation. We describe a protocol where spatial deformations of the many-body Hamiltonian, physically realized on the quantum device, serve as an efficient variational ansatz for a local EH. Optimal variational parameters are determined in a feedback loop, involving quench dynamics with the deformed Hamiltonian as a quantum processing step, and classical optimization. We simulate the protocol for the ground state of Fermi-Hubbard models in quasi-1D geometries, finding excellent agreement of the EH with Bisognano-Wichmann predictions. Subsequent on-device spectroscopy enables a direct measurement of the entanglement spectrum, which we illustrate for a Fermi Hubbard model in a topological phase.

Publication: Physical Review Letters Vol.: 127 No.: 17 ISSN: 0031-9007

ID: CaltechAUTHORS:20211108-205323673

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Abstract: With the rapid development of quantum technology, one of the leading applications that has been identified is the simulation of chemistry. Interestingly, even before full scale quantum computers are available, quantum computer science has exhibited a remarkable string of results that directly impact what is possible in a chemical simulation with any computer. Some of these results even impact our understanding of chemistry in the real world. In this Perspective, we take the position that direct chemical simulation is best understood as a digital experiment. While on the one hand, this clarifies the power of quantum computers to extend our reach, it also shows us the limitations of taking such an approach too directly. Leveraging results that quantum computers cannot outpace the physical world, we build to the controversial stance that some chemical problems are best viewed as problems for which no algorithm can deliver their solution, in general, known in computer science as undecidable problems. This has implications for the predictive power of thermodynamic models and topics such as the ergodic hypothesis. However, we argue that this Perspective is not defeatist but rather helps shed light on the success of existing chemical models such as transition state theory, molecular orbital theory, and thermodynamics as models that benefit from data. We contextualize recent results, showing that data-augmented models are a more powerful rote simulation. These results help us appreciate the success of traditional chemical theory and anticipate new models learned from experimental data. Not only can quantum computers provide data for such models, but they can also extend the class and power of models that utilize data in fundamental ways. These discussions culminate in speculation on new ways for quantum computing and chemistry to interact and our perspective on the eventual roles of quantum computers in the future of chemistry.

Publication: Journal of Chemical Physics Vol.: 155 No.: 15 ISSN: 0021-9606

ID: CaltechAUTHORS:20211105-174820514

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Abstract: In this paper, we generalize Jordan-Lee-Preskill, an algorithm for simulating flat-space quantum field theories, to 3+1 dimensional inflationary spacetime. The generalized algorithm contains the encoding treatment, the initial state preparation, the inflation process, and the quantum measurement of cosmological observables at late time. The algorithm is helpful for obtaining predictions of cosmic non-Gaussianities, serving as useful benchmark problems for quantum devices, and checking assumptions made about interacting vacuum in the inflationary perturbation theory. Components of our work also include a detailed discussion about the lattice regularization of the cosmic perturbation theory, a detailed discussion about the in-in formalism, a discussion about encoding using the Hamilton-Kabat-Lifschytz-Lowe-type formula that might apply for both dS and AdS spacetimes, a discussion about bounding curvature perturbations, a description of the three-party Trotter simulation algorithm for time-dependent Hamiltonians, a ground state projection algorithm for simulating gapless theories, a discussion about the quantum-extended Church-Turing thesis, and a discussion about simulating cosmic reheating in quantum devices.

Publication: Physical Review D Vol.: 104 No.: 8 ISSN: 2470-0010

ID: CaltechAUTHORS:20211014-212144221

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Abstract: We study a disordered one-dimensional fermionic system subject to quasiperiodic driving by two modes with incommensurate frequencies. We show that the system supports a topological phase in which energy is transferred between the two driving modes at a quantized rate. The phase is protected by a combination of disorder-induced spatial localization and frequency localization, a mechanism unique to quasiperiodically driven systems. We demonstrate that an analogue of the phase can be realized in a cavity-qubit system driven by two incommensurate modes.

Publication: Physical Review Letters Vol.: 127 No.: 16 ISSN: 0031-9007

ID: CaltechAUTHORS:20211014-212143566

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Abstract: Quantum many-body systems involving bosonic modes or gauge fields have infinite-dimensional local Hilbert spaces which must be truncated to perform simulations of real-time dynamics on classical or quantum computers. To analyze the truncation error, we develop methods for bounding the rate of growth of local quantum numbers such as the occupation number of a mode at a lattice site, or the electric field at a lattice link. Our approach applies to various models of bosons interacting with spins or fermions, and also to both abelian and non-abelian gauge theories. We show that if states in these models are truncated by imposing an upper limit Λ on each local quantum number, and if the initial state has low local quantum numbers, then an error at most ϵ can be achieved by choosing Λ to scale polylogarithmically with ϵ⁻¹, an exponential improvement over previous bounds based on energy conservation. For the Hubbard-Holstein model, we numerically compute a bound on Λ that achieves accuracy ϵ, obtaining significantly improved estimates in various parameter regimes. We also establish a criterion for truncating the Hamiltonian with a provable guarantee on the accuracy of time evolution. Building on that result, we formulate quantum algorithms for dynamical simulation of lattice gauge theories and of models with bosonic modes; the gate complexity depends almost linearly on spacetime volume in the former case, and almost quadratically on time in the latter case. We establish a lower bound showing that there are systems involving bosons for which this quadratic scaling with time cannot be improved. By applying our result on the truncation error in time evolution, we also prove that spectrally isolated energy eigenstates can be approximated with accuracy ϵ by truncating local quantum numbers at Λ = polylog(ϵ⁻¹).

Publication: arXiv
ID: CaltechAUTHORS:20220113-182219174

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Abstract: Quantifying entanglement properties of mixed states in quantum field theory via entanglement of purification and reflected entropy is a new and challenging subject. In this work, we study both quantities for two spherical subregions far away from each other in the vacuum of a conformal field theory in any number of dimensions. Using lattice techniques, we find an elementary proof that the decay of both the entanglement of purification and reflected entropy is enhanced with respect to the mutual information behavior by a logarithm of the distance between the subregions. In the case of the Ising spin chain at criticality and the related free fermion conformal field theory, we compute also the overall coefficients numerically for the both quantities of interest.

Publication: Physical Review Letters Vol.: 127 No.: 14 ISSN: 0031-9007

ID: CaltechAUTHORS:20211014-212143934

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Abstract: We construct Brownian Sachdev-Ye-Kitaev (SYK) chains subjected to continuous monitoring and explore possible entanglement phase transitions therein. We analytically derive the effective action in the large-N limit and show that an entanglement transition is caused by the symmetry breaking in the enlarged replica space. In the noninteracting case with SYK₂ chains, the model features a continuous O(2) symmetry between two replicas and a transition corresponding to spontaneous breaking of that symmetry upon varying the measurement rate. In the symmetry broken phase at low measurement rate, the emergent replica criticality associated with the Goldstone mode leads to a log-scaling entanglement entropy that can be attributed to the free energy of vortices. In the symmetric phase at higher measurement rate, the entanglement entropy obeys area-law scaling. In the interacting case, the continuous O(2) symmetry is explicitly lowered to a discrete C₄ symmetry, giving rise to volume-law entanglement entropy in the symmetry-broken phase due to the enhanced linear free energy cost of domain walls compared to vortices. The interacting transition is described by C₄ symmetry breaking. We also verify the large-N critical exponents by numerically solving the Schwinger-Dyson equation.

Publication: Physical Review Letters Vol.: 127 No.: 14 ISSN: 0031-9007

ID: CaltechAUTHORS:20211004-232846320

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Abstract: A structured electromagnetic reservoir can result in novel dynamics of quantum emitters. In particular, the reservoir can be tailored to have a memory of past interactions with emitters, in contrast to memory-less Markovian dynamics of typical open systems. In this Article, we investigate the non-Markovian dynamics of a superconducting qubit strongly coupled to a superconducting slow-light waveguide reservoir. Tuning the qubit into the spectral vicinity of the passband of this waveguide, we find non-exponential energy relaxation as well as substantial changes to the qubit emission rate. Further, upon addition of a reflective boundary to one end of the waveguide, we observe revivals in the qubit population on a timescale 30 times longer than the inverse of the qubit's emission rate, corresponding to the round-trip travel time of an emitted photon. By tuning of the qubit-waveguide interaction strength, we probe a crossover between Markovian and non-Markovian qubit emission dynamics. These attributes allow for future studies of multi-qubit circuits coupled to structured reservoirs, in addition to constituting the necessary resources for generation of multiphoton highly entangled states.

Publication: Physical Review X Vol.: 11 No.: 4 ISSN: 2160-3308

ID: CaltechAUTHORS:20200409-164102679

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Abstract: Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators to Turing-complete computation. We discover that quantum cellular automata (QCA) can exhibit complexity in the sense of the complexity science that describes biology, sociology, and economics. QCA exhibit complexity when evolving under 'Goldilocks rules' that we define by balancing activity and stasis. Our Goldilocks rules generate robust dynamical features (entangled breathers), network structure and dynamics consistent with complexity, and persistent entropy fluctuations. Present-day experimental platforms—Rydberg arrays, trapped ions, and superconducting qubits—can implement our Goldilocks protocols, making testable the link between complexity science and quantum computation exposed by our QCA.

Publication: Quantum Science and Technology Vol.: 6 No.: 4 ISSN: 2058-9565

ID: CaltechAUTHORS:20211012-211827418

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Abstract: Quantum state transfer involves two parties who use pre-shared entanglement and noiseless communication in order to transfer parts of a quantum state. In this work, we quantity the communication cost of one-shot state splitting in terms of the partially smoothed max-information. We then give an analysis of state splitting in the moderate deviation regime, where the error in the protocol goes sub-exponentially fast to zero as a function of the number of i.i.d. copies. The main technical tool we derive is a tight relation between the partially smoothed max-information and the hypothesis testing relative entropy, which allows us to obtain the expansion of the partially smoothed max-information for i.i.d. states in the moderate deviation regime. This then also establishes the moderate deviation analysis for other variants of state transfer such as state merging and source coding.

ID: CaltechAUTHORS:20220722-768863000

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Abstract: Magic-angle twisted bilayer graphene (MATBG) exhibits a panoply of many-body phenomena that are intimately tied to the appearance of narrow and well-isolated electronic bands. The microscopic ingredients that are responsible for the complex experimental phenomenology include electron–electron (phonon) interactions and nontrivial Bloch wavefunctions associated with the narrow bands. Inspired by recent experiments, we focus on two independent quantities that are considerably modified by Coulomb interaction-driven band renormalization, namely the density of states and the minimal spatial extent associated with the Wannier functions. First, we show that a filling-dependent enhancement of the density of states, caused by band flattening, in combination with phonon-mediated attraction due to electron-phonon umklapp processes, increases the tendency towards superconducting pairing in a range of angles around magic-angle. Second, we demonstrate that the minimal spatial extent associated with the Wannier functions, which contributes towards increasing the superconducting phase stiffness, also develops a nontrivial enhancement due to the interaction-induced renormalization of the Bloch wavefunctions. While our modeling of superconductivity (SC) assumes a weak electron-phonon coupling and does not consider many of the likely relevant correlation effects, it explains simply the experimentally observed robustness of SC in the wide range of angles that occurs in the relevant range of fillings.

Publication: npj Quantum Materials Vol.: 6ISSN: 2397-4648

ID: CaltechAUTHORS:20210316-084002156

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Abstract: Magic-angle twisted trilayer graphene (MATTG) has emerged as a novel moiré material that exhibits both strong electronic correlations and unconventional superconductivity. However, spectroscopic studies of its electronic properties are lacking, and the nature of superconductivity and the corresponding order parameter in this system remain elusive. Here we perform high-resolution scanning tunneling microscopy and spectroscopy of MATTG and reveal extensive regions of atomic reconstruction that favor mirror-symmetric stacking. In these regions, we observe a cascade of symmetry-breaking electronic transitions and doping-dependent band structure deformations similar to those realized in magic-angle bilayers, as expected theoretically given the commonality of flat bands. More strikingly, in a density window spanning two to three holes per moire unit cell, spectroscopic signatures of superconductivity are manifest as pronounced dips in the tunneling conductance at the Fermi level accompanied by coherence peaks that become gradually suppressed at elevated temperatures and magnetic fields. The observed evolution of the conductance with doping is consistent with a gate-tunable transition from a gapped to a nodal superconductor, which we show theoretically is compatible with a sharp transition from a Bardeen-Cooper-Schrieffer (BCS) to a Bose-Einstein condensation (BEC) superconductor with a nodal order parameter. Within this doping window, we also detect peak-dip-hump structures suggesting that superconductivity is driven by strong coupling to bosonic modes of MATTG. Our results pave the way for further understanding of superconductivity and correlated states in graphene-based moiré structures beyond twisted bilayers, where unconventional superconductivity and nodal pairing were reported.

Publication: arXiv
ID: CaltechAUTHORS:20220113-182215445

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Abstract: Motivated by estimation of quantum noise models, we study the problem of learning a Pauli channel, or more generally the Pauli error rates of an arbitrary channel. By employing a novel reduction to the "Population Recovery" problem, we give an extremely simple algorithm that learns the Pauli error rates of an n-qubit channel to precision ϵ in l∞ using just O(1/ϵ²) log(n/ϵ) applications of the channel. This is optimal up to the logarithmic factors. Our algorithm uses only unentangled state preparation and measurements, and the post-measurement classical runtime is just an O(1/ϵ) factor larger than the measurement data size. It is also impervious to a limited model of measurement noise where heralded measurement failures occur independently with probability ≤ 1/4. We then consider the case where the noise channel is close to the identity, meaning that the no-error outcome occurs with probability 1 - η. In the regime of small η we extend our algorithm to achieve multiplicative precision 1 ± ϵ (i.e., additive precision ϵη) using just O(1/ϵ²η) log (n/ϵ) applications of the channel.

Publication: Quantum Vol.: 5ISSN: 2521-327X

ID: CaltechAUTHORS:20211123-173204089

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Abstract: Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations, and plays an important role in device-independent quantum information processing as well as quantum complexity theory. Prior works on self-testing require the assumption that the system's state is shared among multiple parties that only perform local measurements and cannot communicate. Here, we replace the setting of multiple non-communicating parties, which is difficult to enforce in practice, by a single computationally bounded party. Specifically, we construct a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a change of basis applied to both the device's state and measurements. This means that under computational assumptions, the verifier is able to certify the presence of entanglement, a property usually closely associated with two separated subsystems, inside a single quantum device. To achieve this, we build on techniques first introduced by Brakerski et al. (2018) and Mahadev (2018) which allow a classical verifier to constrain the actions of a quantum device assuming the device does not break post-quantum cryptography.

Publication: Quantum Vol.: 5ISSN: 2521-327X

ID: CaltechAUTHORS:20200417-132557882

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Abstract: The non-Hermitian skin effect, namely, that the eigenvalues and eigenstates of a non-Hermitian tight-binding Hamiltonian have significant differences under open or periodic boundary conditions, is a remarkable phenomenon of non-Hermitian systems. Inspired by the presence of the non-Hermitian skin effect, we study the evolution of wave packets in non-Hermitian systems, which can be determined using the single-particle Green's function. Surprisingly, we find that in the thermodynamic limit, the Green's function does not depend on boundary conditions, despite the presence of skin effect. We provide a general proof for this statement in arbitrary dimension with finite hopping range, with an explicit illustration in the non-Hermitian Su-Schrieffer-Heeger model. We also explore its applications in noninteracting open quantum systems described by the master equation. We demonstrate that the evolution of the density matrix is independent of the boundary condition.

Publication: Physical Review B Vol.: 104 No.: 12 ISSN: 2469-9950

ID: CaltechAUTHORS:20211025-171528994

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Abstract: Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an approximate, fast, and simple algorithm to optimize disentangling unitary tensors. Our algorithm is asymptotically faster than previous iterative algorithms and often results in a residual entanglement entropy that is within 10 to 40% of the minimum. For certain input tensors, our algorithm returns an optimal solution. When disentangling order-4 tensors with equal bond dimensions, our algorithm achieves an entanglement spectrum where nearly half of the singular values are zero. We further validate our algorithm by showing that it can efficiently disentangle random 1D states of qubits.

Publication: SciPost Physics Vol.: 11 No.: 3 ISSN: 2542-4653

ID: CaltechAUTHORS:20211116-160842763

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Abstract: We propose a new framework for simulating U(k) Yang-Mills theory on a universal quantum computer. This construction uses the orbifold lattice formulation proposed by Kaplan, Katz, and Unsal, who originally applied it to supersymmetric gauge theories. Our proposed approach yields a novel perspective on quantum simulation of quantum field theories, carrying certain advantages over the usual Kogut-Susskind formulation. We discuss the application of our constructions to computing static properties and real-time dynamics of Yang-Mills theories, from glueball measurements to AdS/CFT, making use of a variety of quantum information techniques including qubitization, quantum signal processing, Jordan-Lee-Preskill bounds, and shadow tomography. The generalizations to certain supersymmetric Yang-Mills theories appear to be straightforward, providing a path towards the quantum simulation of quantum gravity via holographic duality.

Publication: Journal of High Energy Physics Vol.: 2021 No.: 9 ISSN: 1126-6708

ID: CaltechAUTHORS:20201118-105305247

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Abstract: In this Letter, we propose a guiding principle for how to design the architecture of a quantum neural network in order to achieve a high learning efficiency. This principle is inspired by the equivalence between extracting information from the input state to the readout qubit and scrambling information from the readout qubit to input qubits. We characterize the quantum information scrambling by operator size growth. By Haar random averaging over operator sizes, we propose an averaged operator size to describe the information scrambling ability of a given quantum neural network architecture. The key conjecture of this Letter is that this quantity is positively correlated with the learning efficiency of this architecture. To support this conjecture, we consider several different architectures, and we also consider two typical learning tasks. One is a regression task of a quantum problem, and the other is a classification task on classical images. In both cases, we find that, for the architecture with a larger averaged operator size, the loss function decreases faster or the prediction accuracy increases faster as the training epoch increases, which means higher learning efficiency. Our results can be generalized to more complicated quantum versions of machine learning algorithms.

Publication: Physical Review Research Vol.: 3 No.: 3 ISSN: 2643-1564

ID: CaltechAUTHORS:20210927-213255436

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Abstract: Controlling the dynamics of quantum systems is a current frontier of quantum many-body physics. Recent advancements in experimental techniques suggest exciting new directions in drive-induced quantum states. Here, we present a simple scheme that relies solely on occupation measurements to induce a chiral quantum phase. Namely, we show that by utilizing a pattern of repeated quantum measurements we can produce chiral edge transport of fermions hopping on a Lieb lattice. We study in detail the dependence on measurement frequency, showing that in the Zeno limit the system can be described by a classical stochastic dynamics, yielding protected transport. As the frequency of measurements is reduced, the charge flow is reduced and vanishes when no measurements are done.

Publication: arXiv
ID: CaltechAUTHORS:20220113-182208459

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Abstract: We propose and prove a family of generalized Lieb-Schultz-Mattis (LSM) theorems for symmetry protected topological (SPT) phases on boson/spin models in any dimensions. The "conventional" LSM theorem, applicable to e.g. any translation invariant system with an odd number of spin-1/2 particles per unit cell, forbids a symmetric short-range-entangled ground state in such a system. Here we focus on systems with no LSM anomaly, where global/crystalline symmetries and fractional spins within the unit cell ensure that any symmetric SRE ground state must be a nontrivial SPT phase with anomalous boundary excitations. Depending on models, they can be either strong or "higher-order" crystalline SPT phases, characterized by nontrivial surface/hinge/corner states. Furthermore, given the symmetry group and the spatial assignment of fractional spins, we are able to determine all possible SPT phases for a symmetric ground state, using the real space construction for SPT phases based on the spectral sequence of cohomology theory. We provide examples in one, two and three spatial dimensions, and discuss possible physical realization of these SPT phases based on condensation of topological excitations in fractionalized phases.

Publication: SciPost Physics Vol.: 11 No.: 2 ISSN: 2542-4653

ID: CaltechAUTHORS:20211116-155504417

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Abstract: Quantum emitters, in particular, atomic arrays with subwavelength lattice constant, have been proposed to be an ideal platform for study the interplay between photons and electric dipoles. Previous theoretical studies are based on spin models, where each site is occupied by a point-like atom. In this work, motivated by the recent experiment [1], we develop a full quantum treatment using annihilation and creation operator of atoms in deep optical lattices. We use a diagrammatic approach on the Keldysh contour to derive the cooperative scattering of the light and obtain the general formula for the S matrix. We apply our formulism to study two effects beyond previous treatment with spin-operators, the effect of fractional filling and trapping. Both effects can lead to imperfectness of atomic mirrors. For the fractional filling case, we find the cooperative linewidth is linear in filling fraction n. When there is a mismatch between the trapping potentials for atoms in the ground state and the excited state, multiple resonances can appear in the response function. Our results are consistent with existing experiments.

Publication: arXiv
ID: CaltechAUTHORS:20210831-203952905

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Abstract: In this work, we address the question whether a sufficiently deep quantum neural network can approximate a target function as accurate as possible. We start with typical physical situations that the target functions are physical observables, and then we extend our discussion to situations that the learning targets are not directly physical observables, but can be expressed as physical observables in an enlarged Hilbert space with multiple replicas, such as the Loschmidt echo and the Rényi entropy. The main finding is that an accurate approximation is possible only when all the input wave functions in the dataset do not span the entire Hilbert space that the quantum circuit acts on, and more precisely, the Hilbert space dimension of the former has to be less than half of the Hilbert space dimension of the latter. In some cases, this requirement can be satisfied automatically because of the intrinsic properties of the dataset, for instance, when the input wave function has to be symmetric between different replicas. And if this requirement cannot be satisfied by the dataset, we show that the expressivity capabilities can be restored by adding one ancillary qubit at which the wave function is always fixed at input. Our studies point toward establishing a quantum neural network analogy of the universal approximation theorem that lays the foundation for expressivity of classical neural networks.

Publication: Physical Review Research Vol.: 3 No.: 3 ISSN: 2643-1564

ID: CaltechAUTHORS:20210830-203806681

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Abstract: Continuous-variable measurement-based quantum computation on cluster states has in recent years shown great potential for scalable, universal, and fault-tolerant quantum computation when combined with the Gottesman-Kitaev-Preskill (GKP) code and quantum error correction. However, no complete fault-tolerant architecture exists that includes everything from cluster-state generation with finite squeezing to gate implementations with realistic noise and error correction. In this work, we propose a simple architecture for the preparation of a cluster state in three dimensions in which gates can be efficiently implemented by gate teleportation. To accommodate scalability, we propose architectures that allow both spatial and temporal multiplexing, with the temporally encoded version requiring as little as two squeezed light sources. Because of its three-dimensional structure, the architecture supports topological qubit error correction, while GKP error correction is efficiently realized within the architecture by teleportation. To validate fault tolerance, the architecture is simulated using surface-GKP codes, including noise from GKP states as well as gate noise caused by finite squeezing in the cluster state. We find a fault-tolerant squeezing threshold of 12.7 dB, with room for further improvement.

Publication: PRX Quantum Vol.: 2 No.: 3 ISSN: 2691-3399

ID: CaltechAUTHORS:20210830-203806545

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Abstract: We establish a strong monogamy-of-entanglement property for subspace coset states, which are uniform superpositions of vectors in a linear subspace of F^n₂ to which has been applied a quantum one-time pad. This property was conjectured recently by [Coladangelo, Liu, Liu, and Zhandry, Crypto'21] and shown to have applications to unclonable decryption and copy-protection of pseudorandom functions. We present two proofs, one which directly follows the method of the original paper and the other which uses an observation from [Vidick and Zhang, Eurocrypt'20] to reduce the analysis to a simpler monogamy game based on BB'84 states. Both proofs ultimately rely on the same proof technique, introduced in [Tomamichel, Fehr, Kaniewski and Wehner, New Journal of Physics '13].

Publication: arXiv
ID: CaltechAUTHORS:20211006-152638528

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Abstract: Tensor network theory and quantum simulation are, respectively, the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks consisting of measurable quantum states and classically contractable tensors, inheriting both their distinct features in efficient representation of many-body wave functions. With the example of hybrid tree tensor networks, we demonstrate efficient quantum simulation using a quantum computer whose size is significantly smaller than the one of the target system. We numerically benchmark our method for finding the ground state of 1D and 2D spin systems of up to 8×8 and 9×8 qubits with operations only acting on 8+1 and 9+1 qubits, respectively. Our approach sheds light on simulation of large practical problems with intermediate-scale quantum computers, with potential applications in chemistry, quantum many-body physics, quantum field theory, and quantum gravity thought experiments.

Publication: Physical Review Letters Vol.: 127 No.: 4 ISSN: 0031-9007

ID: CaltechAUTHORS:20210821-163118813

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Abstract: We consider the problem of jointly estimating expectation values of many Pauli observables, a crucial subroutine in variational quantum algorithms. Starting with randomized measurements, we propose an efficient derandomization procedure that iteratively replaces random single-qubit measurements by fixed Pauli measurements; the resulting deterministic measurement procedure is guaranteed to perform at least as well as the randomized one. In particular, for estimating any L low-weight Pauli observables, a deterministic measurement on only of order log(L) copies of a quantum state suffices. In some cases, for example, when some of the Pauli observables have high weight, the derandomized procedure is substantially better than the randomized one. Specifically, numerical experiments highlight the advantages of our derandomized protocol over various previous methods for estimating the ground-state energies of small molecules.

Publication: Physical Review Letters Vol.: 127 No.: 3 ISSN: 0031-9007

ID: CaltechAUTHORS:20210512-104041014

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Abstract: The theory for the vanishing of Néel order in the spin S = 1/2 square lattice antiferromagnet has been the focus of attention for many decades. A consensus appears to have emerged in recent numerical studies on the antiferromagnet with first and second neighbor exchange interactions (the J₁−J₂ model): A gapless spin liquid is present for a narrow window of parameters between the vanishing of the Néel order and the onset of a gapped valence bond solid state. We propose a deconfined critical SU(2) gauge theory for a transition into a stable Z₂ spin liquid with massless Dirac spinon excitations; on the other side of the critical point, the SU(2) spin liquid (the ‘π-flux’ phase) is presumed to be unstable to confinement to the Néel phase. We identify a dangerously irrelevant coupling in the critical SU(2) gauge theory, which contributes a logarithm-squared renormalization. This critical theory is also not Lorentz invariant and weakly breaks the SO(5) symmetry which rotates between the Néel and valence bond solid order parameters. We also propose a distinct deconfined critical U(1) gauge theory for a transition into the same gapless Z₂ spin liquid; on the other side of the critical point, the U(1) spin liquid (the ‘staggered flux’ phase) is presumed to be unstable to confinement to the valence bond solid. This critical theory has no dangerously irrelevant coupling, dynamic critical exponent z ≠ 1, and no SO(5) symmetry. All of these phases and critical points are unified in a SU(2) gauge theory with Higgs fields and fermionic spinons which can naturally realize the observed sequence of phases with increasing J₂/J₁: Néel, gapless Z₂ spin liquid, and valence bond solid.

Publication: Physical Review B Vol.: 104 No.: 4 ISSN: 2469-9950

ID: CaltechAUTHORS:20210709-212640442

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Abstract: Recent progress in studies of holographic dualities, originally motivated by insights from string theory, has led to a confluence with concepts and techniques from quantum information theory. A particularly successful approach has involved capturing holographic properties by means of tensor networks which not only give rise to physically meaningful correlations of holographic boundary states, but also reproduce and refine features of quantum error correction in holography. This topical review provides an overview over recent successful realizations of such models. It does so by building on an introduction of the theoretical foundations of AdS/CFT and necessary quantum information concepts, many of which have themselves developed into independent, rapidly evolving research fields.

Publication: Quantum Science and Technology Vol.: 6 No.: 3 ISSN: 2058-9565

ID: CaltechAUTHORS:20210701-174154858

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Abstract: Among the most actively studied issues in the cuprates are the natures of the pseudogap and strange metal states and their relationship to superconductivity1. There is general agreement that the low-energy physics of the Mott-insulating parent state is well captured by a two-dimensional spin S = 1/2 antiferromagnetic Heisenberg model. However, recent observations of a large thermal Hall conductivity in several parent cuprates appear to defy this simple model and suggest proximity to a magneto-chiral state that breaks all mirror planes that are perpendicular to the CuO₂ layers. Here we use optical second harmonic generation to directly resolve the point group symmetries of the model parent cuprate Sr₂CuO₂Cl₂. We report evidence of an order parameter that breaks all perpendicular mirror planes and is consistent with a magneto-chiral state in zero magnetic field. Although this order is clearly coupled to the antiferromagnetism, we are unable to realize its time-reversed partner by thermal cycling through the antiferromagnetic transition temperature or by sampling different spatial locations. This suggests that the order onsets above the Néel temperature and may be relevant to the mechanism of pseudogap formation.

Publication: Nature Physics Vol.: 17 No.: 7 ISSN: 1745-2473

ID: CaltechAUTHORS:20200909-101851261

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Abstract: We extend quantum Stein’s lemma in asymmetric quantum hypothesis testing to composite null and alternative hypotheses. As our main result, we show that the asymptotic error exponent for testing convex combinations of quantum states ρ^(⊗n) against convex combinations of quantum states σ^(⊗n) can be written as a regularized quantum relative entropy formula. We prove that in general such a regularization is needed but also discuss various settings where our formula as well as extensions thereof become single-letter. This includes an operational interpretation of the relative entropy of coherence in terms of hypothesis testing. For our proof, we start from the composite Stein’s lemma for classical probability distributions and lift the result to the non-commutative setting by using elementary properties of quantum entropy. Finally, our findings also imply an improved recoverability lower bound on the conditional quantum mutual information in terms of the regularized quantum relative entropy—featuring an explicit and universal recovery map.

Publication: Communications in Mathematical Physics Vol.: 385 No.: 1 ISSN: 0010-3616

ID: CaltechAUTHORS:20190801-134523759

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Abstract: We present a novel framework for simulating matrix models on a quantum computer. Supersymmetric matrix models have natural applications to superstring/M-theory and gravitational physics, in an appropriate limit of parameters. Furthermore, for certain states in the Berenstein-Maldacena-Nastase (BMN) matrix model, several supersymmetric quantum field theories dual to superstring/M-theory can be realized on a quantum device. Our prescription consists of four steps: regularization of the Hilbert space, adiabatic state preparation, simulation of real-time dynamics, and measurements. Regularization is performed for the BMN matrix model with the introduction of energy cut-off via the truncation in the Fock space. We use the Wan-Kim algorithm for fast digital adiabatic state preparation to prepare the low-energy eigenstates of this model as well as thermofield double state. Then, we provide an explicit construction for simulating real-time dynamics utilizing techniques of block-encoding, qubitization, and quantum signal processing. Lastly, we present a set of measurements and experiments that can be carried out on a quantum computer to further our understanding of superstring/M-theory beyond analytic results.

Publication: Journal of High Energy Physics Vol.: 2021 No.: 7 ISSN: 1126-6708

ID: CaltechAUTHORS:20201118-111200749

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Abstract: Classical machine learning (ML) provides a potentially powerful approach to solving challenging quantum many-body problems in physics and chemistry. However, the advantages of ML over more traditional methods have not been firmly established. In this work, we prove that classical ML algorithms can efficiently predict ground state properties of gapped Hamiltonians in finite spatial dimensions, after learning from data obtained by measuring other Hamiltonians in the same quantum phase of matter. In contrast, under widely accepted complexity theory assumptions, classical algorithms that do not learn from data cannot achieve the same guarantee. We also prove that classical ML algorithms can efficiently classify a wide range of quantum phases of matter. Our arguments are based on the concept of a classical shadow, a succinct classical description of a many-body quantum state that can be constructed in feasible quantum experiments and be used to predict many properties of the state. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, 2D random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.

Publication: arXiv
ID: CaltechAUTHORS:20220104-233146603

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Abstract: Understanding strongly interacting quantum matter and quantum gravity are both important open issues in theoretical physics, and the holographic duality between quantum field theory and gravity theory nicely brings these two topics together. Nevertheless, direct connections between gravity physics and experimental observations in quantum matter are still rare. Here we utilize the gravity physics picture to understand quench dynamics experimentally observed in a class of random spin models realized in several different quantum systems, where the dynamics of magnetization are measured after the external polarization field is suddenly turned off. Two universal features of the magnetization dynamics, namely, a slow decay described by a stretched exponential function and an oscillatory behavior, are respectively found in different parameter regimes across different systems. This paper addresses the issues of generic conditions under which these two universal features can occur, and we find that a natural answer to this question emerges in the gravity picture. By the holographic duality bridged by a model proposed by Maldacena and Qi, the quench dynamics after suddenly turning off the external polarization field is mapped to disconnecting an eternal traversable wormhole. Our studies show that insight from gravity physics can help unifying different experiments in quantum systems.

Publication: Physical Review Research Vol.: 3 No.: 2 ISSN: 2643-1564

ID: CaltechAUTHORS:20210626-225301379

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Abstract: Forty years ago, Richard Feynman proposed harnessing quantum physics to build a more powerful kind of computer. Realizing Feynman's vision is one of the grand challenges facing 21st century science and technology. In this article, we'll recall Feynman's contribution that launched the quest for a quantum computer, and assess where the field stands 40 years later.

Publication: arXiv
ID: CaltechAUTHORS:20220104-233143218

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Abstract: We demonstrate the possibility of (sub)exponential quantum speedup via a quantum algorithm that follows an adiabatic path of a gapped Hamiltonian with no sign problem. The Hamiltonian that exhibits this speed-up comes from the adjacency matrix of an undirected graph whose vertices are labeled by n-bit strings, and we can view the adiabatic evolution as an efficient O(poly(n))-time quantum algorithm for finding a specific “EXIT” vertex in the graph given the “ENTRANCE” vertex. On the other hand we show that if the graph is given via an adjacency-list oracle, there is no classical algorithm that finds the “EXIT” with probability greater than exp(−n^δ) using at most exp(n^δ) queries for δ= 1/5 − o(1). Our construction of the graph is somewhat similar to the “welded-trees” construction of Childs et al., but uses additional ideas of Hastings for achieving a spectral gap and a short adiabatic path.

ID: CaltechAUTHORS:20220802-839191000

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Abstract: Negativity of the Wigner function is arguably one of the most striking non-classical features of quantum states. Beyond its fundamental relevance, it is also a necessary resource for quantum speedup with continuous variables. As quantum technologies emerge, the need to identify and characterize the resources which provide an advantage over existing classical technologies becomes more pressing. Here we derive witnesses for Wigner negativity of single mode and multimode quantum states, based on fidelities with Fock states, which can be reliably measured using standard detection setups. They possess a threshold expectation value indicating whether the measured state has a negative Wigner function. Moreover, the amount of violation provides an operational quantification of Wigner negativity. We phrase the problem of finding the threshold values for our witnesses as an infinite-dimensional linear optimisation. By relaxing and restricting the corresponding linear programs, we derive two hierarchies of semidefinite programs, which provide numerical sequences of increasingly tighter upper and lower bounds for the threshold values. We further show that both sequences converge to the threshold value. Moreover, our witnesses form a complete family – each Wigner negative state is detected by at least one witness – thus providing a reliable method for experimentally witnessing Wigner negativity of quantum states from few measurements. From a foundational perspective, our findings provide insights on the set of positive Wigner functions which still lacks a proper characterisation.

Publication: Quantum Vol.: 5ISSN: 2521-327X

ID: CaltechAUTHORS:20210630-160717654

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Abstract: The mixing time of Markovian dissipative evolutions of open quantum many-body systems can be bounded using optimal constants of certain quantum functional inequalities, such as the modified logarithmic Sobolev constant. For classical spin systems, the positivity of such constants follows from a mixing condition for the Gibbs measure via quasi-factorization results for the entropy. Inspired by the classical case, we present a strategy to derive the positivity of the modified logarithmic Sobolev constant associated with the dynamics of certain quantum systems from some clustering conditions on the Gibbs state of a local, commuting Hamiltonian. In particular, we show that for the heat-bath dynamics of 1D systems, the modified logarithmic Sobolev constant is positive under the assumptions of a mixing condition on the Gibbs state and a strong quasi-factorization of the relative entropy.

Publication: Journal of Mathematical Physics Vol.: 62 No.: 6 ISSN: 0022-2488

ID: CaltechAUTHORS:20210623-143016235

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Abstract: In this paper, we use the exactly solvable Sachdev-Ye-Kitaev model to address the issue of entropy dynamics when an interacting quantum system is coupled to a non-Markovian environment. We find that at the initial stage, the entropy always increases linearly matching the Markovian result. When the system thermalizes with the environment at a sufficiently long time, if the environment temperature is low and the coupling between system and environment is weak, then the total thermal entropy is low and the entanglement between system and environment is also weak, which yields a small system entropy in the long-time steady state. This manifestation of non-Markovian effects of the environment forces the entropy to decrease in the later stage, which yields the Page curve for the entropy dynamics. We argue that this physical scenario revealed by the exact solution of the Sachdev-Ye-Kitaev model is universally applicable for general chaotic quantum many-body systems and can be verified experimentally in near future.

Publication: Journal of High Energy Physics Vol.: 2021 No.: 6 ISSN: 1029-8479

ID: CaltechAUTHORS:20210701-144159635

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Abstract: Continuous-variable systems protected by bosonic quantum codes have emerged as a promising platform for quantum information. To date, the design of code words has centered on optimizing the state occupation in the relevant basis to generate the distance needed for error correction. Here, we show tuning the phase degree of freedom in the design of code words can affect, and potentially enhance, the protection against Markovian errors that involve excitation exchange with the environment. As illustrations, we first consider phase engineering bosonic codes with uniform spacing in the Fock basis that correct excitation loss with a Kerr unitary and show that these modified codes feature destructive interference between error code words and, with an adapted “two-level” recovery, the error protection is significantly enhanced. We then study protection against energy decay with the presence of mode nonlinearities and analyze the role of phase for optimal code designs. We extend the principle of phase engineering to bosonic codes defined in other bases and multiqubit codes, demonstrating its broad applicability in quantum error correction.

Publication: Physical Review A Vol.: 103 No.: 6 ISSN: 2469-9926

ID: CaltechAUTHORS:20210709-212642251

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Abstract: The out-of-time-ordered correlation (OTOC) and entanglement are two physically motivated and widely used probes of the “scrambling” of quantum information, a phenomenon that has drawn great interest recently in quantum gravity and many-body physics. We argue that the corresponding notions of scrambling can be fundamentally different, by proving an asymptotic separation between the time scales of the saturation of OTOC and that of entanglement entropy in a random quantum-circuit model defined on graphs with a tight bottleneck, such as tree graphs. Our result counters the intuition that a random quantum circuit mixes in time proportional to the diameter of the underlying graph of interactions. It also provides a more rigorous justification for an argument in our previous work [Shor P.W., Scrambling time and causal structure of the photon sphere of a Schwarzschild black hole, arXiv:1807.04363 (2018)], that black holes may be slow information scramblers, which in turn relates to the black-hole information problem. The bounds we obtain for OTOC are interesting in their own right in that they generalize previous studies of OTOC on lattices to the geometries on graphs in a rigorous and general fashion.

Publication: PRX Quantum Vol.: 2 No.: 2 ISSN: 2691-3399

ID: CaltechAUTHORS:20210622-220353587

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Abstract: Recent understanding of the thermodynamics of small-scale systems have enabled the characterization of the thermodynamic requirements of implementing quantum processes for fixed input states. Here, we extend these results to construct optimal universal implementations of a given process, that is, implementations that are accurate for any possible input state even after many independent and identically distributed (i.i.d.) repetitions of the process. We find that the optimal work cost rate of such an implementation is given by the thermodynamic capacity of the process, which is a single-letter and additive quantity defined as the maximal difference in relative entropy to the thermal state between the input and the output of the channel. Beyond being a thermodynamic analogue of the reverse Shannon theorem for quantum channels, our results introduce a new notion of quantum typicality and present a thermodynamic application of convex-split methods.

Publication: Communications in Mathematical Physics Vol.: 384 No.: 3 ISSN: 0010-3616

ID: CaltechAUTHORS:20210512-104034146

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Abstract: Genuinely non-Hermitian topological phases can be realized in open systems with sufficiently strong gain and loss; in such phases, the Hamiltonian cannot be deformed into a gapped Hermitian Hamiltonian without energy bands touching each other. Comparing Green functions for periodic and open boundary conditions we find that, in general, there is no correspondence between topological invariants computed for periodic boundary conditions, and boundary eigenstates observed for open boundary conditions. Instead, we find that the non-Hermitian winding number in one dimension signals a topological phase transition in the bulk: It implies spatial growth of the bulk Green function.

Publication: Physical Review Letters Vol.: 126 No.: 21 ISSN: 0031-9007

ID: CaltechAUTHORS:20190426-083909000

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Abstract: We study the performance of classical and quantum machine learning (ML) models in predicting outcomes of physical experiments. The experiments depend on an input parameter x and involve execution of a (possibly unknown) quantum process E. Our figure of merit is the number of runs of E required to achieve a desired prediction performance. We consider classical ML models that perform a measurement and record the classical outcome after each run of E, and quantum ML models that can access E coherently to acquire quantum data; the classical or quantum data are then used to predict the outcomes of future experiments. We prove that for any input distribution D(x), a classical ML model can provide accurate predictions on average by accessing E a number of times comparable to the optimal quantum ML model. In contrast, for achieving an accurate prediction on all inputs, we prove that the exponential quantum advantage is possible. For example, to predict the expectations of all Pauli observables in an n-qubit system ρ, classical ML models require 2^(Ω(n)) copies of ρ, but we present a quantum ML model using only O(n) copies. Our results clarify where the quantum advantage is possible and highlight the potential for classical ML models to address challenging quantum problems in physics and chemistry.

Publication: Physical Review Letters Vol.: 126 No.: 19 ISSN: 0031-9007

ID: CaltechAUTHORS:20210512-104048123

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Abstract: Recent theoretical studies inspired by experiments on the Kitaev magnet α-RuCl₃ highlight the nontrivial impact of phonons on the thermal Hall conductivity of chiral topological phases. Here we introduce mixed mesoscopic-macroscopic devices that allow refined thermal-transport probes of non-Abelian spin liquids with Ising topological order. These devices feature a quantum-coherent mesoscopic region with negligible phonon conductance, flanked by macroscopic lobes that facilitate efficient thermalization between chiral Majorana edge modes and bulk phonons. We show that our devices enable (i) accurate determination of the quantized thermal Hall conductivity, (ii) identification of non-Abelian Ising anyons via the temperature dependence of the thermal conductance, and most interestingly (iii) single-anyon detection through heat-based anyon interferometry. Analogous results apply broadly to phonon-coupled chiral topological orders.

Publication: arXiv
ID: CaltechAUTHORS:20220104-233139832

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Abstract: The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied computational tasks. In this work, we show that some problems that are classically hard to compute can be easily predicted by classical machines learning from data. Using rigorous prediction error bounds as a foundation, we develop a methodology for assessing potential quantum advantage in learning tasks. The bounds are tight asymptotically and empirically predictive for a wide range of learning models. These constructions explain numerical results showing that with the help of data, classical machine learning models can be competitive with quantum models even if they are tailored to quantum problems. We then propose a projected quantum model that provides a simple and rigorous quantum speed-up for a learning problem in the fault-tolerant regime. For near-term implementations, we demonstrate a significant prediction advantage over some classical models on engineered data sets designed to demonstrate a maximal quantum advantage in one of the largest numerical tests for gate-based quantum machine learning to date, up to 30 qubits.

Publication: Nature Communications Vol.: 12ISSN: 2041-1723

ID: CaltechAUTHORS:20210512-121027702

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Abstract: Maintaining local interactions in the quantum simulation of gauge field theories relegates most states in the Hilbert space to be unphysical—theoretically benign, but experimentally difficult to avoid. Reformulations of the gauge fields can modify the ratio of physical to gauge-variant states often through classically preprocessing the Hilbert space and modifying the representation of the field on qubit degrees of freedom. This paper considers the implications of representing SU(3) Yang-Mills gauge theory on a lattice of irreducible representations in both a global basis of projected global quantum numbers and a local basis in which controlled-plaquette operators support efficient time evolution. Classically integrating over the internal gauge space at each vertex (e.g., color isospin and color hypercharge) significantly reduces both the qubit requirements and the dimensionality of the unphysical Hilbert space. Initiating tuning procedures that may inform future calculations at scale, the time evolution of one and two plaquettes are implemented on one of IBM’s superconducting quantum devices, and early benchmark quantities are identified. The potential advantages of qudit environments, with either constrained two-dimensional hexagonal or one-dimensional nearest-neighbor internal state connectivity, are discussed for future large-scale calculations.

Publication: Physical Review D Vol.: 103 No.: 9 ISSN: 2470-0010

ID: CaltechAUTHORS:20210512-080651380

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Abstract: We study a planar Josephson junction under an applied DC voltage bias in the presence of an in-plane magnetic field. Upon tuning the bias voltage across the junction V_J, the two ends of the junction are shown to simultaneously host both zero and π Majorana modes. These modes can be probed using either a scanning-tunneling-microscopy measurement or through resonant Andreev tunneling from a lead coupled to the junction. While these modes are mostly bound to the junction's ends, they can hybridize with the bulk by absorbing or emitting photons. We analyze this process both numerically and analytically, demonstrating that it can become negligible under typical experimental conditions. Transport signatures of the zero and π Majorana states are shown to be robust to moderate disorder.

Publication: Physical Review Research Vol.: 3 No.: 2 ISSN: 2643-1564

ID: CaltechAUTHORS:20210105-133420695

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Abstract: In three dimensions, gapped phases can support “fractonic” quasiparticle excitations, which are either completely immobile or can only move within a low-dimensional submanifold, a peculiar topological phenomenon going beyond the conventional framework of topological quantum field theory. In this work we explore fractonic topological phases using three-dimensional coupled wire constructions, which have proven to be a successful tool to realize and characterize topological phases in two dimensions. We find that both gapped and gapless phases with fractonic excitations can emerge from the models. In the gapped case, we argue that fractonic excitations are mobile along the wire direction, but their mobility in the transverse plane is generally reduced. We show that the excitations in general have infinite-order fusion structure, distinct from previously known gapped fracton models. Like the two-dimensional coupled-wire constructions, many models exhibit gapless (or even chiral) surface states, which can be described by infinite-component Luttinger liquids. However, the universality class of the surface theory strongly depends on the surface orientation, thus revealing a different type of bulk-boundary correspondence unique to fracton phases.

Publication: Physical Review Research Vol.: 3 No.: 2 ISSN: 2643-1564

ID: CaltechAUTHORS:20210518-102152394

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Abstract: We report the observation of topological phonon transport within a multiscale optomechanical crystal structure consisting of an array of over 800 cavity-optomechanical elements. Using sensitive, spatially resolved optical read-out we detect thermal phonons in a 0.325 − 0.34 GHz band traveling along a topological edge channel, with substantial reduction in backscattering. This represents an important step from the pioneering macroscopic mechanical systems work towards topological phononic systems at the nanoscale.

Publication: arXiv
ID: CaltechAUTHORS:20200915-092939162

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Abstract: We provide strong evidence that the asymptotically free (1+1)-dimensional nonlinear O(3) sigma model can be regularized using a quantum lattice Hamiltonian, referred to as the “Heisenberg comb,” that acts on a Hilbert space with only two qubits per spatial lattice site. The Heisenberg comb consists of a spin-half antiferromagnetic Heisenberg chain coupled antiferromagnetically to a second local spin-half particle at every lattice site. Using a world-line Monte Carlo method, we show that the model reproduces the universal step-scaling function of the traditional model up to correlation lengths of 200000 in lattice units and argue how the continuum limit could emerge. We provide a quantum circuit description of the time evolution of the model and argue that near-term quantum computers may suffice to demonstrate asymptotic freedom.

Publication: Physical Review Letters Vol.: 126 No.: 17 ISSN: 0031-9007

ID: CaltechAUTHORS:20210610-153552455

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Abstract: Motivated by recent experiments on the Kitaev honeycomb magnet α-RuCl₃, we introduce time-domain probes of the edge and quasiparticle content of non-Abelian spin liquids. Our scheme exploits ancillary quantum spins that communicate via time-dependent tunneling of energy into and out of the spin liquid’s chiral Majorana edge state. We show that the ancillary-spin dynamics reveals the edge-state velocity and, in suitable geometries, detects individual non-Abelian anyons and emergent fermions via a time-domain counterpart of quantum-Hall anyon interferometry. We anticipate applications to a wide variety of topological phases in solid-state and cold-atoms settings.

Publication: Physical Review Letters Vol.: 126 No.: 17 ISSN: 0031-9007

ID: CaltechAUTHORS:20201111-081453060

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Abstract: Diverse many-body systems, from soap bubbles to suspensions to polymers, learn and remember patterns in the drives that push them far from equilibrium. This learning may be leveraged for computation, memory, and engineering. Until now, many-body learning has been detected with thermodynamic properties, such as work absorption and strain. We progress beyond these macroscopic properties first defined for equilibrium contexts: We quantify statistical mechanical learning using representation learning, a machine-learning model in which information squeezes through a bottleneck. By calculating properties of the bottleneck, we measure four facets of many-body systems’ learning: classification ability, memory capacity, discrimination ability, and novelty detection. Numerical simulations of a classical spin glass illustrate our technique. This toolkit exposes self-organization that eludes detection by thermodynamic measures: Our toolkit more reliably and more precisely detects and quantifies learning by matter while providing a unifying framework for many-body learning.

Publication: Scientific Reports Vol.: 11ISSN: 2045-2322

ID: CaltechAUTHORS:20210429-144552683

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Abstract: The X-cube model, a prototypical gapped fracton model, was shown in Ref. [1] to have a foliation structure. That is, inside the 3+1 D model, there are hidden layers of 2+1 D gapped topological states. A screw dislocation in a 3+1 D lattice can often reveal nontrivial features associated with a layered structure. In this paper, we study the X-cube model on lattices with screw dislocations. In particular, we find that a screw dislocation results in a finite change in the logarithm of the ground state degeneracy of the model. Part of the change can be traced back to the effect of screw dislocations in a simple stack of 2+1 D topological states, hence corroborating the foliation structure in the model. The other part of the change comes from the induced motion of fractons or sub-dimensional excitations along the dislocation, a feature absent in the stack of 2+1D layers.

Publication: SciPost Physics Vol.: 10 No.: 4 ISSN: 2542-4653

ID: CaltechAUTHORS:20211222-591602700

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Abstract: Excitons are neutral objects that, naively, should have no response to a uniform electric field. Could the Berry curvature of the underlying electronic bands alter this conclusion? In this work, we show that Berry curvature can indeed lead to anomalous transport for excitons in two-dimensional materials subject to a uniform in-plane electric field. By considering the constituent electron and hole dynamics, we demonstrate that there exists a regime for which the corresponding anomalous velocities are in the same direction. We establish the resulting center-of-mass motion of the exciton through both a semiclassical and fully quantum mechanical analysis, and elucidate the critical role of Bloch oscillations in achieving this effect. We identify transition metal dichalcogenide heterobilayers as candidate materials to observe the effect.

Publication: Physical Review B Vol.: 103 No.: 16 ISSN: 2469-9950

ID: CaltechAUTHORS:20201111-135554466

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Abstract: We continue recent efforts to discover examples of deconfined quantum criticality in one-dimensional models. In this work we investigate the transition between a Z₃ ferromagnet and a phase with valence bond solid (VBS) order in a spin chain with Z₃ × Z₃ global symmetry. We study a model with alternating projective representations on the sites of the two sublattices, allowing the Hamiltonian to connect to an exactly solvable point having VBS order with the character of SU(3)-invariant singlets. Such a model does not admit a Lieb-Schultz-Mattis theorem typical of systems realizing deconfined critical points. Nevertheless, we find evidence for a direct transition from the VBS phase to a Z₃ ferromagnet. Finite-entanglement scaling data are consistent with a second-order or weakly first-order transition. We find in our parameter space an integrable lattice model apparently describing the phase transition, with a very long, finite, correlation length of 190878 lattice spacings. Based on exact results for this model, we propose that the transition is extremely weakly first order and is part of a family of deconfined quantum critical points described by walking of renormalization group flows.

Publication: Physical Review B Vol.: 103 No.: 15 ISSN: 2469-9950

ID: CaltechAUTHORS:20201109-081814617

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Abstract: Computing the distribution of permanents of random matrices has been an outstanding open problem for several decades. In quantum computing, "anti-concentration" of this distribution is an unproven input for the proof of hardness of the task of boson-sampling. We study permanents of random i.i.d. complex Gaussian matrices, and more broadly, submatrices of random unitary matrices. Using a hybrid representation-theoretic and combinatorial approach, we prove strong lower bounds for all moments of the permanent distribution. We provide substantial evidence that our bounds are close to being tight and constitute accurate estimates for the moments. Let U(d)^(k×k) be the distribution of k×k submatrices of d×d random unitary matrices, and Gk×k be the distribution of k×k complex Gaussian matrices. (1) Using the Schur-Weyl duality (or the Howe duality), we prove an expansion formula for the 2t-th moment of |Perm(M)| when M is drawn from U(d)^(k×k) or G^(k×k). (2) We prove a surprising size-moment duality: the 2t-th moment of the permanent of random k×k matrices is equal to the 2k-th moment of the permanent of t×t matrices. (3) We design an algorithm to exactly compute high moments of the permanent of small matrices. (4) We prove lower bounds for arbitrary moments of permanents of matrices drawn from G^(k×k) or U(k), and conjecture that our lower bounds are close to saturation up to a small multiplicative error. (5) Assuming our conjectures, we use the large deviation theory to compute the tail of the distribution of log-permanent of Gaussian matrices for the first time. (6) We argue that it is unlikely that the permanent distribution can be uniquely determined from the integer moments and one may need to supplement the moment calculations with extra assumptions to prove the anti-concentration conjecture.

Publication: arXiv
ID: CaltechAUTHORS:20210809-220321102

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Abstract: We study semiconductor nanowires coupled to a bilayer of a disordered superconductor and a magnetic insulator, motivated by recent experiments reporting possible Majorana-zero-mode signatures in related architectures. Specifically, we pursue a quasiclassical Usadel equation approach that treats superconductivity in the bilayer self-consistently in the presence of spin-orbit scattering, magnetic-impurity scattering, and Zeeman splitting induced by both the magnetic insulator and a supplemental applied field. Within this framework we explore prospects for engineering topological superconductivity in a nanowire proximate to the bilayer. We find that a magnetic-insulator-induced Zeeman splitting, mediated through the superconductor alone, cannot induce a topological phase since the destruction of superconductivity (i.e., Clogston limit) preempts the required regime in which the nanowire's Zeeman energy exceeds the induced pairing strength. However, this Zeeman splitting does reduce the critical applied field needed to access the topological phase transition, with fields antiparallel to the magnetization of the magnetic insulator having an optimal effect. Finally, we show that magnetic-impurity scattering degrades the topological phase, and spin-orbit scattering, if present in the superconductor, pushes the Clogston limit to higher fields yet simultaneously increases the critical applied field strength.

Publication: Physical Review B Vol.: 103 No.: 13 ISSN: 2469-9950

ID: CaltechAUTHORS:20210421-103423569

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Abstract: Signatures of self-organized criticality (SOC) have recently been observed in an ultracold atomic gas under continuous laser excitation to strongly-interacting Rydberg states [S. Helmrich et al., Nature, 577, 481--486 (2020)]. This creates a unique possibility to study this intriguing dynamical phenomenon, e.g., to probe its robustness and universality, under controlled experimental conditions. Here we examine the self-organizing dynamics of a driven ultracold gas and identify an unanticipated feedback mechanism, which is especially important for systems coupled to thermal baths. It sustains an extended critical region in the trap center for a notably long time via hydrodynamic transport of particles from the flanks of the cloud toward the center. This compensates the avalanche-induced atom loss and leads to a characteristic flat-top density profile, providing an additional experimental signature for SOC and minimizing effects of inhomogeneity on the SOC features.

Publication: Physical Review Letters Vol.: 126 No.: 12 ISSN: 0031-9007

ID: CaltechAUTHORS:20201019-095613586

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Abstract: An upper limit to distillable entanglement between two disconnected regions of massless noninteracting scalar field theory has an exponential decay defined by a geometric decay constant. When regulated at short distances with a spatial lattice, this entanglement abruptly vanishes beyond a dimensionless separation, defining a negativity sphere. In two spatial dimensions, we determine this geometric decay constant between a pair of disks and the growth of the negativity sphere toward the continuum through a series of lattice calculations. Making the connection to quantum field theories in three-spatial dimensions, assuming such quantum information scales appear also in quantum chromodynamics (QCD), a new relative scale may be present in effective field theories describing the low-energy dynamics of nucleons and nuclei. We highlight potential impacts of the distillable entanglement structure on effective field theories, lattice QCD calculations and future quantum simulations.

Publication: Physical Review D Vol.: 103 No.: 6 ISSN: 2470-0010

ID: CaltechAUTHORS:20210323-073930352

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Abstract: Stacking two graphene layers twisted by the magic angle θ≈1.1∘ generates flat energy bands, which in turn catalyzes various strongly correlated phenomena depending on filling and sample details. At charge neutrality, transport measurements reveal superficially mundane semimetallicity (as expected when correlations are weak) in some samples yet robust insulation in others. We propose that the interplay between interactions and disorder admits either behavior, even when the system is strongly correlated and locally gapped. Specifically, we argue that strong interactions supplemented by weak, smooth disorder stabilize a network of gapped quantum valley Hall domains with spatially varying Chern numbers determined by the disorder landscape—even when an entirely different order is favored in the clean limit. Within this scenario, sufficiently small samples that realize a single domain display insulating transport characteristics. Conversely, multidomain samples exhibit re-emergent massless Dirac fermions formed by gapless domain-wall modes, yielding semimetallic behavior except on the ultralong scales at which localization becomes visible. We discuss experimental tests of this proposal via local probes and transport. Our results highlight the crucial role that randomness can play in ground-state selection of twisted heterostructures, an observation that we expect to have further ramifications at other fillings.

Publication: Physical Review B Vol.: 103 No.: 12 ISSN: 2469-9950

ID: CaltechAUTHORS:20191216-103049254

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Abstract: We introduce a new kind of foliated quantum field theory (FQFT) of gapped fracton orders in the continuum. FQFT is defined on a manifold with a layered structure given by one or more foliations, which each decompose spacetime into a stack of layers. FQFT involves a new kind of gauge field, a foliated gauge field, which behaves similar to a collection of independent gauge fields on this stack of layers. Gauge invariant operators (and their analogous particle mobilities) are constrained to the intersection of one or more layers from different foliations. The level coefficients are quantized and exhibit a duality that spatially transforms the coefficients. This duality occurs because the FQFT is a foliated fracton order. That is, the duality can decouple 2+1D gauge theories from the FQFT through a process we dub exfoliation.

Publication: Physical Review Letters Vol.: 126 No.: 10 ISSN: 0031-9007

ID: CaltechAUTHORS:20210106-102255003

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Abstract: Traditional uncertainty relations dictate a minimal amount of noise in incompatible projective quantum measurements. However, not all measurements are projective. Weak measurements are minimally invasive methods for obtaining partial state information without projection. Recently, weak measurements were shown to obey an uncertainty relation cast in terms of entropies. We experimentally test this entropic uncertainty relation with strong and weak measurements of a superconducting transmon qubit. A weak measurement, we find, can reconcile two strong measurements’ incompatibility, via backaction on the state. Mathematically, a weak value—a preselected and postselected expectation value—lowers the uncertainty bound. Hence we provide experimental support for the physical interpretation of the weak value as a determinant of a weak measurement’s ability to reconcile incompatible operations.

Publication: Physical Review Letters Vol.: 126 No.: 10 ISSN: 0031-9007

ID: CaltechAUTHORS:20210312-141741101

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Abstract: Many quantum algorithms critically rely on quantum walk search, or the use of quantum walks to speed up search problems on graphs. However, the main results on quantum walk search are scattered over different, incomparable frameworks, such as the hitting time framework, the MNRS framework, and the electric network framework. As a consequence, a number of pieces are currently missing. For example, recent work by Ambainis et al. (STOC'20) shows how quantum walks starting from the stationary distribution can always find elements quadratically faster. In contrast, the electric network framework allows quantum walks to start from an arbitrary initial state, but it only detects marked elements. We present a new quantum walk search framework that unifies and strengthens these frameworks, leading to a number of new results. For example, the new framework effectively finds marked elements in the electric network setting. The new framework also allows to interpolate between the hitting time framework, minimizing the number of walk steps, and the MNRS framework, minimizing the number of times elements are checked for being marked. This allows for a more natural tradeoff between resources. In addition to quantum walks and phase estimation, our new algorithm makes use of quantum fast-forwarding, similar to the recent results by Ambainis et al. This perspective also enables us to derive more general complexity bounds on the quantum walk algorithms, e.g., based on Monte Carlo type bounds of the corresponding classical walk. As a final result, we show how in certain cases we can avoid the use of phase estimation and quantum fast-forwarding, answering an open question of Ambainis et al.

Publication: Schloss Dagstuhl - Leibniz-Zentrum für Informatik No.: 187
ID: CaltechAUTHORS:20210517-104446034

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Abstract: Chaotic quantum many-body dynamics typically lead to relaxation of local observables. In this process, known as quantum thermalization, a subregion reaches a thermal state due to quantum correlations with the remainder of the system, which acts as an intrinsic bath. While the bath is generally assumed to be unobserved, modern quantum science experiments have the ability to track both subsystem and bath at a microscopic level. Here, by utilizing this ability, we discover that measurement results associated with small subsystems exhibit universal random statistics following chaotic quantum many-body dynamics, a phenomenon beyond the standard paradigm of quantum thermalization. We explain these observations with an ensemble of pure states, defined via correlations with the bath, that dynamically acquires a close to random distribution. Such random ensembles play an important role in quantum information science, associated with quantum supremacy tests and device verification, but typically require highly-engineered, time-dependent control for their preparation. In contrast, our approach uncovers random ensembles naturally emerging from evolution with a time-independent Hamiltonian. As an application of this emergent randomness, we develop a benchmarking protocol which estimates the many-body fidelity during generic chaotic evolution and demonstrate it using our Rydberg quantum simulator. Our work has wide ranging implications for the understanding of quantum many-body chaos and thermalization in terms of emergent randomness and at the same time paves the way for applications of this concept in a much wider context.

Publication: arXiv
ID: CaltechAUTHORS:20210512-104054951

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Abstract: Quantum chaos in many-body systems provides a bridge between statistical and quantum physics with strong predictive power. This framework is valuable for analyzing properties of complex quantum systems such as energy spectra and the dynamics of thermalization. While contemporary methods in quantum chaos often rely on random ensembles of quantum states and Hamiltonians, this is not reflective of most real-world systems. In this paper, we introduce a new perspective: across a wide range of examples, a single non-random quantum state is shown to encode universal and highly random quantum state ensembles. We characterize these ensembles using the notion of quantum state k-designs from quantum information theory and investigate their universality using a combination of analytic and numerical techniques. In particular, we establish that k-designs arise naturally from generic states as well as individual states associated with strongly interacting, time-independent Hamiltonian dynamics. Our results offer a new approach for studying quantum chaos and provide a practical method for sampling approximately uniformly random states; the latter has wide-ranging applications in quantum information science from tomography to benchmarking.

Publication: arXiv
ID: CaltechAUTHORS:20210512-104037565

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Abstract: Graphene has received much attention as a supercapacitor electrode material due to its chemical inertness in preventing reaction with electrolytes and the large surface area due to its two-dimensional nature. However, when graphene sheets are processed into electrodes, they tend to stack together and form a turbostratic graphite material with a much reduced surface area relative to the total surface area of individual graphene sheets. Separately, electrochemical exfoliation of graphite is one method of producing single-layer graphene, which is often used to produce graphene for supercapacitor electrodes, although such exfoliated graphene still leads to reduced surface areas due to stacking during electrode fabrication. To utilize the large surface area of graphene, graphene must be exfoliated in situ within a supercapacitor device after the device fabrication. However, graphitic electrodes are typically destroyed upon exfoliation, which is largely due to the loss of electrical connectivity among small exfoliated graphene flakes. Here, we report successful in situ exfoliation of graphene nanostripes, a type of quasi-one-dimensional graphene nanomaterial with large length-to-width aspect ratios, as the anode material in supercapacitors. We find that the in situ exfoliation leads to over 400% enhancement in capacitance as the result of retaining the electrical connectivity among exfoliated quasi-one-dimensional graphene nanostripes in addition to increasing the total surface area, paving ways to fully realizing the benefit of graphene electrodes in supercapacitor applications.

Publication: ACS Omega Vol.: 6 No.: 8 ISSN: 2470-1343

ID: CaltechAUTHORS:20210218-161816454

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Abstract: We argue that “stringy” effects in a putative gravity-dual picture for SYK-like models are related to the branching time, a kinetic coefficient defined in terms of the retarded kernel. A bound on the branching time is established assuming that the leading diagrams are ladders with thin rungs. Thus, such models are unlikely candidates for sub-AdS holography. In the weak coupling limit, we derive a relation between the branching time, the Lyapunov exponent, and the quasiparticle lifetime using two different approximations.

Publication: Journal of High Energy Physics Vol.: 2021 No.: 3 ISSN: 1029-8479

ID: CaltechAUTHORS:20210311-125528811

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Abstract: Bulk NiTe₂ is a type-II Dirac semimetal with non-trivial Berry phases associated with the Dirac fermions. Theory suggests that monolayer NiTe₂ is a two-gap superconductor, whereas experimental investigation of bulk NiTe_(1.98) for pressures (P) up to 71.2 GPa do not reveal any superconductivity. Here we report experimental evidences for pressure-induced two-phase superconductivity as well as mixed structures of NiTe₂ and NiTe in Te-deficient NiTe_(2-x) (x = 0.38 ± 0.09) single crystals. Hole-dominant multi-band superconductivity with the P3¯m1 hexagonal-symmetry structure of NiTe₂ appears at P ≥ 0.5 GPa, whereas electron-dominant single-band superconductivity with the P2/m monoclinic-symmetry structure of NiTe emerges at 14.5 GPa < P < 18.4 GPa. The coexistence of hexagonal and monoclinic structures and two-phase superconductivity is accompanied by a zero Hall coefficient up to ∼ 40 GPa, and the second superconducting phase prevails above 40 GPa, reaching a maximum T_c = 7.8 K and persisting up to 52.8 GPa. Our findings suggest the critical role of Te-vacancies in the occurrence of superconductivity and potentially nontrivial topological properties in NiTe_(2-x).

Publication: Materials Today Physics Vol.: 17ISSN: 2542-5293

ID: CaltechAUTHORS:20210119-143307326

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Abstract: This paper is an attempt to extend the recent understanding of the Page curve for evaporating black holes to more general systems coupled to a heat bath. Although calculating the von Neumann entropy by the replica trick is usually a challenge, we have identified two solvable cases. For the initial section of the Page curve, we sum up the perturbation series in the system-bath coupling κ; the most interesting contribution is of order 2s, where s is the number of replicas. For the saturated regime, we consider the effect of an external impulse on the entropy at a later time and relate it to OTOCs. A significant simplification occurs in the maximal chaos case such that the effect may be interpreted in terms of an intermediate object, analogous to the branching surface of a replica wormhole.

Publication: Journal of High Energy Physics Vol.: 2021 No.: 3 ISSN: 1029-8479

ID: CaltechAUTHORS:20210324-090318969

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Abstract: We review recent progress in the study of photogalvanic effects and optical second-harmonic generation in topological and noncentrosymmetric metals.

Publication: Annual Review of Condensed Matter Physics Vol.: 12ISSN: 1947-5454

ID: CaltechAUTHORS:20210506-140539872

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Abstract: We construct a series of one-dimensional non-unitary dynamics consisting of both unitary and imaginary evolutions based on the Sachdev-Ye-Kitaev model. Starting from a short-range entangled state, we analyze the entanglement dynamics using the path integral formalism in the large N limit. Among all the results that we obtain, two of them are particularly interesting: (1) By varying the strength of the imaginary evolution, the interacting model exhibits a first order phase transition from the highly entangled volume law phase to an area law phase; (2) The one-dimensional free fermion model displays an extensive critical regime with emergent two-dimensional conformal symmetry.

Publication: SciPost Physics Vol.: 10 No.: 2 ISSN: 2542-4653

ID: CaltechAUTHORS:20210528-101722127

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Abstract: One challenge of studying the many-body localization transition is defining the length scale that diverges upon the transition to the ergodic phase. In this manuscript we explore the localization properties of a ring with onsite disorder subject to an imaginary magnetic flux. We connect the imaginary flux which delocalizes single-particle orbitals of an Anderson-localized ring with the localization length of an open chain. We thus identify the delocalizing imaginary flux per site with an inverse localization length characterizing the transport properties of the open chain. We put this intuition to use by exploring the phase diagram of a disordered interacting chain, and we find that the inverse imaginary flux per bond provides an accessible description of the transition and its diverging localization length.

Publication: Physical Review B Vol.: 103 No.: 6 ISSN: 2469-9950

ID: CaltechAUTHORS:20200518-153736634

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Abstract: The existence of quantum error-correcting codes is one of the most counterintuitive and potentially technologically important discoveries of quantum-information theory. In this paper, we study a problem called “covariant quantum error correction”, in which the encoding is required to be group covariant. This problem is intimately tied to fault-tolerant quantum computation and the well-known Eastin-Knill theorem. We show that this problem is equivalent to the problem of encoding reference-frame information. In standard quantum error correction, one seeks to protect abstract quantum information, i.e., information that is independent of the physical incarnation of the systems used for storing the information. There are, however, other forms of information that are physical—one of the most ubiquitous being reference-frame information. The basic question we seek to answer is whether or not error correction of physical information is possible and, if so, what limitations govern the process. The main challenge is that the systems used for transmitting physical information, in addition to any actions applied to them, must necessarily obey these limitations. Encoding and decoding operations that obey a restrictive set of limitations need not exist a priori. Equivalently, there may not exist covariant quantum error-correcting codes. Indeed, we prove a no-go theorem showing that no finite-dimensional, group-covariant quantum codes exist for Lie groups with an infinitesimal generator [e.g., U(1), SU(2), and SO(3)]. We then explain how one can circumvent this no-go theorem using infinite-dimensional codes, and we give an explicit example of a covariant quantum error-correcting code using continuous variables for the group U(1). Finally, we demonstrate that all finite groups have finite-dimensional codes, giving both an explicit construction and a randomized approximate construction with exponentially better parameters. Our results imply that one can, in principle, circumvent the Eastin-Knill theorem.

Publication: PRX Quantum Vol.: 2 No.: 1 ISSN: 2691-3399

ID: CaltechAUTHORS:20210218-151442441

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Abstract: Simulating the dynamics of quantum systems is an important application of quantum computers and has seen a variety of implementations on current hardware. We show that by introducing quantum gates implementing unitary transformations generated by the symmetries of the system, one can induce destructive interference between the errors from different steps of the simulation, effectively giving faster quantum simulation by symmetry protection. We derive rigorous bounds on the error of a symmetry-protected simulation algorithm and identify conditions for optimal symmetry protection. In particular, when the symmetry transformations are chosen as powers of a unitary, the error of the algorithm is approximately projected to the so-called quantum Zeno subspaces. We prove a bound on this approximation error, exponentially improving a recent result of Burgarth, Facchi, Gramegna, and Pascazio. We apply the symmetry-protection technique to the simulations of the XXZ Heisenberg interactions with local disorder and the Schwinger model in quantum field theory. For both systems, the technique can reduce the simulation error by several orders of magnitude over the unprotected simulation. Finally, we provide numerical evidence suggesting that the technique can also protect simulation against other types of coherent, temporally correlated errors, such as the 1/f noise commonly found in solid-state experiments.

Publication: PRX Quantum Vol.: 2 No.: 1 ISSN: 2691-3399

ID: CaltechAUTHORS:20210212-131356210

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Abstract: The great promise of quantum computers comes with the dual challenges of building them and finding their useful applications. We argue that these two challenges should be considered together, by codesigning full-stack quantum computer systems along with their applications in order to hasten their development and potential for scientific discovery. In this context, we identify scientific and community needs, opportunities, a sampling of a few use case studies, and significant challenges for the development of quantum computers for science over the next 2–10 years. This document is written by a community of university, national laboratory, and industrial researchers in the field of Quantum Information Science and Technology, and is based on a summary from a U.S. National Science Foundation workshop on Quantum Computing held on October 21–22, 2019 in Alexandria, VA.

Publication: PRX Quantum Vol.: 2 No.: 1 ISSN: 2691-3399

ID: CaltechAUTHORS:20210514-140222766

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Abstract: The generation of certifiable randomness is the most fundamental information-theoretic task that meaningfully separates quantum devices from their classical counterparts. We propose a protocol for exponential certified randomness expansion using a single quantum device. The protocol calls for the device to implement a simple quantum circuit of constant depth on a 2D lattice of qubits. The output of the circuit can be verified classically in linear time, and is guaranteed to contain a polynomial number of certified random bits assuming that the device used to generate the output operated using a (classical or quantum) circuit of sub-logarithmic depth. This assumption contrasts with the locality assumption used for randomness certification based on Bell inequality violation and more recent proposals for randomness certification based on computational assumptions. Furthermore, to demonstrate randomness generation it is sufficient for a device to sample from the ideal output distribution within constant statistical distance. Our procedure is inspired by recent work of Bravyi et al. (Science 362(6412):308–311, 2018), who introduced a relational problem that can be solved by a constant-depth quantum circuit, but provably cannot be solved by any classical circuit of sub-logarithmic depth. We develop the discovery of Bravyi et al. into a framework for robust randomness expansion. Our results lead to a new proposal for a demonstrated quantum advantage that has some advantages compared to existing proposals. First, our proposal does not rest on any complexity-theoretic conjectures, but relies on the physical assumption that the adversarial device being tested implements a circuit of sub-logarithmic depth. Second, success on our task can be easily verified in classical linear time. Finally, our task is more noise-tolerant than most other existing proposals that can only tolerate multiplicative error, or require additional conjectures from complexity theory; in contrast, we are able to allow a small constant additive error in total variation distance between the sampled and ideal distributions.

Publication: Communications in Mathematical Physics Vol.: 382 No.: 1 ISSN: 0010-3616

ID: CaltechAUTHORS:20190320-100502117

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Abstract: Magic-angle twisted bilayer graphene (MATBG) exhibits a range of correlated phenomena that originate from strong electron–electron interactions. These interactions make the Fermi surface highly susceptible to reconstruction when ±1, ±2 and ±3 electrons occupy each moiré unit cell, and lead to the formation of various correlated phases. Although some phases have been shown to have a non-zero Chern number, the local microscopic properties and topological character of many other phases have not yet been determined. Here we introduce a set of techniques that use scanning tunnelling microscopy to map the topological phases that emerge in MATBG in a finite magnetic field. By following the evolution of the local density of states at the Fermi level with electrostatic doping and magnetic field, we create a local Landau fan diagram that enables us to assign Chern numbers directly to all observed phases. We uncover the existence of six topological phases that arise from integer fillings in finite fields and that originate from a cascade of symmetry-breaking transitions driven by correlations. These topological phases can form only for a small range of twist angles around the magic angle, which further differentiates them from the Landau levels observed near charge neutrality. Moreover, we observe that even the charge-neutrality Landau spectrum taken at low fields is considerably modified by interactions, exhibits prominent electron–hole asymmetry, and features an unexpectedly large splitting between zero Landau levels (about 3 to 5 millielectronvolts). Our results show how strong electronic interactions affect the MATBG band structure and lead to correlation-enabled topological phases.

Publication: Nature Vol.: 589 No.: 7843 ISSN: 0028-0836

ID: CaltechAUTHORS:20200922-103631989

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Abstract: We introduce the subsystem symmetry-preserving real-space entanglement renormalization group and apply it to study bifurcating flows generated by linear and fractal subsystem symmetry-protected topological phases in two spatial dimensions. We classify all bifurcating fixed points that are given by subsystem symmetric cluster states with two qubits per unit cell. In particular, we find that the square lattice cluster state is a quotient-bifurcating fixed point, while the cluster states derived from Yoshida's first-order fractal spin liquid models are self-bifurcating fixed points. We discuss the relevance of bifurcating subsystem symmetry-preserving renormalization group fixed points for the classification and equivalence of subsystem symmetry-protected topological phases.

Publication: Physical Review B Vol.: 103 No.: 3 ISSN: 2469-9950

ID: CaltechAUTHORS:20210129-110920638

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Abstract: While designing the energy-momentum relation of photons is key to many linear, nonlinear, and quantum optical phenomena, a new set of light-matter properties may be realized by employing the topology of the photonic bath itself. In this work we experimentally investigate the properties of superconducting qubits coupled to a metamaterial waveguide based on a photonic analog of the Su-Schrieffer-Heeger model. We explore topologically induced properties of qubits coupled to such a waveguide, ranging from the formation of directional qubit-photon bound states to topology-dependent cooperative radiation effects. Addition of qubits to this waveguide system also enables direct quantum control over topological edge states that form in finite waveguide systems, useful for instance in constructing a topologically protected quantum communication channel. More broadly, our work demonstrates the opportunity that topological waveguide-QED systems offer in the synthesis and study of many-body states with exotic long-range quantum correlations.

Publication: Physical Review X Vol.: 11 No.: 1 ISSN: 2160-3308

ID: CaltechAUTHORS:20201028-082500909

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Abstract: The quantum approximate optimization algorithm (QAOA) employs variational states generated by a parameterized quantum circuit to maximize the expected value of a Hamiltonian encoding a classical cost function. Whether or not the QAOA can outperform classical algorithms in some tasks is an actively debated question. Our work exposes fundamental limitations of the QAOA resulting from the symmetry and the locality of variational states. A surprising consequence of our results is that the classical Goemans-Williamson algorithm outperforms the QAOA for certain instances of MaxCut, at any constant level. To overcome these limitations, we propose a nonlocal version of the QAOA and give numerical evidence that it significantly outperforms the standard QAOA for frustrated Ising models.

Publication: Physical Review Letters Vol.: 125 No.: 26 ISSN: 0031-9007

ID: CaltechAUTHORS:20201224-134252357

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Abstract: In the presence of electron-phonon coupling, an excitonic insulator harbors two degenerate ground states described by an Ising-type order parameter. Starting from a microscopic Hamiltonian, we derive the equations of motion for the Ising order parameter in the phonon coupled excitonic insulator Ta₂NiSe₅ and show that it can be controllably reversed on ultrashort timescales using appropriate laser pulse sequences. Using a combination of theory and time-resolved optical reflectivity measurements, we report evidence of such order parameter reversal in Ta₂NiSe₅ based on the anomalous behavior of its coherently excited order-parameter-coupled phonons. Our Letter expands the field of ultrafast order parameter control beyond spin and charge ordered materials.

Publication: Physical Review Letters Vol.: 125 No.: 26 ISSN: 0031-9007

ID: CaltechAUTHORS:20201224-090002408

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Abstract: Conversion of electrical and optical signals lies at the foundation of the global internet. Such converters are used to extend the reach of long-haul fibre-optic communication systems and within data centres for high-speed optical networking of computers. Likewise, coherent microwave-to-optical conversion of single photons would enable the exchange of quantum states between remotely connected superconducting quantum processors1. Despite the prospects of quantum networking, maintaining the fragile quantum state in such a conversion process with superconducting qubits has not yet been achieved. Here we demonstrate the conversion of a microwave-frequency excitation of a transmon—a type of superconducting qubit—into an optical photon. We achieve this by using an intermediary nanomechanical resonator that converts the electrical excitation of the qubit into a single phonon by means of a piezoelectric interaction and subsequently converts the phonon to an optical photon by means of radiation pressure. We demonstrate optical photon generation from the qubit by recording quantum Rabi oscillations of the qubit through single-photon detection of the emitted light over an optical fibre. With proposed improvements in the device and external measurement set-up, such quantum transducers might be used to realize new hybrid quantum networks and, ultimately, distributed quantum computers.

Publication: Nature Vol.: 588 No.: 7839 ISSN: 0028-0836

ID: CaltechAUTHORS:20200416-091933770

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Abstract: We consider simulating quantum systems on digital quantum computers. We show that the performance of quantum simulation can be improved by simultaneously exploiting the commutativity of Hamiltonian, the sparsity of interactions, and the prior knowledge of initial state. We achieve this using Trotterization for a class of interacting electrons that encompasses various physical systems, including the plane-wave-basis electronic structure and the Fermi-Hubbard model. We estimate the simulation error by taking the transition amplitude of nested commutators of Hamiltonian terms within the η-electron manifold. We develop multiple techniques for bounding the transition amplitude and expectation of general fermionic operators, which may be of independent interest. We show that it suffices to use O(n^(5/3)/η^(2/3)+n^(4/3)η^(2/3)) gates to simulate electronic structure in the plane-wave basis with n spin orbitals and η electrons up to a negligible factor, improving the best previous result in second quantization while outperforming the first-quantized simulation when n=O(η²). We also obtain an improvement for simulating the Fermi-Hubbard model. We construct concrete examples for which our bounds are almost saturated, giving a nearly tight Trotterization of interacting electrons.

Publication: arXiv
ID: CaltechAUTHORS:20210408-131650720

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Abstract: Despite the fundamental importance of quantum entanglement in many-body systems, our understanding is mostly limited to bipartite situations. Indeed, even defining appropriate notions of multipartite entanglement is a significant challenge for general quantum systems. In this work, we initiate the study of multipartite entanglement in a rich, yet tractable class of quantum states called stabilizer tensor networks. We demonstrate that, for generic stabilizer tensor networks, the geometry of the tensor network informs the multipartite entanglement structure of the state. In particular, we show that the average number of Greenberger-Horne-Zeilinger (GHZ) triples that can be extracted from a stabilizer tensor network is small, implying that tripartite entanglement is scarce. This, in turn, restricts the higher-partite entanglement structure of the states. Recent research in quantum gravity found that stabilizer tensor networks reproduce important structural features of the AdS / CFT correspondence, including the Ryu-Takayanagi formula for the entanglement entropy and certain quantum error correction properties. Our results imply a new operational interpretation of the monogamy of the Ryu-Takayanagi mutual information and an entropic diagnostic for higher-partite entanglement. Our technical contributions include a spin model for evaluating the average GHZ content of stabilizer tensor networks, as well as a novel formula for the third moment of random stabilizer states, which we expect to find further applications in quantum information.

Publication: Physical Review Letters Vol.: 125 No.: 24 ISSN: 0031-9007

ID: CaltechAUTHORS:20201215-141036428

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Abstract: Symmetry-breaking transitions are a well-understood phenomenon of closed quantum systems in quantum optics, condensed matter, and high energy physics. However, symmetry breaking in open systems is less thoroughly understood, in part due to the richer steady-state and symmetry structure that such systems possess. For the prototypical open system—a Lindbladian—a unitary symmetry can be imposed in a “weak” or a “strong” way. We characterize the possible Z_n symmetry-breaking transitions for both cases. In the case of Z₂, a weak-symmetry-broken phase guarantees at most a classical bit steady-state structure, while a strong-symmetry-broken phase admits a partially protected steady-state qubit. Viewing photonic cat qubits through the lens of strong-symmetry breaking, we show how to dynamically recover the logical information after any gap-preserving strong-symmetric error; such recovery becomes perfect exponentially quickly in the number of photons. Our study forges a connection between driven-dissipative phase transitions and error correction.

Publication: Physical Review Letters Vol.: 125 No.: 24 ISSN: 0031-9007

ID: CaltechAUTHORS:20201215-085507736

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Abstract: Recently, Singh and Chandrasekharan [Phys. Rev. D 100, 054505 (2019)] showed that fixed points of the nonlinear O(3) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. In a paper by the NuQS Collaboration [Phys. Rev. Lett. 123, 090501 (2019)], the proposal is made to simulate such field theories on a quantum computer using the universal properties of a similar model. In this paper, following that direction, we demonstrate how to prepare the ground state of the model from Singh and Chandrasekharan and measure a dynamical quantity of interest, the O(3) Noether charge, on a quantum computer. In particular, we apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes and use shadow tomography to measure the dynamics of local observables. We then present and analyze a quantum algorithm based on nonunitary randomized simulation methods that may yield an approach suitable for intermediate-term noisy quantum devices.

Publication: Physical Review D Vol.: 102 No.: 11 ISSN: 2470-0010

ID: CaltechAUTHORS:20201221-120012194

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Abstract: The Maldacena-Qi model describes two copies of the Sachdev-Ye-Kitaev model coupled with an additional coupling and is dual to the Jackiw-Teitelboim gravity, which exhibits an eternal traversable wormhole in the low-temperature limit. In this work, we study an experimental consequence of the existence of the traversable wormhole by considering the tunneling spectroscopy for the Maldacena-Qi model. Making comparisons to the high-temperature black-hole phase where the bulk geometry is disconnected, we find that both the tunneling probability and the differential conductance in the low-temperature wormhole phase show nontrivial oscillation, which directly provides an unambiguous signature of the underlying SL(2) symmetry of the bulk geometry. We also perform bulk calculations in both high- and low-temperature phases, which match the results from the boundary quantum theory.

Publication: Physical Review B Vol.: 102 No.: 22 ISSN: 2469-9950

ID: CaltechAUTHORS:20201217-133745326

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Abstract: Using the tensor Radon transform and related numerical methods, we study how bulk geometries can be explicitly reconstructed from boundary entanglement entropies in the specific case of AdS₃/CFT₂. We find that, given the boundary entanglement entropies of a 2d CFT, this framework provides a quantitative measure that detects whether the bulk dual is geometric in the perturbative (near AdS) limit. In the case where a well-defined bulk geometry exists, we explicitly reconstruct the unique bulk metric tensor once a gauge choice is made. We then examine the emergent bulk geometries for static and dynamical scenarios in holography and in many-body systems. Apart from the physics results, our work demonstrates that numerical methods are feasible and effective in the study of bulk reconstruction in AdS/CFT.

Publication: Journal of High Energy Physics Vol.: 2020 No.: 12 ISSN: 1126-6708

ID: CaltechAUTHORS:20201216-103316521

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Abstract: For systems with spatial and nonspatial symmetries, the topological classification depends not only on these symmetries but also on the commutation/anticommutation relations between spatial and nonspatial symmetries. The coexistence of spatial and nonspatial symmetries together with appropriate commutation/anticommutation relations between them can give rise to crystalline and higher-order topological phases, which host gapless boundary modes. Alternatively, space-time symmetries in a Floquet system can take the role of spatial symmetries in deciding the topological classification. Promoting a spatial symmetry to a space-time symmetry can alter the commutation relations, which in turn can modify the topological properties of the system. We show how a coherently excited phonon mode can be used to promote a spatial symmetry with which the static system is always trivial to a space-time symmetry which supports a nontrivial Floquet topological phase. We demonstrate this effect by considering two systems: The first is a second-order topological superconductor, and the second is a first-order crystalline topological insulator. In both these cases, a coherently excited phonon mode is responsible for promoting the reflection symmetry to a time-glide symmetry. This newly introduced symmetry allows the previously trivial system to host gapless modes. In the first case, these are protected corner modes, while in the second case, these are gapless edge modes.

Publication: Physical Review Research Vol.: 2 No.: 4 ISSN: 2643-1564

ID: CaltechAUTHORS:20191217-115034328

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Abstract: We study a periodically driven qubit coupled to a quantized cavity mode. Despite its apparent simplicity, this system supports a rich variety of exotic phenomena, such as topological frequency conversion as recently discovered in Martin et al. [Phys. Rev. X 7, 041008 (2017)]. Here we report on a qualitatively different phenomenon that occurs in this platform, where the cavity mode's oscillations lock their frequency to a rational fraction r/q of the driving frequency Ω. This phenomenon, which we term quantum frequency locking, is characterized by the emergence of q-tuplets of stationary (Floquet) states whose quasienergies are separated by Ω/q, up to exponentially small corrections. The Wigner functions of these states are nearly identical, and exhibit highly regular and symmetric structure in phase space. Similarly to Floquet time crystals, these states underlie discrete time-translation symmetry breaking in the model. We develop a semiclassical approach for analyzing and predicting quantum frequency locking in the model, and use it to identify the conditions under which it occurs.

Publication: Physical Review Research Vol.: 2 No.: 4 ISSN: 2643-1564

ID: CaltechAUTHORS:20200519-080742316

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Abstract: Conformal truncation is a powerful numerical method for solving generic strongly-coupled quantum field theories based on purely field-theoretic technics without introducing lattice regularization. We discuss possible speedups for performing those computations using quantum devices, with the help of near-term and future quantum algorithms. We show that this construction is very similar to quantum simulation problems appearing in quantum chemistry (which are widely investigated in quantum information science), and the renormalization group theory provides a field theory interpretation of conformal truncation simulation. Taking two-dimensional Quantum Chromodynamics (QCD) as an example, we give various explicit calculations of variational and digital quantum simulations in the level of theories, classical trials, or quantum simulators from IBM, including adiabatic state preparation, variational quantum eigensolver, imaginary time evolution, and quantum Lanczos algorithm. Our work shows that quantum computation could not only help us understand fundamental physics in the lattice approximation, but also simulate quantum field theory methods directly, which are widely used in particle and nuclear physics, sharpening the statement of the quantum Church-Turing Thesis.

Publication: Journal of High Energy Physics Vol.: 2020 No.: 12 ISSN: 1029-8479

ID: CaltechAUTHORS:20201214-134008056

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Abstract: We study the quantum dynamics of Bose-Einstein condensates when the scattering length is modulated periodically or quasi-periodically in time within the Bogoliubov framework. For the periodically driven case, we consider two protocols where the modulation is a square-wave or a sine-wave. In both protocols for each fixed momentum, there are heating and non-heating phases, and a phase boundary between them. The two phases are distinguished by whether the number of excited particles grows exponentially or not. For the quasi-periodically driven case, we again consider two protocols: the square-wave quasi-periodicity, where the excitations are generated for almost all parameters as an analog of the Fibonacci-type quasi-crystal; and the sine-wave quasi-periodicity, where there is a finite measure parameter regime for the non-heating phase. We also plot the analogs of the Hofstadter butterfly for both protocols.

Publication: SciPost Physics Vol.: 9ISSN: 2542-4653

ID: CaltechAUTHORS:20200824-085218526

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Abstract: An anomalous optical second-harmonic generation (SHG) signal was previously reported in Sr₂IrO₄ and attributed to a hidden odd-parity bulk magnetic state. Here we investigate the origin of this SHG signal using a combination of bulk magnetic susceptibility, magnetic-field-dependent SHG rotational anisotropy, and overlapping wide-field SHG imaging and atomic force microscopy measurements. We find that the anomalous SHG signal exhibits a twofold rotational symmetry as a function of in-plane magnetic field orientation that is associated with a crystallographic distortion. We also show a change in SHG signal across step edges that tracks the bulk antiferromagnetic stacking pattern. While we do not rule out the existence of hidden order in Sr₂IrO₄, our results altogether show that the anomalous SHG signal in parent Sr₂IrO₄ originates instead from a surface-magnetization-induced electric-dipole process that is enhanced by strong spin-orbit coupling.

Publication: Physical Review B Vol.: 102 No.: 20 ISSN: 2469-9950

ID: CaltechAUTHORS:20201113-100152383

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Abstract: We propose a method for detecting bipartite entanglement in a many-body mixed state based on estimating moments of the partially transposed density matrix. The estimates are obtained by performing local random measurements on the state, followed by postprocessing using the classical shadows framework. Our method can be applied to any quantum system with single-qubit control. We provide a detailed analysis of the required number of experimental runs, and demonstrate the protocol using existing experimental data [Brydges et al., Science 364, 260 (2019)].

Publication: Physical Review Letters Vol.: 125 No.: 20 ISSN: 0031-9007

ID: CaltechAUTHORS:20201111-102025217

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Abstract: The energy damping time in a mechanical resonator is critical to many precision metrology applications, such as timekeeping and force measurements. We present measurements of the phonon lifetime of a microwave-frequency, nanoscale silicon acoustic cavity incorporating a phononic bandgap acoustic shield. Using pulsed laser light to excite a colocalized optical mode of the cavity, we measured the internal acoustic modes with single-phonon sensitivity down to millikelvin temperatures, yielding a phonon lifetime of up to τ_(ph,0) ≈ 1.5 seconds (quality factor Q = 5 × 10¹⁰) and a coherence time of τ_(coh,0) ≈ 130 microseconds for bandgap-shielded cavities. These acoustically engineered nanoscale structures provide a window into the material origins of quantum noise and have potential applications ranging from tests of various collapse models of quantum mechanics to miniature quantum memory elements in hybrid superconducting quantum circuits.

Publication: Science Vol.: 370 No.: 6518 ISSN: 0036-8075

ID: CaltechAUTHORS:20190115-155728077

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Abstract: We study the Sachdev-Ye-Kitaev (SYK₄) model with a weak SYK₂ term of magnitude Γ beyond the simplest perturbative limit considered previously. For intermediate values of the perturbation strength, J/N ≪ Γ ≪ J/√N, fluctuations of the Schwarzian mode are suppressed, and the SYK₄ mean-field solution remains valid beyond the timescale t₀ ∼ N/J up to t∗∼J/Γ². The out-of-time-order correlation function displays at short time intervals exponential growth with maximal Lyapunov exponent 2πT, but its prefactor scales as T at low temperatures T ≤ Γ.

Publication: Physical Review Letters Vol.: 125 No.: 19 ISSN: 0031-9007

ID: CaltechAUTHORS:20201104-130324443

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Abstract: We theoretically predict and experimentally demonstrate a nonthermal pathway to optically enhance superexchange interaction energies in a material based on exciting ligand-to-metal charge-transfer transitions, which introduces lower-order virtual hopping contributions that are absent in the ground state. We demonstrate this effect in the layered ferromagnetic insulator CrSiTe₃ by exciting Te-to-Cr charge-transfer transitions using ultrashort laser pulses and detecting coherent phonon oscillations that are impulsively generated by superexchange enhancement via magneto-elastic coupling. This mechanism kicks in below the temperature scale where short-range in-plane spin correlations begin to develop and disappears when the excitation energy is tuned away from the charge-transfer resonance, consistent with our predictions.

Publication: Physical Review Letters Vol.: 125 No.: 19 ISSN: 0031-9007

ID: CaltechAUTHORS:20191217-085020547

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Abstract: Aaronson and Ambainis (2009) and Chailloux (2018) showed that fully symmetric (partial) functions do not admit exponential quantum query speedups. This raises a natural question: how symmetric must a function be before it cannot exhibit a large quantum speedup? In this work, we prove that hypergraph symmetries in the adjacency matrix model allow at most a polynomial separation between randomized and quantum query complexities. We also show that, remarkably, permutation groups constructed out of these symmetries are essentially the only permutation groups that prevent super-polynomial quantum speedups. We prove this by fully characterizing the primitive permutation groups that allow super-polynomial quantum speedups. In contrast, in the adjacency list model for bounded-degree graphs-where graph symmetry is manifested differently-we exhibit a property testing problem that shows an exponential quantum speedup. These results resolve open questions posed by Ambainis, Childs, and Liu (2010) and Montanaro and de Wolf (2013).

ID: CaltechAUTHORS:20210630-171353593

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Abstract: We report a high-yield single-step method for synthesizing nitrogen-doped graphene nanostripes (N-GNSPs) with an unprecedentedly high percentage of pyridinic-type doping (>86% of the nitrogen sites), and investigate the performance of the resulting N-GNSPs as a lithium-ion battery (LIB) anode material. The as-grown N-GNSPs are compared with undoped GNSPs using scanning electron microscopy (SEM), Raman spectroscopy, X-ray photoelectron spectroscopy (XPS), helium ion-beam microscopy (HIM), and electrochemical methods. As an anode material we find that pyridinic-type N-GNSPs perform similarly to undoped GNSPs, suggesting that pyridinic sites alone are not responsible for the enhanced performance of nitrogen-doped graphene observed in previous studies, which contradicts common conjectures. In addition, post-mortem XPS measurements of nitrogen-doped graphene cycled as a lithium-ion battery anode are conducted for the first time, which reveal direct evidence for irreversible chemical changes at the nitrogen sites during cycling. These findings therefore provide new insights into the mechanistic models of doped graphene as LIB anodes, which are important in improving the anode designs for better LIB performance.

Publication: RSC Advances Vol.: 10 No.: 65 ISSN: 2046-2069

ID: CaltechAUTHORS:20201030-102416804

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Abstract: We study whether one can write a Matrix Product Density Operator (MPDO) as the Gibbs state of a quasi-local parent Hamiltonian. We conjecture this is the case for generic MPDO and give supporting evidences. To investigate the locality of the parent Hamiltonian, we take the approach of checking whether the quantum conditional mutual information decays exponentially. The MPDO we consider are constructed from a chain of 1-input/2-output (`Y-shaped') completely-positive maps, i.e. the MPDO have a local purification. We derive an upper bound on the conditional mutual information for bistochastic channels and strictly positive channels, and show that it decays exponentially if the correctable algebra of the channel is trivial. We also introduce a conjecture on a quantum data processing inequality that implies the exponential decay of the conditional mutual information for every Y-shaped channel with trivial correctable algebra. We additionally investigate a close but nonequivalent cousin: MPDO measured in a local basis. We provide sufficient conditions for the exponential decay of the conditional mutual information of the measured states, and numerically confirmed they are generically true for certain random MPDO.

Publication: arXiv
ID: CaltechAUTHORS:20210511-131755023

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Abstract: Fault-tolerant quantum computing promises significant computational speedup over classical computing for a variety of important problems. One of the biggest challenges for realizing fault-tolerant quantum computing is preparing magic states with sufficiently low error rates. Magic state distillation is one of the most efficient schemes for preparing high-quality magic states. However, since magic state distillation circuits are not fault-tolerant, all the operations in the distillation circuits must be encoded in a large distance error-correcting code, resulting in a significant resource overhead. Here, we propose a fault-tolerant scheme for directly preparing high-quality magic states, which makes magic state distillation unnecessary. In particular, we introduce a concept that we call redundant ancilla encoding. The latter combined with flag qubits allows for circuits to both measure stabilizer generators of some code, while also being able to measure global operators to fault-tolerantly prepare magic states, all using nearest neighbor interactions. We apply such schemes to a planar architecture of the triangular color code family and demonstrate that our scheme requires at least an order of magnitude fewer qubits and space–time overhead compared to the most competitive magic state distillation schemes. Since our scheme requires only nearest-neighbor interactions in a planar architecture, it is suitable for various quantum computing platforms currently under development.

Publication: npj Quantum Information Vol.: 6ISSN: 2056-6387

ID: CaltechAUTHORS:20201130-140223226

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Abstract: We introduce a three-player nonlocal game, with a finite number of classical questions and answers, such that the optimal success probability of 1 in the game can only be achieved in the limit of strategies using arbitrarily high-dimensional entangled states. Precisely, there exists a constant 0 < c ≤ 1 such that to succeed with probability 1 − ε in the game it is necessary to use an entangled state of at leastΩ(ε^(−c)) qubits, and it is sufficient to use a state of at most O(ε⁻¹) qubits. The game is based on the coherent state exchange game of Leung et al. (CJTCS 2013). In our game, the task of the quantum verifier is delegated to a third player by a classical referee. Our results complement those of Slofstra (arXiv:1703.08618) and Dykema et al. (arXiv:1709.05032), who obtained two-player games with similar (though quantitatively weaker) properties based on the representation theory of finitely presented groups and C∗-algebras respectively.

Publication: Quantum Vol.: 4ISSN: 2521-327X

ID: CaltechAUTHORS:20190204-154622144

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Abstract: Twisted bilayer graphene at the magic twist angle features flat energy bands, which lead to superconductivity and strong correlation physics. These unique properties are typically limited to a narrow range of twist angles around the magic angle with a small allowed tolerance. Here, we report on a mechanism that enables flattening of the band structure using coherent optical illumination, leading to emergence of flat isolated Floquet-Bloch bands. We show that the effect can be realized with relatively weak optical beams at the visible-infrared range (below the material bandwidth) and persist for a wide range of small twist angles, increasing the allowed twist tolerance by an order of magnitude. We discuss the conditions under which these bands exhibit a nonzero Chern number. These optically induced flat bands could potentially host strongly correlated nonequilibrium electronic states of matter.

Publication: Physical Review B Vol.: 102 No.: 15 ISSN: 2469-9950

ID: CaltechAUTHORS:20201016-153328923

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Abstract: Breakthroughs in two-dimensional van der Waals heterostructures have revealed that twisting creates a moiré pattern that quenches the kinetic energy of electrons, allowing for exotic many-body states. We show that cold atomic, trapped ion, and metamaterial systems can emulate the effects of a twist in many models from one to three dimensions. Further, we demonstrate at larger angles (and argue at smaller angles) that by considering incommensurate effects, the magic-angle effect becomes a single-particle quantum phase transition (including in a model for twisted bilayer graphene in the chiral limit). We call these models “magic-angle semimetals”. Each contains nodes in the band structure and an incommensurate modulation. At magic-angle criticality, we report a nonanalytic density of states, flat bands, multifractal wave functions that Anderson delocalize in momentum space, and an essentially divergent effective interaction scale. As a particular example, we discuss how to observe this effect in an ultracold Fermi gas.

Publication: npj Quantum Materials Vol.: 5ISSN: 2397-4648

ID: CaltechAUTHORS:20201022-112713785

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Abstract: Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here, we study the compatibility of these two important principles. If a logical quantum system is encoded into n physical subsystems, we say that the code is covariant with respect to a symmetry group G if a G transformation on the logical system can be realized by performing transformations on the individual subsystems. For a G-covariant code with G a continuous group, we derive a lower bound on the error-correction infidelity following erasure of a subsystem. This bound approaches zero when the number of subsystems n or the dimension d of each subsystem is large. We exhibit codes achieving approximately the same scaling of infidelity with n or d as the lower bound. Leveraging tools from representation theory, we prove an approximate version of the Eastin-Knill theorem for quantum computation: If a code admits a universal set of transversal gates and corrects erasure with fixed accuracy, then, for each logical qubit, we need a number of physical qubits per subsystem that is inversely proportional to the error parameter. We construct codes covariant with respect to the full logical unitary group, achieving good accuracy for large d (using random codes) or n (using codes based on W states). We systematically construct codes covariant with respect to general groups, obtaining natural generalizations of qubit codes to, for instance, oscillators and rotors. In the context of the AdS/CFT correspondence, our approach provides insight into how time evolution in the bulk corresponds to time evolution on the boundary without violating the Eastin-Knill theorem, and our five-rotor code can be stacked to form a covariant holographic code.

Publication: Physical Review X Vol.: 10 No.: 4 ISSN: 2160-3308

ID: CaltechAUTHORS:20201027-095348367

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Abstract: Predicting the properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a ‘classical shadow’, can be used to predict many different properties; order log(M) measurements suffice to accurately predict M different functions of the state with high success probability. The number of measurements is independent of the system size and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods.

Publication: Nature Physics Vol.: 16 No.: 10 ISSN: 1745-2473

ID: CaltechAUTHORS:20200427-084340790

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Abstract: Hayden and Preskill proposed a thought experiment in which Bob can recover the information Alice throws into a black hole if he has a quantum computer entangled with the black hole, and for which Yoshida and Kitaev recently proposed a concrete decoding scheme. In the context of quantum many-body physics, the parallel question is that after a small system is thermalized with a large system, how can one decode the initial state information with the help of two entangled many-body systems? Here, we propose to realize this decoding protocol in a physical system of two Dicke models, with two cavity fields prepared in a thermofield double state. We show that the Yoshida-Kitaev protocol allows us to read out the initial spin information after it is scrambled into the cavity. We show that the readout efficiency reaches a maximum when the model parameters are tuned to the regime where the system is the most chaotic, characterized by the shortest scrambling time in the out-of-time-ordered correlation function. Our proposal opens up the possibility of discussing this profound thought experiment in a realistic setting.

Publication: Physical Review Research Vol.: 2 No.: 4 ISSN: 2643-1564

ID: CaltechAUTHORS:20201006-131507338

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Abstract: Some deep conjectures about quantum gravity are closely related to the role of symmetries in the gravitational background, especially for quantum black holes. In this paper, we systematically study the theory of quantum information for a charged, chaotic system. We show how the quantum information in the whole system has been represented by its charge sectors, using the theory of quantum chaos and quantum error correction, with concrete examples in the context of the complex Sachdev-Ye-Kitaev model. We discuss possible implications for black-hole thought experiments and conjectures about quantum gravity in the dynamical setup. We believe this work will have potential applications from theories of quantum gravity to quantum simulation in quantum devices.

Publication: Physical Review Research Vol.: 2 No.: 4 ISSN: 2643-1564

ID: CaltechAUTHORS:20201102-104838060

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Abstract: In this work, we study the universal relations for one-dimensional spin-orbital-coupled fermions near both s- and p-wave resonances using effective field theory. Since the spin-orbital coupling mixes different partial waves, a contact matrix is introduced to capture the nontrivial correlation between dimers. We find the signature of the spin-orbital coupling appears at the leading order for the off-diagonal components of the momentum distribution matrix, which is proportional to 1/q³ (q is the relative momentum). We further derive the large frequency behavior of the Raman spectroscopy, which serves as an independent measurable quantity for contacts. Finally, we give an explicit example of contacts by considering a two-body problem.

Publication: Physical Review A Vol.: 102 No.: 4 ISSN: 2469-9926

ID: CaltechAUTHORS:20201020-123849274

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Abstract: Quantum state tomography is a powerful, but resource-intensive, general solution for numerous quantum information processing tasks. This motivates the design of robust tomography procedures that use relevant resources as sparingly as possible. Important cost factors include the number of state copies and measurement settings, as well as classical postprocessing time and memory. In this work, we present and analyze an online tomography algorithm designed to optimize all the aforementioned resources at the cost of a worse dependence on accuracy. The protocol is the first to give provably optimal performance in terms of rank and dimension for state copies, measurement settings and memory. Classical runtime is also reduced substantially and numerical experiments demonstrate a favorable comparison with other state-of-the-art techniques. Further improvements are possible by executing the algorithm on a quantum computer, giving a quantum speedup for quantum state tomography.

Publication: arXiv
ID: CaltechAUTHORS:20210511-142009646

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Abstract: In the study of three-dimensional gapped models, two-dimensional gapped states should be considered as a free resource. This is the basic idea underlying the notion of “foliated fracton order” proposed in Shirley et al. [Phys. Rev. X 8, 031051 (2018)]. We have found that many of the known type-I fracton models, although they appear very different, have the same foliated fracton order, known as “X-cube” order. In this paper, we identify three-dimensional fracton models with different kinds of foliated fracton order. Whereas the X-cube order corresponds to the gauge theory of a simple paramagnet with subsystem planar symmetry, the different orders correspond to twisted versions of the gauge theory for which the system prior to gauging has nontrivial order protected by the planar subsystem symmetry. We present constructions of the twisted models and demonstrate that they possess nontrivial order by studying their fractional excitation contents.

Publication: Physical Review B Vol.: 102 No.: 11 ISSN: 2469-9950

ID: CaltechAUTHORS:20190807-104405031

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Abstract: A periodic drive could alter the effective exchange interactions in magnetic materials. Here, we explore how exchange pathways affect the effective interactions of periodically driven magnetic materials. Aiming to apply Floquet engineering methods to two-dimensional magnetic materials, we consider realistic models and discuss the effect of a periodic drive on ligand-mediated exchange interactions. We show that depending on bond angles and the number of ligand ions involved in the exchange process, drive-induced changes can be very different from those calculated from direct-hopping models considered earlier. We study these effects and find that the presence of ligand ions must be taken into account, especially for TMTCs where ligand ion mediated next-neighbor interactions play a crucial role in determining the magnetic ground state of the system.

Publication: arXiv
ID: CaltechAUTHORS:20200928-150652942

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Abstract: A recent experiment [C. Schweizer, F. Grusdt, M. Berngruber, L. Barbiero, E. Demler, N. Goldman, I. Bloch, and M. Aidelsburger, Nat. Phys. 15, 1168 (2019)] has realized a dynamical gauge system with a ℤ₂ gauge symmetry in a double-well potential. In this work we propose a method to generalize this model from a single double well to a one-dimensional chain. We show that although there are no disordered potentials in the original model, the phenomenon of many-body localization can occur. The key ingredient is that different symmetry sectors with different local gauge charges play the role of different disorder configurations, which becomes clear after exactly mapping our model to a transverse Ising model in a random longitudinal field. We show that both the ergodic regime and the many-body localized regime exist in this model from four different metrics, which include level statistics, volume law versus area law of entanglement entropy of eigenstates, quench dynamics of entanglement entropy, and physical observables.

Publication: Physical Review B Vol.: 102 No.: 10 ISSN: 2469-9950

ID: CaltechAUTHORS:20200924-144351451

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Abstract: We study the spectrum and OPE coefficients of the three-dimensional critical O(2) model, using four-point functions of the leading scalars with charges 0, 1, and 2 (s, ϕ, and t). We obtain numerical predictions for low-twist OPE data in several charge sectors using the extremal functional method. We compare the results to analytical estimates using the Lorentzian inversion formula and a small amount of numerical input. We find agreement between the analytic and numerical predictions. We also give evidence that certain scalar operators lie on double-twist Regge trajectories and obtain estimates for the leading Regge intercepts of the O(2) model.

Publication: Journal of High Energy Physics Vol.: 2020 No.: 9 ISSN: 1029-8479

ID: CaltechAUTHORS:20200924-144352084

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Abstract: The speed of information propagation is finite in quantum systems with local interactions. In many such systems, local operators spread ballistically in time and can be characterized by a butterfly velocity", which can be measured via out-of-time-ordered correlation functions. In general, the butterfly velocity can depend asymmetrically on the direction of information propagation. In this work, we construct a family of simple 2-local Hamiltonians for understanding the asymmetric hydrodynamics of operator spreading. Our models live on a one dimensional lattice and exhibit asymmetric butterfly velocities between the left and right spatial directions. This asymmetry is transparently understood in a free (non-interacting) limit of our model Hamiltonians, where the butterfly speed can be understood in terms of quasiparticle velocities.

Publication: SciPost Physics Vol.: 9ISSN: 2542-4653

ID: CaltechAUTHORS:20191111-085640192

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Abstract: Deposition of layers of graphene on silicon has the potential for a wide range of optoelectronic and mechanical applications. However, direct growth of graphene on silicon has been difficult due to the inert, oxidized silicon surfaces. Transferring graphene from metallic growth substrates to silicon is not a good solution either, because most transfer methods involve multiple steps that often lead to polymer residues or degradation of sample quality. Here we report a single-step method for large-area direct growth of continuous horizontal graphene sheets and vertical graphene nano-walls on silicon substrates by plasma-enhanced chemical vapor deposition (PECVD) without active heating. Comprehensive studies utilizing Raman spectroscopy, x-ray/ultraviolet photoelectron spectroscopy (XPS/UPS), atomic force microscopy (AFM), scanning electron microscopy (SEM) and optical transmission are carried out to characterize the quality and properties of these samples. Data gathered by the residual gas analyzer (RGA) during the growth process further provide information about the synthesis mechanism. Additionally, ultra-low friction (with a frictional coefficient ~0.015) on multilayer graphene-covered silicon surface is achieved, which is approaching the superlubricity limit (for frictional coefficients <0.01). Our growth method therefore opens up a new pathway towards scalable and direct integration of graphene into silicon technology for potential applications ranging from structural superlubricity to nanoelectronics, optoelectronics, and even the next-generation lithium-ion batteries.

Publication: Nanotechnology Vol.: 31 No.: 33 ISSN: 0957-4484

ID: CaltechAUTHORS:20200506-092128313

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Abstract: We propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair correlations between these operators can be organized into a matrix with a random-matrix-like spectrum. This approach is particularly useful for locally interacting systems, which do not generically show exponential Lyapunov growth of out-of-time-ordered correlators. We demonstrate the validity of this characterization by numerically studying the Sachdev-Ye-Kitaev model and a one-dimensional spin chain with random magnetic field (XXZ model).

Publication: Physical Review E Vol.: 102 No.: 2 ISSN: 2470-0045

ID: CaltechAUTHORS:20200825-130210033

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Abstract: Trapped neutral atoms have become a prominent platform for quantum science, where entanglement fidelity records have been set using highly excited Rydberg states. However, controlled two-qubit entanglement generation has so far been limited to alkali species, leaving the exploitation of more complex electronic structures as an open frontier that could lead to improved fidelities and fundamentally different applications such as quantum-enhanced optical clocks. Here, we demonstrate a novel approach utilizing the two-valence electron structure of individual alkaline-earth Rydberg atoms. We find fidelities for Rydberg state detection, single-atom Rabi operations and two-atom entanglement that surpass previously published values. Our results pave the way for novel applications, including programmable quantum metrology and hybrid atom–ion systems, and set the stage for alkaline-earth based quantum computing architectures.

Publication: Nature Physics Vol.: 16 No.: 8 ISSN: 1745-2473

ID: CaltechAUTHORS:20200312-141649005

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Abstract: According to Harlow and Hayden [arXiv:1301.4504] the task of distilling information out of Hawking radiation appears to be computationally hard despite the fact that the quantum state of the black hole and its radiation is relatively un-complex. We trace this computational difficulty to a geometric obstruction in the Einstein-Rosen bridge connecting the black hole and its radiation. Inspired by tensor network models, we conjecture a precise formula relating the computational hardness of distilling information to geometric properties of the wormhole — specifically to the exponential of the difference in generalized entropies between the two non-minimal quantum extremal surfaces that constitute the obstruction. Due to its shape, we call this obstruction the ‘Python’s Lunch’, in analogy to the reptile’s postprandial bulge.

Publication: Journal of High Energy Physics Vol.: 2020 No.: 8 ISSN: 1029-8479

ID: CaltechAUTHORS:20200831-085554082

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Abstract: Building a quantum computer that surpasses the computational power of its classical counterpart is a great engineering challenge. Quantum software optimizations can provide an accelerated pathway to the first generation of quantum computing (QC) applications that might save years of engineering effort. Current quantum software stacks follow a layered approach similar to the stack of classical computers, which was designed to manage the complexity. In this review, we point out that greater efficiency of QC systems can be achieved by breaking the abstractions between these layers. We review several works along this line, including two hardware-aware compilation optimizations that break the quantum instruction set architecture (ISA) abstraction and two error-correction/information-processing schemes that break the qubit abstraction. Last, we discuss several possible future directions.

Publication: Proceedings of the IEEE Vol.: 108 No.: 8 ISSN: 0018-9219

ID: CaltechAUTHORS:20200624-155135309

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Abstract: Rare-earth ions embedded in crystals are promising optically addressable spin qubits. We demonstrate this potential by measuring the optical and spin transition properties of single ¹⁷¹Yb³⁺ ions coupled to nanophotonic resonators fabricated in YVO₄.

ID: CaltechAUTHORS:20210611-082710176

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Abstract: Why the Hall conductance is quantized was an open problem in condensed matter theory for much of the past 40 years. Spyridon Michalakis who worked on the solution — published in 2015 — gives a personal take on how the field evolved.

Publication: Nature Reviews Physics Vol.: 2 No.: 8 ISSN: 2522-5820

ID: CaltechAUTHORS:20200701-103607111

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Abstract: A tremendous amount of recent attention has focused on characterizing the dynamical properties of periodically driven many-body systems. Here, we use a novel numerical tool termed “density matrix truncation” (DMT) to investigate the late-time dynamics of large-scale Floquet systems. We find that DMT accurately captures two essential pieces of Floquet physics, namely, prethermalization and late-time heating to infinite temperature. Moreover, by implementing a spatially inhomogeneous drive, we demonstrate that an interplay between Floquet heating and diffusive transport is crucial to understanding the system’s dynamics. Finally, we show that DMT also provides a powerful method for quantitatively capturing the emergence of hydrodynamics in static (undriven) Hamiltonians; in particular, by simulating the dynamics of generic, large-scale quantum spin chains (up to L=100), we are able to directly extract the energy diffusion coefficient.

Publication: Physical Review Letters Vol.: 125 No.: 3 ISSN: 0031-9007

ID: CaltechAUTHORS:20200715-154527286

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Abstract: Magic-angle twisted bilayer graphene (TBG), with rotational misalignment close to 1.1 degrees, features isolated flat electronic bands that host a rich phase diagram of correlated insulating, superconducting, ferromagnetic and topological phases. Correlated insulators and superconductivity have been previously observed only for angles within 0.1 degree of the magic angle and occur in adjacent or overlapping electron-density ranges; nevertheless, the origins of these states and the relation between them remain unclear, owing to their sensitivity to microscopic details. Beyond twist angle and strain, the dependence of the TBG phase diagram on the alignment and thickness of the insulating hexagonal boron nitride (hBN) used to encapsulate the graphene sheets indicates the importance of the microscopic dielectric environment. Here we show that adding an insulating tungsten diselenide (WSe₂) monolayer between the hBN and the TBG stabilizes superconductivity at twist angles much smaller than the magic angle. For the smallest twist angle of 0.79 degrees, superconductivity is still observed despite the TBG exhibiting metallic behaviour across the whole range of electron densities. Finite-magnetic-field measurements further reveal weak antilocalization signatures as well as breaking of fourfold spin–valley symmetry, consistent with spin–orbit coupling induced in the TBG via its proximity to WSe₂. Our results constrain theoretical explanations for the emergence of superconductivity in TBG and open up avenues towards engineering quantum phases in moiré systems.

Publication: Nature Vol.: 583 No.: 7816 ISSN: 0028-0836

ID: CaltechAUTHORS:20200225-102617489

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Abstract: The one-dimensional (1D) Affleck-Kennedy-Lieb-Tasaki (AKLT) model is a paradigm of antiferromagnetism, and its ground state exhibits symmetry-protected topological order. On a two-dimensional (2D) lattice, the AKLT model has recently gained attention because it too displays symmetry-protected topological order, and its ground state can act as a resource state for measurement-based quantum computation. While the 1D model has been shown to be gapped, it remains an open problem to prove the existence of a spectral gap on the 2D square lattice, which would guarantee the robustness of the resource state. Recently, it has been shown that one can deduce this spectral gap by analyzing the model's boundary theory via a tensor network representation of the ground state. In this work, we express the boundary state of the 2D AKLT model in terms of a classical loop model, where loops, vertices, and crossings are each given a weight. We use numerical techniques to sample configurations of loops and subsequently evaluate the boundary state and boundary Hamiltonian on a square lattice. As a result, we evidence a spectral gap in the square-lattice AKLT model. In addition, by varying the weights of the loops, vertices, and crossings, we indicate the presence of three distinct phases exhibited by the classical loop model.

Publication: Physical Review B Vol.: 102 No.: 3 ISSN: 2469-9950

ID: CaltechAUTHORS:20200710-151322063

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Abstract: For all n ≥ 1, we give an explicit construction of m × m matrices A_1,…,A_n with m = 2^([n/2]) such that for any d and d × d matrices A′_1,…,A′_n that satisfy ∥A_′i−A′_j∥S_1 ≤ ∥A_i−A_j∥S_1 ≤ (1+δ)∥A′_i−A′_j∥S_1 for all i,j∈{1,…,n} and small enough δ = O(n^(−c)), where c > 0 is a universal constant, it must be the case that d ≥ 2^([n/2]−1). This stands in contrast to the metric theory of commutative ℓ_p spaces, as it is known that for any p ≥ 1, any n points in ℓ_p embed exactly in ℓ^d_p for d = n(n−1)/2. Our proof is based on matrices derived from a representation of the Clifford algebra generated by n anti-commuting Hermitian matrices that square to identity, and borrows ideas from the analysis of nonlocal games in quantum information theory.

No.: 2266
ID: CaltechAUTHORS:20190320-095834301

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Abstract: Optomechanical systems offer new opportunities in quantum information processing and quantum sensing. Many solid-state quantum devices operate at millikelvin temperatures—however, it has proven challenging to operate nanoscale optomechanical devices at these ultralow temperatures due to their limited thermal conductance and parasitic optical absorption. Here, we present a two-dimensional optomechanical crystal resonator capable of achieving large cooperativity C and small effective bath occupancy n_b, resulting in a quantum cooperativity C_(eff) ≡ C/n_b > 1 under continuous-wave optical driving. This is realized using a two-dimensional phononic bandgap structure to host the optomechanical cavity, simultaneously isolating the acoustic mode of interest in the bandgap while allowing heat to be removed by phonon modes outside of the bandgap. This achievement paves the way for a variety of applications requiring quantum-coherent optomechanical interactions, such as transducers capable of bi-directional conversion of quantum states between microwave frequency superconducting quantum circuits and optical photons in a fiber optic network.

Publication: Nature Communications Vol.: 11ISSN: 2041-1723

ID: CaltechAUTHORS:20200330-152420978

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Abstract: We study the effectiveness of quantum error correction against coherent noise. Coherent errors (for example, unitary noise) can interfere constructively, so that in some cases the average infidelity of a quantum circuit subjected to coherent errors may increase quadratically with the circuit size; in contrast, when errors are incoherent (for example, depolarizing noise), the average infidelity increases at worst linearly with circuit size. We consider the performance of quantum stabilizer codes against a noise model in which a unitary rotation is applied to each qubit, where the axes and angles of rotation are nearly the same for all qubits. In particular, we show that for the toric code subject to such independent coherent noise, and for minimal-weight decoding, the logical channel after error correction becomes increasingly incoherent as the length of the code increases, provided the noise strength decays inversely with the code distance. A similar conclusion holds for weakly correlated coherent noise. Our methods can also be used for analyzing the performance of other codes and fault-tolerant protocols against coherent noise. However, our result does not show that the coherence of the logical channel is suppressed in the more physically relevant case where the noise strength is held constant as the code block grows, and we recount the difficulties that prevented us from extending the result to that case. Nevertheless our work supports the idea that fault-tolerant quantum computing schemes will work effectively against coherent noise, providing encouraging news for quantum hardware builders who worry about the damaging effects of control errors and coherent interactions with the environment.

Publication: New Journal of Physics Vol.: 22 No.: 7 ISSN: 1367-2630

ID: CaltechAUTHORS:20200827-141821017

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Abstract: One of the unique features of discrete-time quantum walks is called trapping, meaning the inability of the quantum walker to completely escape from its initial position, although the system is translationally invariant. The effect is dependent on the dimension and the explicit form of the local coin. A four-state discrete-time quantum walk on a square lattice is defined by its unitary coin operator, acting on the four-dimensional coin Hilbert space. The well-known example of the Grover coin leads to a partial trapping, i.e., there exists some escaping initial state for which the probability of staying at the initial position vanishes. On the other hand, some other coins are known to exhibit strong trapping, where such an escaping state does not exist. We present a systematic study of coins leading to trapping, explicitly construct all such coins for discrete-time quantum walks on the two-dimensional square lattice, and classify them according to the structure of the operator and the manifestation of the trapping effect. We distinguish three types of trapping coins exhibiting distinct dynamical properties, as exemplified by the existence or nonexistence of the escaping state and the area covered by the spreading wave packet.

Publication: Physical Review A Vol.: 102 No.: 1 ISSN: 2469-9926

ID: CaltechAUTHORS:20200707-120236607

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Abstract: Microelectromechanical systems and integrated photonics provide the basis for many reliable and compact circuit elements in modern communication systems. Electro-opto-mechanical devices are currently one of the leading approaches to realize ultra-sensitive, low-loss transducers for an emerging quantum information technology. Here we present an on-chip microwave frequency converter based on a planar aluminum on silicon nitride platform that is compatible with slot-mode coupled photonic crystal cavities. We show efficient frequency conversion between two propagating microwave modes mediated by the radiation pressure interaction with a metalized dielectric nanobeam oscillator. We achieve bidirectional coherent conversion with a total device efficiency of up to ~60%, a dynamic range of 2 × 10⁹ photons/s and an instantaneous bandwidth of up to 1.7 kHz. A high fidelity quantum state transfer would be possible if the drive dependent output noise of currently ~14 photons s⁻¹ Hz⁻¹ is further reduced. Such a silicon nitride based transducer is in situ reconfigurable and could be used for on-chip classical and quantum signal routing and filtering, both for microwave and hybrid microwave-optical applications.

Publication: Quantum Science and Technology Vol.: 5 No.: 3 ISSN: 2058-9565

ID: CaltechAUTHORS:20200504-123037615

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Abstract: Recent thermal-conductivity measurements evidence a magnetic-field-induced non-Abelian spin-liquid phase in the Kitaev material α−RuCl₃. Although the platform is a good Mott insulator, we propose experiments that electrically probe the spin liquid’s hallmark chiral Majorana edge state and bulk anyons, including their exotic exchange statistics. We specifically introduce circuits that exploit interfaces between electrically active systems and Kitaev materials to “perfectly” convert electrons from the former into emergent fermions in the latter—thereby enabling variations of transport probes invented for topological superconductors and fractional quantum-Hall states. Along the way, we resolve puzzles in the literature concerning interacting Majorana fermions, and also develop an anyon-interferometry framework that incorporates nontrivial energy-partitioning effects. Our results illuminate a partial pathway toward topological quantum computation with Kitaev materials.

Publication: Physical Review X Vol.: 10 No.: 3 ISSN: 2160-3308

ID: CaltechAUTHORS:20200225-103848261

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Abstract: Metallic LiOsO₃ undergoes a continuous ferroelectric-like structural phase transition below T_c=140K to realize a polar metal. To understand the microscopic interactions that drive this transition, we study its critical behavior above T_c via electromechanical coupling—distortions of the lattice induced by short-range dipole-dipole correlations arising from Li off-center displacements. By mapping the full angular distribution of second harmonic electric-quadrupole radiation from LiOsO₃ and performing a simplified hyper-polarizable bond model analysis, we uncover subtle symmetry-preserving lattice distortions over a broad temperature range extending from T_c up to around 230 K, characterized by nonuniform changes in the short and long Li-O bond lengths. Such an extended region of critical fluctuations may explain anomalous features reported in specific heat and Raman scattering data and suggests the presence of competing interactions that are not accounted for in existing theoretical treatments. More broadly, our results showcase how electromechanical effects serve as a probe of critical behavior near inversion symmetry-breaking transitions in metals.

Publication: Physical Review Research Vol.: 2 No.: 3 ISSN: 2643-1564

ID: CaltechAUTHORS:20200731-134646814

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Abstract: We derive some of the axioms of the algebraic theory of anyon (Kitaev, 2006) from a conjectured form of entanglement area law for two-dimensional gapped systems. We derive the fusion rules of topological charges and show that the multiplicities of the fusion rules satisfy these axioms. Moreover, even though we make no assumption about the exact value of the constant sub-leading term of the entanglement entropy of a disk-like region, this term is shown to be equal to ln D, where D is the total quantum dimension of the underlying anyon theory. These derivations are rigorous and follow from the entanglement area law alone. More precisely, our framework starts from two local entropic constraints which are implied by the area law. From these constraints, we prove what we refer to as the “isomorphism theorem.” The existence of superselection sectors and fusion multiplicites follow from this theorem, even without assuming anything about the parent Hamiltonian. These objects and the axioms of the anyon theory are shown to emerge from the structure and the internal self-consistency relations of the information convex sets.

Publication: Annals of Physics Vol.: 418ISSN: 0003-4916

ID: CaltechAUTHORS:20200409-144558293

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Abstract: Surface codes are among the best candidates to ensure the fault tolerance of a quantum computer. In order to avoid the accumulation of errors during a computation, it is crucial to have at our disposal a fast decoding algorithm to quickly identify and correct errors as soon as they occur. We propose a linear-time maximum likelihood decoder for surface codes over the quantum erasure channel. This decoding algorithm for dealing with qubit loss is optimal both in terms of performance and speed.

Publication: Physical Review Research Vol.: 2 No.: 3 ISSN: 2643-1564

ID: CaltechAUTHORS:20171108-153301401

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Abstract: We examine the advantages that quantum strategies afford in communication-limited games. Inspired by the card game blackjack, we focus on cooperative, two-party sequential games in which a single classical bit of communication is allowed from the player who moves first to the player who moves second. Within this setting, we explore the usage of quantum entanglement between the players and find analytic and numerical conditions for quantum advantage over classical strategies. Using these conditions, we study a family of blackjack-type games with varying numbers of card types, and find a range of parameters where quantum advantage is achieved.

Publication: Physical Review A Vol.: 102 No.: 1 ISSN: 2469-9926

ID: CaltechAUTHORS:20200728-122746866

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Abstract: We construct quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of rotational states of a rigid body. These codes, which protect against both drift in the body’s orientation and small changes in its angular momentum, may be well suited for robust storage and coherent processing of quantum information using rotational states of a polyatomic molecule. Extensions of such codes to rigid bodies with a symmetry axis are compatible with rotational states of diatomic molecules as well as nuclear states of molecules and atoms. We also describe codes associated with general non-Abelian groups and develop orthogonality relations for coset spaces, laying the groundwork for quantum information processing with exotic configuration spaces.

Publication: Physical Review X Vol.: 10 No.: 3 ISSN: 2160-3308

ID: CaltechAUTHORS:20200413-094120710

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Abstract: The quantum dynamics away from equilibrium is of fundamental interest for interacting lattice systems. In this work, we study strongly tilted lattice systems using the effective Hamiltonian derived from the microscopic description. We first give general arguments for the density relaxation rate satisfying 1/τ ∝ k⁴ for a large class of systems, including the tilted Fermi Hubbard model that has been realized in the recent experiment, E. Guardado-Sanchez et al. [Phys. Rev. X 10, 011042 (2020)]. Here k is the wave vector of the density wave. The main ingredients are the emergence of the reflection symmetry and dipole moment conservation to the leading nontrivial order of the large tilted strength. To support our analysis, we then construct a solvable model with large local Hilbert space dimension by coupling sites discribed by the Sachdev-Ye-Kitaev models, where the density response can be computed explicitly. The the tilt strength and the temperature dependence of the subdiffusion constant are also discussed.

Publication: Physical Review Research Vol.: 2 No.: 3 ISSN: 2643-1564

ID: CaltechAUTHORS:20200724-100654276

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Abstract: Topological entanglement entropy has been extensively used as an indicator of topologically ordered phases. We study the conditions needed for two-dimensional topologically trivial states to exhibit spurious contributions that contaminate topological entanglement entropy. We show that, if the state at the boundary of a subregion is a stabilizer state, then it has a nonzero spurious contribution to the region if and only if the state is in a nontrivial one-dimensional G₁×G₂ symmetry-protected-topological (SPT) phase under an on-site symmetry. However, we provide a candidate of a boundary state that has a nonzero spurious contribution but does not belong to any such SPT phase.

Publication: Physical Review Research Vol.: 2 No.: 3 ISSN: 2643-1564

ID: CaltechAUTHORS:20200707-115529620

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Abstract: The spectral gap problem—determining whether the energy spectrum of a system has an energy gap above ground state, or if there is a continuous range of low-energy excitations—pervades quantum many-body physics. Recently, this important problem was shown to be undecidable for quantum-spin systems in two (or more) spatial dimensions: There exists no algorithm that determines in general whether a system is gapped or gapless, a result which has many unexpected consequences for the physics of such systems. However, there are many indications that one-dimensional spin systems are simpler than their higher-dimensional counterparts: For example, they cannot have thermal phase transitions or topological order, and there exist highly effective numerical algorithms such as the density matrix renormalization group—and even provably polynomial-time ones—for gapped 1D systems, exploiting the fact that such systems obey an entropy area law. Furthermore, the spectral gap undecidability construction crucially relied on aperiodic tilings, which are not possible in 1D. So does the spectral gap problem become decidable in 1D? In this paper, we prove this is not the case by constructing a family of 1D spin chains with translationally invariant nearest-neighbor interactions for which no algorithm can determine the presence of a spectral gap. This not only proves that the spectral gap of 1D systems is just as intractable as in higher dimensions, but it also predicts the existence of qualitatively new types of complex physics in 1D spin chains. In particular, it implies there are 1D systems with a constant spectral gap and nondegenerate classical ground state for all systems sizes up to an uncomputably large size, whereupon they switch to a gapless behavior with dense spectrum.

Publication: Physical Review X Vol.: 10 No.: 3 ISSN: 2160-3308

ID: CaltechAUTHORS:20200818-151254755

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Abstract: Optical networks that distribute entanglement among various quantum systems will form a powerful framework for quantum science but are yet to interface with leading quantum hardware such as superconducting qubits. Consequently, these systems remain isolated because microwave links at room temperature are noisy and lossy. Building long distance connectivity requires interfaces that map quantum information between microwave and optical fields. While preliminary microwave-to-optical transducers have been realized, developing efficient, low-noise devices that match superconducting qubit frequencies (gigahertz) and bandwidths (10 kilohertz – 1 megahertz) remains a challenge. Here we demonstrate a proof-of-concept on-chip transducer using trivalent ytterbium-171 ions in yttrium orthovanadate coupled to a nanophotonic waveguide and a microwave transmission line. The device′s miniaturization, material, and zero-magnetic-field operation are important advances for rare-earth ion magneto-optical devices. Further integration with high quality factor microwave and optical resonators will enable efficient transduction and create opportunities toward multi-platform quantum networks.

Publication: Nature Communications Vol.: 11ISSN: 2041-1723

ID: CaltechAUTHORS:20200116-082522715

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Abstract: The Sachdev-Ye-Kitaev model is an N-modes fermionic model with infinite range random interactions. In this work, we study the thermal Rényi entropy for a subsystem of the SYK model using the path-integral formalism in the large-N limit. The results are consistent with exact diagonalization [1] and can be well approximated by thermal entropy with an effective temperature [2] when subsystem size M ≤ N/2. We also consider generalizations of the SYK model with quadratic random hopping term or U(1) charge conservation.

Publication: SciPost Physics Vol.: 8ISSN: 2542-4653

ID: CaltechAUTHORS:20200511-102846854

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Abstract: We present a quasi-polynomial time classical algorithm that estimates the partition function of quantum many-body systems at temperatures above the thermal phase transition point. It is known that in the worst case, the same problem is NP-hard below this point. Together with our work, this shows that the transition in the phase of a quantum system is also accompanied by a transition in the hardness of approximation. We also show that in a system of n particles above the phase transition point, the correlation between two observables whose distance is at least Ω(logn) decays exponentially. We can improve the factor of logn to a constant when the Hamiltonian has commuting terms or is on a 1D chain. The key to our results is a characterization of the phase transition and the critical behavior of the system in terms of the complex zeros of the partition function. Our work extends a seminal work of Dobrushin and Shlosman on the equivalence between the decay of correlations and the analyticity of the free energy in classical spin models. On the algorithmic side, our result extends the scope of a recent approach due to Barvinok for solving classical counting problems to quantum many-body systems.

ID: CaltechAUTHORS:20210226-083215255

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Abstract: We present an algorithmic framework for quantum-inspired classical algorithms on close-to-low-rank matrices, generalizing the series of results started by Tang’s breakthrough quantum-inspired algorithm for recommendation systems [STOC’19]. Motivated by quantum linear algebra algorithms and the quantum singular value transformation (SVT) framework of Gilyén et al. [STOC’19], we develop classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions. Our results give compelling evidence that in the corresponding QRAM data structure input model, quantum SVT does not yield exponential quantum speedups. Since the quantum SVT framework generalizes essentially all known techniques for quantum linear algebra, our results, combined with sampling lemmas from previous work, suffices to generalize all recent results about dequantizing quantum machine learning algorithms. In particular, our classical SVT framework recovers and often improves the dequantization results on recommendation systems, principal component analysis, supervised clustering, support vector machines, low-rank regression, and semidefinite program solving. We also give additional dequantization results on low-rank Hamiltonian simulation and discriminant analysis. Our improvements come from identifying the key feature of the quantum-inspired input model that is at the core of all prior quantum-inspired results: ℓ²-norm sampling can approximate matrix products in time independent of their dimension. We reduce all our main results to this fact, making our exposition concise, self-contained, and intuitive.

ID: CaltechAUTHORS:20210226-083945792

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Abstract: A proof of quantumness is a method for provably demonstrating (to a classical verifier) that a quantum device can perform computational tasks that a classical device with comparable resources cannot. Providing a proof of quantumness is the first step towards constructing a useful quantum computer. There are currently three approaches for exhibiting proofs of quantumness: (i) Inverting a classically-hard one-way function (e.g. using Shor’s algorithm). This seems technologically out of reach. (ii) Sampling from a classically-hard-to-sample distribution (e.g. BosonSampling). This may be within reach of near-term experiments, but for all such tasks known verification requires exponential time. (iii) Interactive protocols based on cryptographic assumptions. The use of a trapdoor scheme allows for efficient verification, and implementation seems to require much less resources than (i), yet still more than (ii). In this work we propose a significant simplification to approach (iii) by employing the random oracle heuristic. (We note that we do not apply the Fiat-Shamir paradigm.) We give a two-message (challenge-response) proof of quantumness based on any trapdoor claw-free function. In contrast to earlier proposals we do not need an adaptive hard-core bit property. This allows the use of smaller security parameters and more diverse computational assumptions (such as Ring Learning with Errors), significantly reducing the quantum computational effort required for a successful demonstration.

Publication: arXiv
ID: CaltechAUTHORS:20200728-144326318

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Abstract: We prove that the quantum Gibbs states of spin systems above a certain threshold temperature are approximate quantum Markov networks, meaning that the conditional mutual information decays rapidly with distance. We demonstrate the exponential decay for short-ranged interacting systems and power-law decay for long-ranged interacting systems. Consequently, we establish the efficiency of quantum Gibbs sampling algorithms, a strong version of the area law, the quasilocality of effective Hamiltonians on subsystems, a clustering theorem for mutual information, and a polynomial-time algorithm for classical Gibbs state simulations.

Publication: Physical Review Letters Vol.: 124 No.: 22 ISSN: 0031-9007

ID: CaltechAUTHORS:20200601-141729048

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Abstract: We develop new tools for isolating CFTs using the numerical bootstrap. A “cutting surface” algorithm for scanning OPE coefficients makes it possible to find islands in high-dimensional spaces. Together with recent progress in large-scale semidefinite programming, this enables bootstrap studies of much larger systems of correlation functions than was previously practical. We apply these methods to correlation functions of charge-0, 1, and 2 scalars in the 3d O(2) model, computing new precise values for scaling dimensions and OPE coefficients in this theory. Our new determinations of scaling dimensions are consistent with and improve upon existing Monte Carlo simulations, sharpening the existing decades-old 8σ discrepancy between theory and experiment.

Publication: Journal of High Energy Physics Vol.: 2020 No.: 6 ISSN: 1029-8479

ID: CaltechAUTHORS:20200624-104211278

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Abstract: Sachdev-Ye-Kitaev (SYK) is a concrete solvable model with non-Fermi liquid behavior and maximal chaos. In this work, we study the entanglement Rényi entropy for the subsystems of the SYK model in the Kourkoulou-Maldacena states. We use the path-integral approach and take the saddle point approximation in the large-N limit. We find a first-order transition exist when tuning the subsystem size for the q = 4 case, while it is absent for the q = 2 case. We further study the entanglement dynamics for such states under the real-time evolution for noninteracting, weakly interacting and strongly interacting SYK(-like) models.

Publication: Journal of High Energy Physics Vol.: 2020 No.: 6 ISSN: 1029-8479

ID: CaltechAUTHORS:20200624-104211372

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Abstract: We study the contacts, large-momentum tail, radio-frequency spectroscopy, and some other universal relations for an ultracold one-dimensional (1D) two-component Fermi gas with spin-orbit coupling (SOC). Different from previous studies, we find that the q⁻⁸ tail in the spin-mixing (off-diagonal) terms of the momentum distribution matrix is dependent on the two SOC parameters in the laboratory frame for 1D systems, where q is the relative momentum. This tail can be observed through time-of-flight measurement as a direct manifestation of the SOC effects on the many-body level. Besides the traditional 1D even-wave scattering length, we find that two new physical quantities must be introduced due to the SOC. Consequently, two new adiabatic energy relations with respect to the two SOC parameters are obtained. Furthermore, we derive the pressure relation and virial theorem at short distances for this system. To find how the SOC modifies the large-momentum behavior, we take the SOC parameters as perturbations since the strength of the SOC should be much smaller than the corresponding strength scale of the interatomic interactions. In addition, by using the operator product expansion method, we derive the asymptotic behavior of the large-momentum distribution matrix up to the q⁻⁸ order and find that the diagonal terms of the distribution matrix include the contact of traditional 1D even-wave scattering length as the leading term and the SOC modified terms beyond the leading term, the off-diagonal term is beyond the subleading term and is corrected by the SOC parameters. We also find that the momentum distribution matrix shows spin-dependent and anisotropic features. Furthermore, we calculate the momentum distribution matrix in the laboratory frame for the experimental implication. In addition, we calculate the high-frequency tail of the radio-frequency spectroscopy and find that the presence of the contact related to the center-of-mass momentum in the radio-frequency spectral is due to the SOC effects. This paper paves the way for exploring the profound properties of many-body quantum systems with SOC in one dimension.

Publication: Physical Review A Vol.: 101 No.: 6 ISSN: 2469-9926

ID: CaltechAUTHORS:20200615-132514406

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Abstract: Motivated by recent studies of the information paradox in (1+1)-D anti-de Sitter spacetime with a bath described by a (1+1)-D conformal field theory, we study the dynamics of second Ŕenyi entropy of the Sachdev-Ye-Kitaev (SYK) model (χ) coupled to a Majorana chain bath (ψ). The system is prepared in the thermofield double (TFD) state and then evolved by H_L + H_R. For small system-bath coupling, we find that the second Rényi entropy S(2)_(χL,χR) of the SYK model undergoes a first order transition during the evolution. In the sense of holographic duality, the long-time solution corresponds to a “replica wormhole”. The transition time corresponds to the Page time of a black hole coupled to a thermal bath. We further study the information scrambling and retrieval by introducing a classical control bit, which controls whether or not we add a perturbation in the SYK system. The mutual information between the bath and the control bit shows a positive jump at the Page time, indicating that the entanglement wedge of the bath includes an island in the holographic bulk.

Publication: Journal of High Energy Physics Vol.: 2020 No.: 6 ISSN: 1029-8479

ID: CaltechAUTHORS:20200624-104212537

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Abstract: We reconsider the black hole firewall puzzle, emphasizing that quantum error- correction, computational complexity, and pseudorandomness are crucial concepts for understanding the black hole interior. We assume that the Hawking radiation emitted by an old black hole is pseudorandom, meaning that it cannot be distinguished from a perfectly thermal state by any efficient quantum computation acting on the radiation alone. We then infer the existence of a subspace of the radiation system which we interpret as an encoding of the black hole interior. This encoded interior is entangled with the late outgoing Hawking quanta emitted by the old black hole, and is inaccessible to computationally bounded observers who are outside the black hole. Specifically, efficient operations acting on the radiation, those with quantum computational complexity polynomial in the entropy of the remaining black hole, commute with a complete set of logical operators acting on the encoded interior, up to corrections which are exponentially small in the entropy. Thus, under our pseudorandomness assumption, the black hole interior is well protected from exterior observers as long as the remaining black hole is macroscopic. On the other hand, if the radiation is not pseudorandom, an exterior observer may be able to create a firewall by applying a polynomial-time quantum computation to the radiation.

Publication: Journal of High Energy Physics Vol.: 2020 No.: 6 ISSN: 1029-8479

ID: CaltechAUTHORS:20200608-102711610

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Abstract: The quantum neural network is one of the promising applications for near-term noisy intermediate-scale quantum computers. A quantum neural network distills the information from the input wave function into the output qubits. In this Letter, we show that this process can also be viewed from the opposite direction: the quantum information in the output qubits is scrambled into the input. This observation motivates us to use the tripartite information—a quantity recently developed to characterize information scrambling—to diagnose the training dynamics of quantum neural networks. We empirically find strong correlation between the dynamical behavior of the tripartite information and the loss function in the training process, from which we identify that the training process has two stages for randomly initialized networks. In the early stage, the network performance improves rapidly and the tripartite information increases linearly with a universal slope, meaning that the neural network becomes less scrambled than the random unitary. In the latter stage, the network performance improves slowly while the tripartite information decreases. We present evidences that the network constructs local correlations in the early stage and learns large-scale structures in the latter stage. We believe this two-stage training dynamics is universal and is applicable to a wide range of problems. Our work builds bridges between two research subjects of quantum neural networks and information scrambling, which opens up a new perspective to understand quantum neural networks.

Publication: Physical Review Letters Vol.: 124 No.: 20 ISSN: 0031-9007

ID: CaltechAUTHORS:20200521-154830923

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Abstract: We show that every language in QMA admits a classical-verifier, quantum-prover zero-knowledge argument system which is sound against quantum polynomial-time provers and zero-knowledge for classical (and quantum) polynomial-time verifiers. The protocol builds upon two recent results: a computational zero-knowledge proof system for languages in QMA, with a quantum verifier, introduced by Broadbent et al. (FOCS 2016), and an argument system for languages in QMA, with a classical verifier, introduced by Mahadev (FOCS 2018).

Publication: Quantum Vol.: 4ISSN: 2521-327X

ID: CaltechAUTHORS:20190320-095213331

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Abstract: Quantum computational supremacy arguments, which describe a way for a quantum computer to perform a task that cannot also be done by a classical computer, typically require some sort of computational assumption related to the limitations of classical computation. One common assumption is that the polynomial hierarchy (PH) does not collapse, a stronger version of the statement that P≠NP, which leads to the conclusion that any classical simulation of certain families of quantum circuits requires time scaling worse than any polynomial in the size of the circuits. However, the asymptotic nature of this conclusion prevents us from calculating exactly how many qubits these quantum circuits must have for their classical simulation to be intractable on modern classical supercomputers. We refine these quantum computational supremacy arguments and perform such a calculation by imposing fine-grained versions of the non-collapse conjecture. Our first two conjectures poly3-NSETH(a) and per-int-NSETH(b) take specific classical counting problems related to the number of zeros of a degree-3 polynomial in n variables over F₂ or the permanent of an n×n integer-valued matrix, and assert that any non-deterministic algorithm that solves them requires 2^(cn) time steps, where c∈{a,b}. A third conjecture poly3-ave-SBSETH(a′) asserts a similar statement about average-case algorithms living in the exponential-time version of the complexity class SBP. We analyze evidence for these conjectures and argue that they are plausible when a=1/2, b=0.999 and a′=1/2. Imposing poly3-NSETH(1/2) and per-int-NSETH(0.999), and assuming that the runtime of a hypothetical quantum circuit simulation algorithm would scale linearly with the number of gates/constraints/optical elements, we conclude that Instantaneous Quantum Polynomial-Time (IQP) circuits with 208 qubits and 500 gates, Quantum Approximate Optimization Algorithm (QAOA) circuits with 420 qubits and 500 constraints and boson sampling circuits (i.e. linear optical networks) with 98 photons and 500 optical elements are large enough for the task of producing samples from their output distributions up to constant multiplicative error to be intractable on current technology. Imposing poly3-ave-SBSETH(1/2), we additionally rule out simulations with constant additive error for IQP and QAOA circuits of the same size. Without the assumption of linearly increasing simulation time, we can make analogous statements for circuits with slightly fewer qubits but requiring 10⁴ to 10⁷ gates.

Publication: Quantum Vol.: 4ISSN: 2521-327X

ID: CaltechAUTHORS:20200605-083021823

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Abstract: The existence of nontrivial Berry phases associated with two inequivalent valleys in graphene provides interesting opportunities for investigating the valley-projected topological states. Examples of such studies include observation of anomalous quantum Hall effect in monolayer graphene, demonstration of topological zero modes in “molecular graphene” assembled by scanning tunneling microscopy, and detection of topological valley transport either in graphene superlattices or at bilayer graphene domain walls. However, all aforementioned experiments involved nonscalable approaches of either mechanically exfoliated flakes or atom-by-atom constructions. Here, we report an approach to manipulating the topological states in monolayer graphene via nanoscale strain engineering at room temperature. By placing strain-free monolayer graphene on architected nanostructures to induce global inversion symmetry breaking, we demonstrate the development of giant pseudo-magnetic fields (up to ~800 T), valley polarization, and periodic one-dimensional topological channels for protected propagation of chiral modes in strained graphene, thus paving a pathway toward scalable graphene-based valleytronics.

Publication: Science Advances Vol.: 6 No.: 19 ISSN: 2375-2548

ID: CaltechAUTHORS:20200508-111719364

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Abstract: We define the notion of a proof of knowledge in the setting where the verifier is classical, but the prover is quantum, and where the witness that the prover holds is in general a quantum state. We establish simple properties of our definition, including that nondestructive classical proofs of quantum knowledge are impossible for nontrivial states, and that, under certain conditions on the parameters in our definition, a proof of knowledge protocol for a hard-to-clone state can be used as a (destructive) quantum money verification protocol. In addition, we provide two examples of protocols (both inspired by private-key classical verification protocols for quantum money schemes) which we can show to be proofs of quantum knowledge under our definition. In so doing, we introduce new techniques for the analysis of such protocols which build on results from the literature on nonlocal games. Finally, we show that, under our definition, the verification protocol introduced by Mahadev (FOCS 2018) is a classical argument of quantum knowledge for QMA relations.

Publication: arXiv
ID: CaltechAUTHORS:20200728-145122122

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Abstract: Projected least squares is an intuitive and numerically cheap technique for quantum state tomography: compute the least-squares estimator and project it onto the space of states. The main result of this paper equips this point estimator with rigorous, non-asymptotic convergence guarantees expressed in terms of the trace distance. The estimator's sample complexity is comparable to the strongest convergence guarantees available in the literature and—in the case of the uniform POVM—saturates fundamental lower bounds. Numerical simulations support these competitive features.

Publication: Journal of Physics A: Mathematical and General Vol.: 53 No.: 20 ISSN: 0305-4470

ID: CaltechAUTHORS:20190212-160252658

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Abstract: We extend the tools of quantum resource theories to scenarios in which multiple quantities (or resources) are present, and their interplay governs the evolution of physical systems. We derive conditions for the interconversion of these resources, which generalise the first law of thermodynamics. We study reversibility conditions for multi-resource theories, and find that the relative entropy distances from the invariant sets of the theory play a fundamental role in the quantification of the resources. The first law for general multi-resource theories is a single relation which links the change in the properties of the system during a state transformation and the weighted sum of the resources exchanged. In fact, this law can be seen as relating the change in the relative entropy from different sets of states. In contrast to typical single-resource theories, the notion of free states and invariant sets of states become distinct in light of multiple constraints. Additionally, generalisations of the Helmholtz free energy, and of adiabatic and isothermal transformations, emerge. We thus have a set of laws for general quantum resource theories, which generalise the laws of thermodynamics. We first test this approach on thermodynamics with multiple conservation laws, and then apply it to the theory of local operations under energetic restrictions.

Publication: Quantum Vol.: 4ISSN: 2521-327X

ID: CaltechAUTHORS:20190211-154327639

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Abstract: Yu-Shiba-Rusinov (YSR) states arise when magnetic impurities interact with superconductivity. The intricacy of coupling and the nature of the superconductivity determine the behavior of the YSR state, whose detailed correlations are not yet fully understood. Here, we study the YSR state of a single Fe adatom on the surface of 2H-NbSe₂ with combined low temperature scanning tunneling microscopy/spectroscopy, density functional theory calculations and tight-binding modeling. It is found that the Fe adatom occupies the hollow site of the Se surface layer. A prominent YSR state close to the Fermi level is observed. The YSR state exhibits a threefold symmetry along the diagonal direction of the Se lattice. The spatial decay of the YSR state follows a behavior in three-dimensional superconductivity. This behavior contrasts with a previous study of imbedded Fe impurities, whose YSR state shows a six-fold symmetry and a two-dimensional long-range decay. According to our theoretical modeling, the coupling configurations affect the adatom-substrate hopping and the interlayer coupling of the substrate. Both factors are crucial for the consequent behavior of the YSR state.

Publication: Nanoscale Vol.: 12 No.: 15 ISSN: 2040-3364

ID: CaltechAUTHORS:20200406-084809823

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Abstract: The quantum dynamics away from equilibrium is of fundamental interest for interacting many-body systems. In this letter, we study tilted many-body systems using the effective Hamiltonian derived from the microscopic description. We first give general arguments for the density relaxation rate satisfying 1/τ∝k⁴ for a large class of systems, including the Fermi Hubbard model case as observed in the the recent experiment [1]. Here k is the wave vector of the density wave. The main ingredients are the emergence of the reflection symmetry and dipole moment conservation to the leading non-trivial order of the large tilted strength. To support our analysis, we then construct a solvable model with large local Hilbert space dimension by coupling sites discribed by the Sachdev-Ye-Kitaev models, where the density response can be computed explicitly. The the tilt strength and the temperature dependence of the subdiffusion constant are also discussed.

Publication: arXiv
ID: CaltechAUTHORS:20200601-095228090

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Abstract: Distributing entanglement over long distances using optical networks is an intriguing macroscopic quantum phenomenon with applications in quantum systems for advanced computing and secure communication. Building quantum networks requires scalable quantum light–matter interfaces based on atoms, ions or other optically addressable qubits. Solid-state emitters5, such as quantum dots and defects in diamond or silicon carbide , have emerged as promising candidates for such interfaces. So far, it has not been possible to scale up these systems, motivating the development of alternative platforms. A central challenge is identifying emitters that exhibit coherent optical and spin transitions while coupled to photonic cavities that enhance the light–matter interaction and channel emission into optical fibres. Rare-earth ions in crystals are known to have highly coherent 4f–4f optical and spin transitions suited to quantum storage and transduction, but only recently have single rare-earth ions been isolated and coupled to nanocavities. The crucial next steps towards using single rare-earth ions for quantum networks are realizing long spin coherence and single-shot readout in photonic resonators. Here we demonstrate spin initialization, coherent optical and spin manipulation, and high-fidelity single-shot optical readout of the hyperfine spin state of single ¹⁷¹Yb³⁺ ions coupled to a nanophotonic cavity fabricated in an yttrium orthovanadate host crystal. These ions have optical and spin transitions that are first-order insensitive to magnetic field fluctuations, enabling optical linewidths of less than one megahertz and spin coherence times exceeding thirty milliseconds for cavity-coupled ions, even at temperatures greater than one kelvin. The cavity-enhanced optical emission rate facilitates efficient spin initialization and single-shot readout with conditional fidelity greater than 95 per cent. These results showcase a solid-state platform based on single coherent rare-earth ions for the future quantum internet.

Publication: Nature Vol.: 580 No.: 7802 ISSN: 0028-0836

ID: CaltechAUTHORS:20200115-161119221

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Abstract: We study the stability of the Wilson-Fisher fixed point of the quantum O(2N) vector model to quenched disorder in the large-N limit. While a random mass is strongly relevant at the Gaussian fixed point, its effect is screened by the strong interactions of the Wilson-Fisher fixed point. This enables a perturbative renormalization group study of the interplay of disorder and interactions about this fixed point. We show that, in contrast to the spiralling flows obtained in earlier double-ε expansions, the theory flows directly to a quantum critical point characterized by finite disorder and interactions. The critical exponents we obtain for this transition are in remarkable agreement with numerical studies of the superfluid-Mott glass transition. We additionally discuss the stability of this fixed point to scalar and vector potential disorder and use proposed boson-fermion dualities to make conjectures regarding the effects of weak disorder on dual Abelian Higgs and Chern-Simons-Dirac fermion theories when N = 1.

Publication: Physical Review B Vol.: 101 No.: 14 ISSN: 2469-9950

ID: CaltechAUTHORS:20200423-140429651

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Abstract: Floquet higher-order topological insulators and superconductors (HOTI/SCs) with an order-two space-time symmetry or antisymmetry are classified. This is achieved by considering unitary loops, whose nontrivial topology leads to the anomalous Floquet topological phases, subject to a space-time symmetry/antisymmetry. By mapping these unitary loops to static Hamiltonians with an order-two crystalline symmetry/antisymmetry, one is able to obtain the K groups for the unitary loops and thus complete the classification of Floquet HOTI/SCs. Interestingly, we found that for every order-two nontrivial space-time symmetry/antisymmetry involving a half-period time translation, there exists a unique order-two static crystalline symmetry/antisymmetry, such that the two symmetries/antisymmetries give rise to the same topological classification. Moreover, by exploiting the frequency-domain formulation of the Floquet problem, a general recipe that constructs model Hamiltonians for Floquet HOTI/SCs is provided, which can be used to understand the classification of Floquet HOTI/SCs from an intuitive and complimentary perspective.

Publication: Physical Review Research Vol.: 2 No.: 1 ISSN: 2643-1564

ID: CaltechAUTHORS:20200103-092333676

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Abstract: Small, out-of-equilibrium, and quantum systems defy simple thermodynamic expressions. Such systems are exemplified by molecular switches, which exchange heat with a bath. These molecules can photoisomerize, or change conformation, or switch, on absorbing light. The photoisomerization probability depends on kinetic details that couple the molecule's energetics to its dissipation. Therefore, a simple, general, thermodynamic-style bound on the photoisomerization probability seems out of reach. We derive such a bound using a resource theory. The resource-theory framework is a set of mathematical tools, developed in quantum information theory, used to generalize thermodynamics to small and quantum settings. From this toolkit has been derived a generalization of the second law, the thermomajorization preorder. We use thermomajorization to upper-bound the photoisomerization probability. Then, we compare the bound with an equilibrium prediction and with a Lindbladian model. We identify a realistic parameter regime in which the Lindbladian evolution saturates the thermomajorization bound. We also quantify the energy coherence in the electronic degree of freedom, and we argue that this coherence cannot promote photoisomerization. This work illustrates how quantum-information-theoretic thermodynamics can elucidate complex quantum processes in nature, experiments, and synthetics.

Publication: Physical Review A Vol.: 101 No.: 4 ISSN: 2469-9926

ID: CaltechAUTHORS:20190207-150038978

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Abstract: In statistical mechanics, a small system exchanges conserved quantities—heat, particles, electric charge, etc.—with a bath. The small system thermalizes to the canonical ensemble or the grand canonical ensemble, etc., depending on the quantities. The conserved quantities are represented by operators usually assumed to commute with each other. This assumption was removed within quantum-information-theoretic (QI-theoretic) thermodynamics recently. The small system's long-time state was dubbed “the non-Abelian thermal state (NATS).” We propose an experimental protocol for observing a system thermalize to the NATS. We illustrate with a chain of spins, a subset of which forms the system of interest. The conserved quantities manifest as spin components. Heisenberg interactions push the conserved quantities between the system and the effective bath, the rest of the chain. We predict long-time expectation values, extending the NATS theory from abstract idealization to finite systems that thermalize with finite couplings for finite times. Numerical simulations support the analytics: The system thermalizes to near the NATS, rather than to the canonical prediction. Our proposal can be implemented with ultracold atoms, nitrogen-vacancy centers, trapped ions, quantum dots, and perhaps nuclear magnetic resonance. This work introduces noncommuting conserved quantities from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.

Publication: Physical Review E Vol.: 101 No.: 4 ISSN: 2470-0045

ID: CaltechAUTHORS:20200103-094850055

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Abstract: We initiate a study of subregion dualities, entropy, and redundant encoding of bulk points in holographic theories deformed by TT and its generalizations. This includes both cut off versions of Anti de Sitter spacetime, as well as the generalization to bulk de Sitter spacetime, for which we introduce two additional examples capturing different patches of the bulk and incorporating the second branch of the square root dressed energy formula. We provide new calculations of entanglement entropy (EE) for more general divisions of the system than the symmetric ones previously available. We find precise agreement between the gravity side and deformed-CFT side results to all orders in the deformation parameter at large central charge. An analysis of the fate of strong subadditivity for relatively boosted regions indicates nonlocality reminiscent of string theory. We introduce the structure of operator algebras in these systems. The causal and entanglement wedges generalize to appropriate deformed theories but exhibit qualitatively new behaviors, e.g. the causal wedge may exceed the entanglement wedge. This leads to subtleties which we express in terms of the Hamiltonian and modular Hamiltonian evolution. Finally, we exhibit redundant encoding of bulk points, including the cosmological case.

Publication: Journal of High Energy Physics Vol.: 2020 No.: 4 ISSN: 1126-6708

ID: CaltechAUTHORS:20191028-151748156

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Abstract: Computing quantum state fidelity will be important to verify and characterize states prepared on a quantum computer. In this work, we propose novel lower and upper bounds for the fidelity F(ρ,σ) based on the “truncated fidelity'” F(ρ_m,σ) which is evaluated for a state ρ_m obtained by projecting ρ onto its mm-largest eigenvalues. Our bounds can be refined, i.e., they tighten monotonically with mm. To compute our bounds, we introduce a hybrid quantum-classical algorithm, called Variational Quantum Fidelity Estimation, that involves three steps: (1) variationally diagonalize ρ, (2) compute matrix elements of σ in the eigenbasis of ρ, and (3) combine these matrix elements to compute our bounds. Our algorithm is aimed at the case where σ is arbitrary and ρ is low rank, which we call low-rank fidelity estimation, and we prove that no classical algorithm can efficiently solve this problem under reasonable assumptions. Finally, we demonstrate that our bounds can detect quantum phase transitions and are often tighter than previously known computable bounds for realistic situations.

Publication: Quantum Vol.: 4ISSN: 2521-327X

ID: CaltechAUTHORS:20200423-104102695

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Abstract: Large-scale quantum computing poses a major threat to classical public-key cryptography. Recently, strong “quantum access” security models have shown that numerous symmetric-key cryptosystems are also vulnerable. In this paper, we consider classical encryption in a model that grants the adversary quantum oracle access to encryption and decryption, but where we restrict the latter to non-adaptive (i.e., pre-challenge) queries only. We formalize this model using appropriate notions of ciphertext indistinguishability and semantic security (which are equivalent by standard arguments) and call it QCCA1 in analogy to the classical CCA1 security model. We show that the standard pseudorandom function ( PRF )-based encryption schemes are QCCA1 -secure when instantiated with quantum-secure primitives. Our security proofs use a strong bound on quantum random-access codes with shared randomness. Revisiting plain IND−CPA -secure Learning with Errors ( LWE ) encryption, we show that leaking only a single quantum decryption query (and no other leakage or queries of any kind) allows the adversary to recover the full secret key with constant success probability. Information-theoretically, full recovery of the key in the classical setting requires at least a linear number of decryption queries. Our results thus challenge the notion that LWE is unconditionally “just as secure” quantumly as it is classically. The algorithm at the core of our attack is a new variant of the well-known Bernstein–Vazirani algorithm. Finally, we emphasize that our results should not be interpreted as a weakness of these cryptosystems in their stated security setting (i.e., post-quantum chosen-plaintext secrecy). Rather, our results mean that, if these cryptosystems are exposed to chosen-ciphertext attacks (e.g., as a result of deployment in an inappropriate real-world setting) then quantum attacks are even more devastating than classical ones.

Publication: Cryptography Vol.: 4 No.: 1 ISSN: 2410-387X

ID: CaltechAUTHORS:20200323-103442039

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Abstract: In this work, we consider a Casimir apparatus that is put into free fall (e.g., falling into a black hole). Working in 1 + 1D, we find that two main effects occur: First, the Casimir energy density experiences a tidal effect where negative energy is pushed toward the plates and the resulting force experienced by the plates is increased. Second, the process of falling is inherently nonequilibrium and we treat it as such, demonstrating that the Casimir energy density moves back and forth between the plates after being “dropped,” with the force modulating in synchrony. In this way, the Casimir energy behaves as a classical liquid might, putting (negative) pressure on the walls as it moves about in its container. In particular, we consider this in the context of a black hole and the multiple vacua that can be achieved outside of the apparatus.

Publication: Physical Review D Vol.: 101 No.: 6 ISSN: 2470-0010

ID: CaltechAUTHORS:20200316-150843290

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Abstract: Time crystals form when arbitrary physical states of a periodically driven system spontaneously break discrete time-translation symmetry. We introduce one-dimensional time-crystalline topological superconductors, for which time-translation symmetry breaking and topological physics intertwine—yielding anomalous Floquet Majorana modes that are not possible in free-fermion systems. Such a phase exhibits a bulk magnetization that returns to its original form after two drive periods, together with Majorana end modes that recover their initial form only after four drive periods. We propose experimental implementations and detection schemes for this new state.

Publication: Physical Review Letters Vol.: 124 No.: 9 ISSN: 0031-9007

ID: CaltechAUTHORS:20191014-105123769

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Abstract: Quantum transduction, the process of converting quantum signals from one form of energy to another, is an important area of quantum science and technology. The present perspective article reviews quantum transduction between microwave and optical photons, an area that has recently seen a lot of activity and progress because of its relevance for connecting superconducting quantum processors over long distances, among other applications. Our review covers the leading approaches to achieving such transduction, with an emphasis on those based on atomic ensembles, opto-electro-mechanics, and electro-optics. We briefly discuss relevant metrics from the point of view of different applications, as well as challenges for the future.

Publication: Quantum Science and Technology Vol.: 5 No.: 2 ISSN: 2058-9565

ID: CaltechAUTHORS:20200317-140314586

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Abstract: We classify subsystem symmetry-protected topological (SSPT) phases in 3 + 1 dimensions (3 + 1D) protected by planar subsystem symmetries: short-range entangled phases which are dual to long-range entangled Abelian fracton topological orders via a generalized “gauging” duality. We distinguish between weak SSPTs, which can be constructed by stacking 2 + 1D SPTs, and strong SSPTs, which cannot. We identify signatures of strong phases, and show by explicit construction that such phases exist. A classification of strong phases is presented for an arbitrary finite Abelian group. Finally, we show that fracton orders realizable via p-string condensation are dual to weak SSPTs, while those dual to strong SSPTs exhibit statistical interactions prohibiting such a realization.

Publication: Physical Review Research Vol.: 2 No.: 1 ISSN: 2643-1564

ID: CaltechAUTHORS:20200313-142322991

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Abstract: Fractons are a new type of quasiparticle which are immobile in isolation, but can often move by forming bound states. Fractons are found in a variety of physical settings, such as spin liquids and elasticity theory, and exhibit unusual phenomenology, such as gravitational physics and localization. The past several years have seen a surge of interest in these exotic particles, which have come to the forefront of modern condensed matter theory. In this review, we provide a broad treatment of fractons, ranging from pedagogical introductory material to discussions of recent advances in the field. We begin by demonstrating how the fracton phenomenon naturally arises as a consequence of higher moment conservation laws, often accompanied by the emergence of tensor gauge theories. We then provide a survey of fracton phases in spin models, along with the various tools used to characterize them, such as the foliation framework. We discuss in detail the manifestation of fracton physics in elasticity theory, as well as the connections of fractons with localization and gravitation. Finally, we provide an overview of some recently proposed platforms for fracton physics, such as Majorana islands and hole-doped antiferromagnets. We conclude with some open questions and an outlook on the field.

Publication: International Journal of Modern Physics A Vol.: 35 No.: 6 ISSN: 0217-751X

ID: CaltechAUTHORS:20200409-115738925

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Abstract: We introduce an entropic quantity for two-dimensional quantum spin systems to characterize gapped quantum phases modeled by local commuting projector code Hamiltonians. The definition is based on a recently introduced specific operator algebra defined on an annular region, which encodes the superselection sectors of the model. The quantity is calculable from local properties, and it is invariant under any constant-depth local quantum circuit, and thus an indicator of gapped quantum spin-liquids. We explicitly calculate the quantity for Kitaev's quantum double models, and show that the value is exactly same as the topological entanglement entropy (TEE) of the models. Our method circumvents some of the problems around extracting the TEE, allowing us to prove invariance under constant-depth quantum circuits.

Publication: Journal of Physics A: Mathematical and Theoretical Vol.: 53 No.: 8 ISSN: 1751-8113

ID: CaltechAUTHORS:20190212-155447238

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Abstract: We experimentally demonstrate an approach to scale up quantum devices by harnessing spin defects in the environment of a quantum probe. We follow this approach to identify, locate, and control two electron-nuclear spin defects in the environment of a single nitrogen-vacancy center in diamond. By performing spectroscopy at various orientations of the magnetic field, we extract the unknown parameters of the hyperfine and dipolar interaction tensors, which we use to locate the two spin defects and design control sequences to initialize, manipulate, and readout their quantum state. Finally, we create quantum coherence among the three electron spins, paving the way for the creation of genuine tripartite entanglement. This approach will be useful in assembling multispin quantum registers for applications in quantum sensing and quantum information processing.

Publication: Physical Review Letters Vol.: 124 No.: 8 ISSN: 0031-9007

ID: CaltechAUTHORS:20200226-110309782

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Abstract: We consider fermionic systems in which fermion parity is conserved within rigid subsystems, and describe an explicit procedure for gauging such subsystem fermion parity symmetries to obtain bosonic spin Hamiltonians. We show that gauging planar or fractal subsystem fermion parity symmetry in three spatial dimensions gives rise to a plethora of exactly solvable spin models exhibiting novel gapped fractonic orders characterized by emergent fermionic gauge theory. The low energy excitations of these models include fractional quasiparticles with constrained mobility and emergent fermionic statistics. We illustrate this phenomenon through a series of examples including fermionic analogs of both foliated fracton phases and fractal spin liquids. We find that the foliated analogs actually exhibit the same fractonic order as their bosonic counterparts, while this is not generally the case for fermionic fractal spin liquids.

Publication: arXiv
ID: CaltechAUTHORS:20200406-103524633

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Abstract: Monolayer transition-metal dichalcogenides (TMDCs) in the 2H-phase are semiconductors promising for opto-valleytronic and opto-spintronic applications because of their strong spin-valley coupling. Here we report detailed studies of opto-valleytronic properties of heterogeneous domains in CVD-grown monolayer WS₂ single crystals. By illuminating WS₂ with off-resonance circularly-polarized light and measuring the resulting spatially resolved circularly-polarized emission (P_circ), we find significantly large circular polarization (P_(circ) up to 60% and 45% for α- and β-domains, respectively) already at 300 K, which increases to nearly 90% in the α-domains at 80 K. Studies of spatially resolved photoluminescence (PL) spectroscopy, Raman spectroscopy, x-ray photoelectron spectroscopy (XPS), Kelvin-probe force microscopy (KPFM) and conductive atomic force microscopy (CAFM) reveal direct correlation among the PL intensity, defect densities and chemical potential, with the α-domains showing lower defect densities and a smaller work function by 0.13 eV than the β-domains. This work function difference indicates the occurrence of type-two band alignments between the α- and β-domains. We adapt a classical model to explain how electronically active defects may serve as non-radiative recombination centers, and find good agreement between experiments and the model. Scanning tunneling microscopic/spectroscopic (STM/STS) studies provide further evidences for tungsten vacancies (WVs) being the primary defects responsible for the suppressed PL and circular polarization in WS₂. These results therefore suggest a pathway to control the opto-valleytronic properties of TMDCs via defect engineering.

Publication: ACS Nano Vol.: 14 No.: 2 ISSN: 1936-0851

ID: CaltechAUTHORS:20190826-083214491

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Abstract: Topological quantum computation encodes quantum information nonlocally by nucleating non-Abelian anyons separated by distances L, typically spanning the qubit device size. This nonlocality renders topological qubits exponentially immune to dephasing from all sources of classical noise with operator support local on the scale of L. We perform detailed analytical and numerical analyses of a time-domain Ramsey-type protocol for noisy Majorana-based qubits that is designed to validate this coveted topological protection in near-term devices such as the so-called “tetron” design. By assessing dependence of dephasing times on tunable parameters, e.g., magnetic field, our proposed protocol can clearly distinguish a bona fide Majorana qubit from one constructed from semilocal Andreev bound states, which can otherwise closely mimic the true topological scenario in local probes. In addition, we analyze leakage of the qubit out of its low-energy manifold due to classical-noise-induced generation of quasiparticle excitations; leakage limits the qubit lifetime when the bulk gap collapses, and hence our protocol further reveals the onset of a topological phase transition. This experiment requires measurement of two nearby Majorana modes for both initialization and readout—achievable, for example, by tunnel coupling to a nearby quantum dot—but no further Majorana manipulations, and thus constitutes an enticing prebraiding experiment. Along the way, we address conceptual subtleties encountered when discussing dephasing and leakage in the context of Majorana qubits.

Publication: Physical Review B Vol.: 101 No.: 7 ISSN: 2469-9950

ID: CaltechAUTHORS:20200203-105634945

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Abstract: The accurate computation of Hamiltonian ground, excited and thermal states on quantum computers stands to impact many problems in the physical and computer sciences, from quantum simulation to machine learning. Given the challenges posed in constructing large-scale quantum computers, these tasks should be carried out in a resource-efficient way. In this regard, existing techniques based on phase estimation or variational algorithms display potential disadvantages; phase estimation requires deep circuits with ancillae, that are hard to execute reliably without error correction, while variational algorithms, while flexible with respect to circuit depth, entail additional high-dimensional classical optimization. Here, we introduce the quantum imaginary time evolution and quantum Lanczos algorithms, which are analogues of classical algorithms for finding ground and excited states. Compared with their classical counterparts, they require exponentially less space and time per iteration, and can be implemented without deep circuits and ancillae, or high-dimensional optimization. We furthermore discuss quantum imaginary time evolution as a subroutine to generate Gibbs averages through an analogue of minimally entangled typical thermal states. Finally, we demonstrate the potential of these algorithms via an implementation using exact classical emulation as well as through prototype circuits on the Rigetti quantum virtual machine and Aspen-1 quantum processing unit.

Publication: Nature Physics Vol.: 16 No.: 2 ISSN: 1745-2473

ID: CaltechAUTHORS:20190801-134541389

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Abstract: A distributed sensing protocol uses a network of local sensing nodes to estimate a global feature of the network, such as a weighted average of locally detectable parameters. In the noiseless case, continuous-variable (CV) multipartite entanglement shared by the nodes can improve the precision of parameter estimation relative to the precision attainable by a network without shared entanglement; for an entangled protocol, the root mean square estimation error scales like 1/M with the number M of sensing nodes, the so-called Heisenberg scaling, while for protocols without entanglement, the error scales like 1√M. However, in the presence of loss and other noise sources, although multipartite entanglement still has some advantages for sensing displacements and phases, the scaling of the precision with M is less favorable. In this paper, we show that using CV error correction codes can enhance the robustness of sensing protocols against imperfections and reinstate Heisenberg scaling up to moderate values of M. Furthermore, while previous distributed sensing protocols could measure only a single quadrature, we construct a protocol in which both quadratures can be sensed simultaneously. Our work demonstrates the value of CV error correction codes in realistic sensing scenarios.

Publication: New Journal of Physics Vol.: 22 No.: 2 ISSN: 1367-2630

ID: CaltechAUTHORS:20200430-121016107

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Abstract: We describe numerous properties of the Sachdev-Ye-Kitaev model for complex fermions with N ≫ 1 flavors and a global U(1) charge. We provide a general definition of the charge in the (G, Σ) formalism, and compute its universal relation to the infrared asymmetry of the Green function. The same relation is obtained by a renormalization theory. The conserved charge contributes a compact scalar field to the effective action, from which we derive the many-body density of states and extract the charge compressibility. We compute the latter via three distinct numerical methods and obtain consistent results. Finally, we present a two dimensional bulk picture with free Dirac fermions for the zero temperature entropy.

Publication: Journal of High Energy Physics Vol.: 2020 No.: 2 ISSN: 1029-8479

ID: CaltechAUTHORS:20200226-133542550

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Abstract: The transition metal thiophosphates MPS₃ (M=Mn, Fe, Ni) are a class of van der Waals stacked insulating antiferromagnets that can be exfoliated down to the ultrathin limit. MnPS₃ is particularly interesting because its Néel ordered state breaks both spatial-inversion and time-reversal symmetries, allowing for a linear magnetoelectric phase that is rare among van der Waals materials. However, it is unknown whether this unique magnetic structure of bulk MnPS₃ remains stable in the ultrathin limit. Using optical second harmonic generation rotational anisotropy, we show that long-range linear magnetoelectric type Néel order in MnPS₃ persists down to at least 5.3 nm thickness. However an unusual mirror symmetry breaking develops in ultrathin samples on SiO₂ substrates that is absent in bulk materials, which is likely related to substrate induced strain.

Publication: Physical Review Letters Vol.: 124 No.: 2 ISSN: 0031-9007

ID: CaltechAUTHORS:20200116-131511286

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Abstract: Strange metal behavior is ubiquitous in correlated materials, ranging from cuprate superconductors to bilayer graphene, and may arise from physics beyond the quantum fluctuations of a Landau order parameter. In quantum-critical heavy-fermion antiferromagnets, such physics may be realized as critical Kondo entanglement of spin and charge and probed with optical conductivity. We present terahertz time-domain transmission spectroscopy on molecular beam epitaxy–grown thin films of YbRh₂Si₂, a model strange-metal compound. We observed frequency over temperature scaling of the optical conductivity as a hallmark of beyond-Landau quantum criticality. Our discovery suggests that critical charge fluctuations play a central role in the strange metal behavior, elucidating one of the long-standing mysteries of correlated quantum matter.

Publication: Science Vol.: 367 No.: 6475 ISSN: 0036-8075

ID: CaltechAUTHORS:20200116-140345082

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Abstract: We investigate an approach for studying the ground state of a quantum many-body Hamiltonian that is based on treating the correlation functions as variational parameters. In this approach, the challenge set by the exponentially-large Hilbert space is circumvented by approximating the positivity of the density matrix, order-by-order, in a way that keeps track of a limited set of correlation functions. In particular, the density-matrix description is replaced by a correlation matrix whose dimension is kept linear in system size, to all orders of the approximation. Unlike the conventional variational principle which provides an upper bound on the ground-state energy, in this approach one obtains a lower bound instead. By treating several one-dimensional spin 1/2 Hamiltonians, we demonstrate the ability of this approach to produce long-range correlations, and a ground-state energy that converges to the exact result. Possible extensions, including to higher-excited states are discussed.

Publication: arXiv
ID: CaltechAUTHORS:20200303-081122185

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Abstract: Self-organized criticality is an elegant explanation of how complex structures emerge and persist throughout nature, and why such structures often exhibit similar scale-invariant properties. Although self-organized criticality is sometimes captured by simple models that feature a critical point as an attractor for the dynamics, the connection to real-world systems is exceptionally hard to test quantitatively. Here we observe three key signatures of self-organized criticality in the dynamics of a driven–dissipative gas of ultracold potassium atoms: self-organization to a stationary state that is largely independent of the initial conditions; scale-invariance of the final density characterized by a unique scaling function; and large fluctuations of the number of excited atoms (avalanches) obeying a characteristic power-law distribution. This work establishes a well-controlled platform for investigating self-organization phenomena and non-equilibrium criticality, with experimental access to the underlying microscopic details of the system.

Publication: Nature Vol.: 577 No.: 7791 ISSN: 0028-0836

ID: CaltechAUTHORS:20200122-094408831

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Abstract: Plasma enhanced chemical vapor deposition (PECVD) techniques have been shown to be an efficient method to achieve single-step synthesis of high-quality monolayer graphene (MLG) without the need of active heating. Here we report PECVD-growth of single-crystalline hexagonal bilayer graphene (BLG) flakes and mm-size BLG films with the interlayer twist angle controlled by the growth parameters. The twist angle has been determined by three experimental approaches, including direct measurement of the relative orientation of crystalline edges between two stacked monolayers by scanning electron microscopy, analysis of the twist angle-dependent Raman spectral characteristics, and measurement of the Moiré period with scanning tunneling microscopy. In mm-sized twisted BLG (tBLG) films, the average twist angle can be controlled from 0° to approximately 20°, and the angular spread for a given growth condition can be limited to < 7°. Different work functions between MLG and BLG have been verified by the Kelvin probe force microscopy and ultraviolet photoelectron spectroscopy. Electrical measurements of back-gated field-effect-transistor devices based on small-angle tBLG samples revealed high-quality electric characteristics at 300 K and insulating temperature dependence down to 100 K. This controlled PECVD-growth of tBLG thus provides an efficient approach to investigate the effect of varying Moiré potentials on tBLG.

Publication: Carbon Vol.: 156ISSN: 0008-6223

ID: CaltechAUTHORS:20190923-100220892

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Abstract: At the heart of recent progress in AdS/CFT is the question of subregion duality, or entanglement wedge reconstruction: which part(s) of the boundary CFT are dual to a given subregion of the bulk? This question can be answered by appealing to the quantum error correcting properties of holography, and it was recently shown that robust bulk (entanglement wedge) reconstruction can be achieved using a universal recovery channel known as the twirled Petz map. In short, one can use the twirled Petz map to recover bulk data from a subset of the boundary. However, this map involves an averaging procedure over bulk and boundary modular time, and hence it can be somewhat intractable to evaluate in practice. We show that a much simpler channel, the Petz map, is sufficient for entanglement wedge reconstruction for any code space of fixed finite dimension — no twirling is required. Moreover, the error in the reconstruction will always be non-perturbatively small. From a quantum information perspective, we prove a general theorem extending the use of the Petz map as a general-purpose recovery channel to subsystem and operator algebra quantum error correction.

Publication: Journal of High Energy Physics Vol.: 2020 No.: 1 ISSN: 1029-8479

ID: CaltechAUTHORS:20200129-105110731

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Abstract: A fully homomorphic encryption system hides data from unauthorized parties while still allowing them to perform computations on the encrypted data. Aside from the straightforward benefit of allowing users to delegate computations to a more powerful server without revealing their inputs, a fully homomorphic cryptosystem can be used as a building block in the construction of a number of cryptographic functionalities. Designing such a scheme remained an open problem until 2009, decades after the idea was first conceived, and the past few years have seen the generalization of this functionality to the world of quantum machines. Quantum schemes prior to the one implemented here were able to replicate some features in particular use cases often associated with homomorphic encryption but lacked other crucial properties, for example, relying on continual interaction to perform a computation or leaking information about the encrypted data. We present the first experimental realization of a quantum fully homomorphic encryption scheme. To demonstrate the versatility of a a quantum fully homomorphic encryption scheme, we further present a toy two-party secure computation task enabled by our scheme.

Publication: Physical Review X Vol.: 10 No.: 1 ISSN: 2160-3308

ID: CaltechAUTHORS:20200218-145344990

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Abstract: Recent evidence from magnetic torque, electron spin resonance, and second harmonic generation indicate that the prototypical quantum spin liquid candidate, herbertsmithite, has a symmetry lower than its x-ray refined trigonal space group. Here we consider known and possible distortions of this mineral class, along with related copper kagome oxides and fluorides, relate these to possible valence bond patterns, and comment on their relevance to the physics of these interesting materials.

Publication: Physical Review Research Vol.: 2 No.: 1 ISSN: 2643-1564

ID: CaltechAUTHORS:20200116-095411449

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Abstract: The AKLT spin chain is the prototypical example of a frustration-free quantum spin system with a spectral gap above its ground state. Affleck, Kennedy, Lieb, and Tasaki also conjectured that the two-dimensional version of their model on the hexagonal lattice exhibits a spectral gap. In this paper, we introduce a family of variants of the two-dimensional AKLT model depending on a positive integer n, which is defined by decorating the edges of the hexagonal lattice with one-dimensional AKLT spin chains of length n. We prove that these decorated models are gapped for all n ≥ 3.

Publication: Contemporary Mathematics No.: 741 ISSN: 0271-4132

ID: CaltechAUTHORS:20200922-071519332

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Abstract: The resource theory of thermal operations, an established model for small-scale thermodynamics, provides an extension of equilibrium thermodynamics to nonequilibrium situations. On a lattice of any dimension with any translation-invariant local Hamiltonian, we identify a large set of translation-invariant states that can be reversibly converted to and from the thermal state with thermal operations and a small amount of coherence. These are the spatially ergodic states, i.e., states that have sharp statistics for any translation-invariant observable, and mixtures of such states with the same thermodynamic potential. As an intermediate result, we show for a general state that if the gap between the min- and the max-relative entropies to the thermal state is small, then the state can be approximately reversibly converted to and from the thermal state with thermal operations and a small source of coherence. Our proof provides a quantum version of the Shannon-McMillan-Breiman theorem for the relative entropy and a quantum Stein’s lemma for ergodic states and local Gibbs states. Our results provide a strong link between the abstract resource theory of thermodynamics and more realistic physical systems as we achieve a robust and operational characterization of the emergence of a thermodynamic potential in translation-invariant lattice systems.

Publication: Physical Review Letters Vol.: 123 No.: 25 ISSN: 0031-9007

ID: CaltechAUTHORS:20190801-134555157

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Abstract: In this paper, we study the evaporation dynamics of the Sachdev-Ye-Kitaev model, with an initial temperature T_χ, by coupling it to a thermal bath with lower temperature T_ψ < T_χ modeled by a larger SYK model. The coupling between the small system and the bath is turned on at time t = 0. Then the system begins to evolve and finally becomes thermalized. Using the Keldysh approach, we analyze the relaxation process of the system for different temperatures and couplings. For marginal or irrelevant coupling, after a short-time energy absorption, we find a smooth thermalization of the small system where the energy relaxes before the system become thermalized. The relaxation rate of effective temperature is found to be bounded by T, while the energy thermalization rate increases without saturation when increasing the coupling strength. On the contrary, for the relevant coupling case, both energy and effective temperature show oscillations. We find this oscillations frequency to be coincident with the typical excitation energy of the small SYK system.

Publication: Physical Review B Vol.: 100 No.: 24 ISSN: 2469-9950

ID: CaltechAUTHORS:20191203-133552677

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Abstract: The concept of quantum complexity has far-reaching implications spanning theoretical computer science, quantum many-body physics, and high energy physics. The quantum complexity of a unitary transformation or quantum state is defined as the size of the shortest quantum computation that executes the unitary or prepares the state. It is reasonable to expect that the complexity of a quantum state governed by a chaotic many-body Hamiltonian grows linearly with time for a time that is exponential in the system size; however, because it is hard to rule out a short-cut that improves the efficiency of a computation, it is notoriously difficult to derive lower bounds on quantum complexity for particular unitaries or states without making additional assumptions. To go further, one may study more generic models of complexity growth. We provide a rigorous connection between complexity growth and unitary k-designs, ensembles which capture the randomness of the unitary group. This connection allows us to leverage existing results about design growth to draw conclusions about the growth of complexity. We prove that local random quantum circuits generate unitary transformations whose complexity grows linearly for a long time, mirroring the behavior one expects in chaotic quantum systems and verifying conjectures by Brown and Susskind. Moreover, our results apply under a strong definition of quantum complexity based on optimal distinguishing measurements.

Publication: arXiv
ID: CaltechAUTHORS:20210512-095238258

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Abstract: We demonstrate quantum many-body state reconstruction from experimental data generated by a programmable quantum simulator by means of a neural-network model incorporating known experimental errors. Specifically, we extract restricted Boltzmann machine wave functions from data produced by a Rydberg quantum simulator with eight and nine atoms in a single measurement basis and apply a novel regularization technique to mitigate the effects of measurement errors in the training data. Reconstructions of modest complexity are able to capture one- and two-body observables not accessible to experimentalists, as well as more sophisticated observables such as the Rényi mutual information. Our results open the door to integration of machine learning architectures with intermediate-scale quantum hardware.

Publication: Physical Review Letters Vol.: 123 No.: 23 ISSN: 0031-9007

ID: CaltechAUTHORS:20190809-100641765

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Abstract: An elusive goal in the field of driven quantum matter is the induction of long-range order. Here, we propose a mechanism based on light-induced evaporative cooling of holes in a correlated fermionic system. Since the entropy of a filled narrow band grows rapidly with hole doping, the isentropic transfer of holes from a doped Mott insulator to such a band results in a drop of temperature. Strongly correlated Fermi liquids and symmetry-broken states could thus be produced by dipolar excitations. Using nonequilibrium dynamical mean field theory, we show that suitably designed chirped pulses may realize this cooling effect. In particular, we demonstrate the emergence of antiferromagnetic order in a system which is initially in a weakly correlated state above the maximum Néel temperature. Our work suggests a general strategy for inducing strong correlation phenomena in periodically modulated atomic gases in optical lattices or light-driven materials.

Publication: Nature Communications Vol.: 10ISSN: 2041-1723

ID: CaltechAUTHORS:20190425-142141029

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Abstract: We present a scheme to control the spin-exchange interactions by manipulating the orbital degrees of freedom using a periodic drive. We discuss two different protocols for orbital Floquet engineering. In one case, a periodic drive modifies the properties of the ligand orbitals which mediate magnetic interactions between transition-metal ions. In the other case, we consider drive-induced mixing of d orbitals on each magnetic ion. We first find that an AC Stark shift of orbitals induces a change comparable to that induced from photoinduced hopping schemes, but expands the applicable frequency ranges. Next, we find that radiatively induced coherent vibrations provide a realistic path for Floquet orbital engineering with short pulses of electric fields weaker than 0.5 V/Å producing 5%–10% changes in the magnetic coupling of Mott insulators such as the rare-earth titanates.

Publication: Physical Review B Vol.: 100 No.: 22 ISSN: 2469-9950

ID: CaltechAUTHORS:20190520-132243974

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Abstract: We study fermionic topological phases using the technique of fermion condensation. We give a prescription for performing fermion condensation in bosonic topological phases that contain a fermion. Our approach to fermion condensation can roughly be understood as coupling the parent bosonic topological phase to a phase of physical fermions and condensing pairs of physical and emergent fermions. There are two distinct types of objects in the resulting fermionic fusion categories, which we call “m-type” and “q-type” objects. The endomorphism algebras of q-type objects are complex Clifford algebras, and they have no analogs in bosonic theories. We construct a fermionic generalization of the tube category, which allows us to compute the quasiparticle excitations arising from the condensed theories. We prove a series of results relating data in fermionic theories to data in their parent bosonic theories; for example, if C is a modular tensor category containing a fermion, then the tube category constructed from the condensed theory satisfies Tube(C/ψ)≅C×(C/ψ). We also study how modular transformations, fusion rules, and coherence relations are modified in the fermionic setting, prove a fermionic version of the Verlinde dimension formula, construct a commuting projector lattice Hamiltonian for fermionic theories, and write down a fermionic version of the Turaev-Viro-Barrett-Westbury state sum. A large portion of this work is devoted to three detailed examples of performing fermion condensation to produce fermionic topological phases: we condense fermions in the Ising theory, the SO(3)₆ theory, and the ½E₆ theory and compute the quasiparticle excitation spectrum in each of the condensed theories.

Publication: Journal of Mathematical Physics Vol.: 60 No.: 12 ISSN: 0022-2488

ID: CaltechAUTHORS:20180129-085443018

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Abstract: A non-interactive zero-knowledge (NIZK) proof system for a language L∈NP allows a prover (who is provided with an instance x∈L, and a witness w for x) to compute a classical certificate π for the claim that x∈L such that π has the following properties: 1) π can be verified efficiently, and 2) π does not reveal any information about w, besides the fact that it exists (i.e. that x∈L). NIZK proof systems have recently been shown to exist for all languages in NP in the common reference string (CRS) model and under the learning with errors (LWE) assumption. We initiate the study of NIZK arguments for languages in QMA. Our first main result is the following: if LWE is hard for quantum computers, then any language in QMA has an NIZK argument with preprocessing. The preprocessing in our argument system consists of (i) the generation of a CRS and (ii) a single (instance-independent) quantum message from verifier to prover. The instance-dependent phase of our argument system involves only a single classical message from prover to verifier. Importantly, verification in our protocol is entirely classical, and the verifier needs not have quantum memory; its only quantum actions are in the preprocessing phase. Our second contribution is to extend the notion of a classical proof of knowledge to the quantum setting. We introduce the notions of arguments and proofs of quantum knowledge (AoQK/PoQK), and we show that our non-interactive argument system satisfies the definition of an AoQK. In particular, we explicitly construct an extractor which can recover a quantum witness from any prover who is successful in our protocol. We also show that any language in QMA has an (interactive) proof of quantum knowledge.

Publication: arXiv
ID: CaltechAUTHORS:20200110-140701565

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Abstract: We establish a set of recursion relations for the coefficients in the chromatic polynomial of a graph or a hypergraph. As an application we provide a generalization of Whitney's broken cycle theorem for hypergraphs, as well as deriving an explicit formula for the linear coefficient of the chromatic polynomial of the -complete hypergraph in terms of roots of the Taylor polynomials for the exponential function.

Publication: Discussiones Mathematicae Graph Theory Vol.: 42 No.: 1 ISSN: 1234-3099

ID: CaltechAUTHORS:20220127-789177900

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Abstract: In this paper we discuss the Casimir effect in a small cavity, freely falling from spatial infinity in spacetime geometry outside of a Schwarzschild black hole. Our main goal is to search for possible changes in the vacuum energy, as well as particle creation inside the falling cavity, with respect to a comoving observer. Working in the Lemaître chart and assuming a cavity size L much smaller than the Schwarzschild radius (L/r_g≪1), we solve the Klein-Gordon equation for a massless scalar field confined within the cavity in the reference frame of the comoving observer. We follow Schwinger’s proper time approach, evaluating the one-loop effective action for the field in the falling cavity hence evaluating the corrections to the vacuum energy. We find a small reduction in the absolute value of Casimir energy as the cavity approaches the black hole horizon due to the changing spacetime geometry. Since the spacetime geometry for the cavity changes dynamically, we further find the energy density of the created particles due to the dynamical Casimir effect. These dynamical contributions exactly match the deficit to the static Casimir energy. Combined, the observer measures a net increase in energy within the cavity as she falls.

Publication: Physical Review D Vol.: 100 No.: 10 ISSN: 2470-0010

ID: CaltechAUTHORS:20191112-093022435

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Abstract: We introduce a protocol between a classical polynomial-time verifier and a quantum polynomial-time prover that allows the verifier to securely delegate to the prover the preparation of certain single-qubit quantum states The prover is unaware of which state he received and moreover, the verifier can check with high confidence whether the preparation was successful. The delegated preparation of single-qubit states is an elementary building block in many quantum cryptographic protocols. We expect our implementation of "random remote state preparation with verification", a functionality first defined in (Dunjko and Kashefi 2014), to be useful for removing the need for quantum communication in such protocols while keeping functionality. The main application that we detail is to a protocol for blind and verifiable delegated quantum computation (DQC) that builds on the work of (Fitzsimons and Kashefi 2018), who provided such a protocol with quantum communication. Recently, both blind an verifiable DQC were shown to be possible, under computational assumptions, with a classical polynomial-time client (Mahadev 2017, Mahadev 2018). Compared to the work of Mahadev, our protocol is more modular, applies to the measurement-based model of computation (instead of the Hamiltonian model) and is composable. Our proof of security builds on ideas introduced in (Brakerski et al. 2018).

ID: CaltechAUTHORS:20200109-143243905

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Abstract: Twisted bilayer graphene with a twist angle of around 1.1° features a pair of isolated flat electronic bands and forms a platform for investigating strongly correlated electrons. Here, we use scanning tunnelling microscopy to probe the local properties of highly tunable twisted bilayer graphene devices and show that the flat bands deform when aligned with the Fermi level. When the bands are half-filled, we observe the development of gaps originating from correlated insulating states. Near charge neutrality, we find a previously unidentified correlated regime featuring an enhanced splitting of the flat bands. We describe this within a microscopic model that predicts a strong tendency towards nematic ordering. Our results provide insights into symmetry-breaking correlation effects and highlight the importance of electronic interactions for all filling fractions in twisted bilayer graphene.

Publication: Nature Physics Vol.: 15 No.: 11 ISSN: 1745-2473

ID: CaltechAUTHORS:20190426-084652512

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Abstract: Fractional excitations in fracton models exhibit novel features not present in conventional topological phases: their mobility is constrained, there are an infinitude of types, and they bear an exotic sense of ‘braiding’. Hence, they require a new framework for proper characterization. Based on our definition of foliated fracton phases in which equivalence between models includes the possibility of adding layers of gapped 2D states, we propose to characterize fractional excitations in these phases up to the addition of quasiparticles with 2D mobility. That is, two quasiparticles differing by a set of quasiparticles that move along 2D planes are considered to be equivalent; likewise, ‘braiding’ statistics are measured in a way that is insensitive to the attachment of 2D quasiparticles. The fractional excitation types and statistics defined in this way provide a universal characterization of the underlying foliated fracton order which can subsequently be used to establish phase relations. We demonstrate as an example the equivalence between the X-cube model and the semionic X-cube model both in terms of fractional excitations and through an exact mapping.

Publication: Annals of Physics Vol.: 410ISSN: 0003-4916

ID: CaltechAUTHORS:20181023-102132294

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Abstract: Quantum mechanics and the theory of operator algebras have been intertwined since their origin. In the 1930s [20] von Neumann laid the foundations for the theory of (what are now known as) von Neumann algebras with the explicit goal of establishing Heisenberg’s matrix mechanics on a rigorous footing (quoting from the preface, in the translation by Beyer: “The object of this book is to present the new quantum mechanics in a unified representation which, so far as it is possible and useful, is mathematically rigorous”). Following the initial explorations of Murray and von Neumann, the new theory took on a life of its own, eventually leading to multiple applications unrelated to quantum mechanics, such as to free probability or noncommutative geometry.

Publication: Notices of the American Mathematical Society Vol.: 66 No.: 10 ISSN: 0002-9920

ID: CaltechAUTHORS:20200728-152043230

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Abstract: The efficient validation of quantum devices is critical for emerging technological applications. In a wide class of use cases the precise engineering of a Hamiltonian is required both for the implementation of gate-based quantum information processing as well as for reliable quantum memories. Inferring the experimentally realized Hamiltonian through a scalable number of measurements constitutes the challenging task of Hamiltonian learning. In particular, assessing the quality of the implementation of topological codes is essential for quantum error correction. Here, we introduce a neural-net-based approach to this challenge. We capitalize on a family of exactly solvable models to train our algorithm and generalize to a broad class of experimentally relevant sources of errors. We discuss how our algorithm scales with system size and analyze its resilience toward various noise sources.

Publication: Physical Review Research Vol.: 1 No.: 3 ISSN: 2643-1564

ID: CaltechAUTHORS:20191112-093455800

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Abstract: We study multiprover interactive proof systems. The power of classical multiprover interactive proof systems, in which the provers do not share entanglement, was characterized in a famous work by Babai, Fortnow, and Lund (Computational Complexity 1991), whose main result was the equality MIP = NEXP. The power of quantum multiprover interactive proof systems, in which the provers are allowed to share entanglement, has proven to be much more difficult to characterize. The best known lower-bound on MIP* is NEXP ⊆ MIP*, due to Ito and Vidick (FOCS 2012). As for upper bounds, MIP* could be as large as RE, the class of recursively enumerable languages. The main result of this work is the inclusion of NEEXP = NTIME[2^(2poly(n))] ⊆ MIP*. This is an exponential improvement over the prior lower bound and shows that proof systems with entangled provers are at least exponentially more powerful than classical provers. In our protocol the verifier delegates a classical, exponentially large MIP protocol for NEEXP to two entangled provers: the provers obtain their exponentially large questions by measuring their shared state, and use a classical PCP to certify the correctness of their exponentially-long answers. For the soundness of our protocol, it is crucial that each player should not only sample its own question correctly but also avoid performing measurements that would reveal the other player's sampled question. We ensure this by commanding the players to perform a complementary measurement, relying on the Heisenberg uncertainty principle to prevent the forbidden measurements from being performed.

ID: CaltechAUTHORS:20200109-143243997

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Abstract: Nearest-neighbor interacting S = 1/2 spins on the ideal Kagomé lattice are predicted to form a variety of novel quantum entangled states, including quantum spin-liquid (SL) and valence bond solid (VBS) phases. In real materials, the presence of additional perturbative spin interactions may further expand the variety of entangled states, which recent theoretical analyses show are identifiable through the spontaneous loss of particular discrete point group symmetries. Here we comprehensively resolve the ground state point group symmetries of the prototypical Kagomé SL candidate ZnCu₃(OH)₆Cl₂ (Herbertsmithite) using a combination of optical ellipsometry and wavelength-dependent multi-harmonic optical polarimetry. We uncover a subtle parity breaking monoclinic structural distortion at a temperature above the nearest-neighbor exchange energy scale. Surprisingly, the parity-breaking order parameter is dramatically enhanced upon cooling and closely tracks the build-up of nearest-neighbor spin correlations, suggesting that it is energetically favored by the SL state. The refined low temperature symmetry group greatly restricts the number of viable ground states, and, in the perturbative limit, points toward the formation of a nematic Z₂ striped SL ground state - a SL analogue of a liquid crystal.

Publication: arXiv
ID: CaltechAUTHORS:20191218-130358489

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Abstract: Gerrymandering is a long-standing issue within the U.S. political system, and it has received scrutiny recently by the U.S. Supreme Court. In this note, we prove that deciding whether there exists a fair redistricting among legal maps is -hard. To make this precise, we use simplified notions of “legal” and “fair” that account for desirable traits such as geographic compactness of districts and sufficient representation of voters. The proof of our result is inspired by the work of Mahanjan, Minbhorkar and Varadarajan that proves that planar k-means is -hard.

Publication: Theoretical Computer Science Vol.: 791ISSN: 0304-3975

ID: CaltechAUTHORS:20190528-132709883

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Abstract: The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2⁵³ (about 10¹⁶). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times—our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy for this specific computational task, heralding a much-anticipated computing paradigm.

Publication: Nature Vol.: 574 No.: 7779 ISSN: 0028-0836

ID: CaltechAUTHORS:20191028-155653039

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Abstract: Inspired by a recently constructed commuting-projector Hamiltonian for a two-dimensional (2D) time-reversal-invariant topological superconductor [Z. Wang et al., Phys. Rev. B 98, 094502 (2018)], we introduce a commuting-projector model that describes an interacting yet exactly solvable 2D topological insulator. We explicitly show that both the gapped and gapless boundaries of our model are consistent with those of band-theoretic, weakly interacting topological insulators. Interestingly, on certain lattices our time-reversal-symmetric models also enjoy CP symmetry, leading to intuitive interpretations of the bulk invariant for a CP-symmetric topological insulator upon putting the system on a Klein bottle. We also briefly discuss how these many-body invariants may be able to characterize models with only time-reversal symmetry.

Publication: Physical Review B Vol.: 100 No.: 15 ISSN: 2469-9950

ID: CaltechAUTHORS:20191004-085117901

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Abstract: Currently, the most accurate and stable clocks use optical interrogation of either a single ion or an ensemble of neutral atoms confined in an optical lattice. Here, we demonstrate a new optical clock system based on an array of individually trapped neutral atoms with single-atom readout, merging many of the benefits of ion and lattice clocks as well as creating a bridge to recently developed techniques in quantum simulation and computing with neutral atoms. We evaluate single-site resolved frequency shifts and short-term stability via self-comparison. Atom-by-atom feedback control enables direct experimental estimation of laser noise contributions. Results agree well with an ab initio Monte Carlo simulation that incorporates finite temperature, projective read-out, laser noise, and feedback dynamics. Our approach, based on a tweezer array, also suppresses interaction shifts while retaining a short dead time, all in a comparatively simple experimental setup. These results establish the foundations for a third optical clock platform suited to advance stationary and transportable clock systems, while providing a novel starting point for entanglement-enhanced metrology and quantum clock networks as well as applications in quantum computing and communication with individual neutral atoms requiring optical clock state control.

Publication: Physical Review X Vol.: 9 No.: 4 ISSN: 2160-3308

ID: CaltechAUTHORS:20191022-085737494

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Abstract: The performance of solid-state quantum sensors based on electronic spin defects is often limited by the presence of environmental spin impurities that cause decoherence. A promising approach to improve these quantum sensors is to convert environment spins into useful resources for sensing, in particular, entangled states. However, the sensitivity enhancement that can be achieved from entangled states is limited by experimental constraints, such as control errors, decoherence, and time overheads. Here we experimentally demonstrate the efficient use of an unknown electronic spin defect in the proximity of a nitrogen-vacancy center in diamond to achieve both an entangled quantum sensor and a quantum memory for readout. We show that, whereas entanglement alone does not provide an enhancement in sensitivity, combining both entanglement and repetitive readout achieves an enhancement in performance over the use of a single-spin sensor, and more broadly we discuss regimes where sensitivity could be enhanced. Our results critically highlight the challenges in improving quantum sensors using entangled states of electronic spins, while providing an important benchmark in the quest for entanglement-assisted metrology.

Publication: Physical Review Applied Vol.: 12 No.: 4 ISSN: 2331-7019

ID: CaltechAUTHORS:20191022-154116538

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Abstract: The t-J model is believed to be a minimal model that may be capable of describing the low-energy physics of the cuprate superconductors. However, although the t-J model is simple in appearance, obtaining a detailed understanding of its phase diagram has proved to be challenging. We are therefore motivated to study modifications to the t-J model such that its phase diagram and mechanism for d-wave superconductivity can be understood analytically without making uncontrolled approximations. The modified model we consider is a t'-J_z-V model on a square lattice, which has a second-nearest-neighbor hopping t' (instead of a nearest-neighbor hopping t), an Ising (instead of Heisenberg) antiferromagnetic coupling J_z, and a nearest-neighbor repulsion V. In a certain strongly interacting limit, the ground state is an antiferromagnetic superconductor that can be described exactly by a Hamiltonian where the only interaction is a nearest-neighbor attraction. BCS theory can then be applied with arbitrary analytical control, from which nodeless d-wave or s-wave superconductivity can result.

Publication: SciPost Physics Vol.: 7 No.: 4 ISSN: 2542-4653

ID: CaltechAUTHORS:20190807-104734541

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Abstract: A key feature of ground states of gapped local 1D Hamiltonians is their relatively low entanglement --- they are well approximated by matrix product states (MPS) with bond dimension scaling polynomially in the length N of the chain, while general states require a bond dimension scaling exponentially. We show that the bond dimension of these MPS approximations can be improved to a constant, independent of the chain length, if we relax our notion of approximation to be more local: for all length-k segments of the chain, the reduced density matrices of our approximations are ϵ-close to those of the exact state. If the state is a ground state of a gapped local Hamiltonian, the bond dimension of the approximation scales like (k/ϵ)^(1+o(1)), and at the expense of worse but still poly(k,1/ϵ) scaling of the bond dimension, we give an alternate construction with the additional features that it can be generated by a constant-depth quantum circuit with nearest-neighbor gates, and that it applies generally for any state with exponentially decaying correlations. For a completely general state, we give an approximation with bond dimension exp(O(k/ϵ)), which is exponentially worse, but still independent of N. Then, we consider the prospect of designing an algorithm to find a local approximation for ground states of gapped local 1D Hamiltonians. When the Hamiltonian is translationally invariant, we show that the ability to find O(1)-accurate local approximations to the ground state in T(N) time implies the ability to estimate the ground state energy to O(1) precision in O(T(N)log(N)) time.

Publication: Quantum Vol.: 3ISSN: 2521-327X

ID: CaltechAUTHORS:20190801-134544835

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Abstract: Quantum error correction was invented to allow for fault-tolerant quantum computation. Systems with topological order turned out to give a natural physical realization of quantum error correcting codes (QECC) in their ground spaces. More recently, in the context of the anti-de Sitter/conformal field theory correspondence, it has been argued that eigenstates of CFTs with a holographic dual should also form QECCs. These two examples raise the question of how generally eigenstates of many-body models form quantum codes. In this Letter we establish new connections between quantum chaos and translation invariance in many-body spin systems, on one hand, and approximate quantum error correcting codes (AQECC), on the other hand. We first observe that quantum chaotic systems obeying the eigenstate thermalization hypothesis have eigenstates forming approximate quantum error-correcting codes. Then we show that AQECC can be obtained probabilistically from translation-invariant energy eigenstates of every translation-invariant spin chain, including integrable models. Applying this result to 1D classical systems, we describe a method for using local symmetries to construct parent Hamiltonians that embed these codes into the low-energy subspace of gapless 1D quantum spin chains. As explicit examples we obtain local AQECC in the ground space of the 1D ferromagnetic Heisenberg model and the Motzkin spin chain model with periodic boundary conditions, thereby yielding nonstabilizer codes in the ground space and low energy subspace of physically plausible 1D gapless models.

Publication: Physical Review Letters Vol.: 123 No.: 11 ISSN: 0031-9007

ID: CaltechAUTHORS:20190206-155714600

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Abstract: A topological superconductor is characterized by having a pairing gap in the bulk and gapless self-hermitian Majorana modes at its boundary. In one dimension, these are zero-energy modes bound to the ends, while in two dimensions these are chiral gapless modes traveling along the edge. Majorana modes have attracted a lot of interest due to their exotic properties, which include non-abelian exchange statistics. Progress in realizing topological superconductivity has been made by combining spin–orbit coupling, conventional superconductivity, and magnetism. The existence of protected Majorana modes, however, does not inherently require the breaking of time-reversal symmetry by magnetic fields. Indeed, pairs of Majorana modes can reside at the boundary of a time-reversal-invariant topological superconductor (TRITOPS). It is the time-reversal symmetry which then protects this so-called Majorana Kramers’ pair from gapping out. This is analogous to the case of the two-dimensional topological insulator, with its pair of helical gapless boundary modes, protected by time-reversal symmetry. Realizing the TRITOPS phase will be a major step in the study of topological phases of matter. In this paper we describe the physical properties of the TRITOPS phase, and review recent proposals for engineering and detecting them in condensed matter systems, in one and two spatial dimensions. We mostly focus on extrinsic superconductors, where superconductivity is introduced through the proximity effect. We emphasize the role of interplay between attractive and repulsive electron–electron interaction as an underlying mechanism. When discussing the detection of the TRITOPS phase, we focus on the physical imprint of Majorana Kramers’ pairs, and review proposals of transport measurement which can reveal their existence.

Publication: Physics Reports Vol.: 825ISSN: 0370-1573

ID: CaltechAUTHORS:20190814-101137520

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Abstract: Anderson localization on treelike graphs such as the Bethe lattice, Cayley tree, or random regular graphs has attracted attention due to its apparent mathematical tractability, hypothesized connections to many-body localization, and the possibility of nonergodic extended regimes. This behavior has been conjectured to also appear in many-body localization as a “bad metal” phase, and constitutes an intermediate possibility between the extremes of ergodic quantum chaos and integrable localization. Despite decades of research, a complete consensus understanding of this model remains elusive. Here we use cages, maximally treelike structures from extremal graph theory; and numerical continuous unitary Wegner flows of the Anderson Hamiltonian to develop an intuitive picture which, after extrapolating to the infinite Bethe lattice, appears to capture ergodic, nonergodic extended, and fully localized behavior.

Publication: Physical Review B Vol.: 100 No.: 9 ISSN: 2469-9950

ID: CaltechAUTHORS:20190425-135640601

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Abstract: With the help of recent developments in quantum algorithms for semidefinite programming, we discuss the possibility for quantum speedup for the numerical conformal bootstrap in conformal field theory. We show that quantum algorithms may have significant improvement in the computational performance for several numerical bootstrap problems.

Publication: Nuclear Physics B Vol.: 946ISSN: 0550-3213

ID: CaltechAUTHORS:20181119-150510184

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Abstract: Motivated by the close relationship between quantum error-correction, topological order, the holographic AdS/CFT duality, and tensor networks, we initiate the study of approximate quantum error-detecting codes in matrix product states (MPS). We first show that using open-boundary MPS to define boundary to bulk encoding maps yields at most constant distance error-detecting codes. These are degenerate ground spaces of gapped local Hamiltonians. To get around this no-go result, we consider excited states, i.e., we use the excitation ansatz to construct encoding maps: these yield error-detecting codes with distance Ω(n^(1−ν)) for any ν ∈ (0, 1) and Ω(log n) encoded qubits. This shows that gapped systems contain — within isolated energy bands — error-detecting codes spanned by momentum eigenstates. We also consider the gapless Heisenberg-XXX model, whose energy eigenstates can be described via Bethe ansatz tensor networks. We show that it contains — within its low-energy eigenspace — an error-detecting code with the same parameter scaling. All these codes detect arbitrary d-local (not necessarily geometrically local) errors even though they are not permutation-invariant. This suggests that a wide range of naturally occurring many-body systems possess intrinsic error-detecting features.

Publication: Journal of High Energy Physics Vol.: 2019 No.: 9 ISSN: 1029-8479

ID: CaltechAUTHORS:20190905-141023968

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Abstract: We examine the advantages that quantum strategies afford in communication-limited games. Inspired by the card game blackjack, we focus on cooperative, two-party sequential games in which a single classical bit of communication is allowed from the player who moves first to the player who moves second. Within this setting, we explore the usage of quantum entanglement between the players and find analytic and numerical conditions for quantum advantage over classical strategies. Using these conditions, we study a family of blackjack-type games with varying numbers of card types, and find a range of parameters where quantum advantage is achieved. Furthermore, we give an explicit quantum circuit for the strategy achieving quantum advantage.

Publication: arXiv
ID: CaltechAUTHORS:20200417-132554488

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Abstract: We study the entanglement entropy of eigenstates (including the ground state) of the Sachdev-Ye-Kitaev model. We argue for a volume law, whose coefficient can be calculated analytically from the density of states. The coefficient depends on not only the energy density of the eigenstate but also the subsystem size. Very recent numerical results of Liu et al. confirm our analytical results.

Publication: Physical Review D Vol.: 100 No.: 4 ISSN: 2470-0010

ID: CaltechAUTHORS:20190805-081806167

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Abstract: We derive new bounds on higher-dimension operator coefficients in four-dimensional Einstein-Maxwell theory. Positivity of classically generated corrections to the Wald entropy of thermodynamically stable, rotating dyonic black holes implies a multiparameter family of field basis invariant inequalities that exhibit electromagnetic duality and are satisfied by examples from field and string theory. These bounds imply that effective operators modify the extremality condition of large black holes so as to permit their decay to smaller ones, thus satisfying the weak gravity conjecture.

Publication: Physical Review D Vol.: 100 No.: 4 ISSN: 2470-0010

ID: CaltechAUTHORS:20190408-135605710

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Abstract: We establish the presence of foliated fracton order in the Majorana checkerboard model. In particular, we describe an entanglement renormalization group transformation which utilizes toric code layers as resources of entanglement and furthermore discuss entanglement signatures and fractional excitations of the model. In fact, we give an exact local unitary equivalence between the Majorana checkerboard model and the semionic X-cube model augmented with decoupled fermionic modes. This mapping demonstrates that the model lies within the X-cube foliated fracton phase.

Publication: Physical Review B Vol.: 100 No.: 8 ISSN: 2469-9950

ID: CaltechAUTHORS:20190624-080757714

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Abstract: The mixing of orbital and spin character in the wave functions of the 5d iridates has led to predictions of strong couplings among their lattice, electronic, and magnetic degrees of freedom. As well as realizing a novel spin-orbit assisted Mott-insulating ground state, the perovskite iridate Sr_2IrO_4 has strong similarities with the cuprate La_2CuO_4, which on doping hosts a charge-density wave that appears intimately connected to high-temperature superconductivity. These phenomena can be sensitively probed through momentum-resolved measurements of the lattice dynamics, made possible by meV-resolution inelastic x-ray scattering. Here we report the first such measurements for both parent and electron-doped Sr_2IrO_4. We find that the low-energy phonon dispersions and intensities in both compounds are well described by the same nonmagnetic density functional theory calculation. In the parent compound, no changes of the phonons on magnetic ordering are discernible within the experimental resolution, and in the doped compound no anomalies are apparent due to charge-density waves. These measurements extend our knowledge of the lattice properties of (Sr_(1−x)La_x)_2IrO_4 and constrain the couplings of the phonons to magnetic and charge order.

Publication: Physical Review B Vol.: 100 No.: 8 ISSN: 2469-9950

ID: CaltechAUTHORS:20190819-101754313

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Abstract: Quantum entanglement involving coherent superpositions of macroscopically distinct states is among the most striking features of quantum theory, but its realization is challenging because such states are extremely fragile. Using a programmable quantum simulator based on neutral atom arrays with interactions mediated by Rydberg states, we demonstrate the creation of “Schrödinger cat” states of the Greenberger-Horne-Zeilinger (GHZ) type with up to 20 qubits. Our approach is based on engineering the energy spectrum and using optimal control of the many-body system. We further demonstrate entanglement manipulation by using GHZ states to distribute entanglement to distant sites in the array, establishing important ingredients for quantum information processing and quantum metrology.

Publication: Science Vol.: 365 No.: 6453 ISSN: 0036-8075

ID: CaltechAUTHORS:20190808-135256638

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Abstract: Tunneling spectroscopy reveals evidence for interlayer electron-hole correlations in quantum Hall bilayer two-dimensional electron systems at layer separations near, but above, the transition to the incompressible exciton condensate at total Landau level filling ν_T = 1. These correlations are manifested by a nonlinear suppression of the Coulomb pseudogap which inhibits low energy interlayer tunneling in weakly coupled bilayers. The pseudogap suppression is strongest at ν_T = 1 and grows rapidly as the critical layer separation for exciton condensation is approached from above.

Publication: Physical Review Letters Vol.: 123 No.: 6 ISSN: 0031-9007

ID: CaltechAUTHORS:20190513-075922050

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Abstract: Different fields of physics characterize differently how much two quantum operations disagree: quantum information theory features uncertainty relations cast in terms of entropies. The higher an uncertainty bound, the less compatible the operations. In condensed matter and high-energy physics, initially localized, far-apart operators come to disagree as entanglement spreads through a quantum many-body system. This spread, called “scrambling,” is quantified with the out-of-time-ordered correlator (OTOC). We unite these two measures of operation disagreement by proving entropic uncertainty relations for scrambling. The uncertainty bound depends on the quasiprobability (the nonclassical generalization of a probability) known to average to the OTOC. The quasiprobability strengthens the uncertainty bound, we find, when a spin chain scrambles in numerical simulations. Hence our entropic uncertainty relations reflect the same incompatibility as scrambling, uniting two fields’ notions of quantum-operation disagreement.

Publication: Communications Physics Vol.: 2ISSN: 2399-3650

ID: CaltechAUTHORS:20180614-124115479

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Abstract: We show that interactions can drive a class of higher order topological superconductors (HOTSCs) into symmetry-enriched topologically ordered phases exemplified by topological quantum error correcting codes. In two dimensions, interacting HOTSCs realize various topologically ordered surface and color codes. In three dimensions, interactions can drive HOTSCs protected by subsystem symmetries into recently discovered fracton phases. We explicitly relate fermion parity operators underlying the gapless excitations of the HOTSC to the Wilson algebra of symmetry-enriched quantum codes. Arrays of crossed Majorana wires provide an experimental platform for realizing fracton matter and for probing the quantum phase transition between HOTSCs and the topologically ordered phase.

Publication: Physical Review B Vol.: 100 No.: 5 ISSN: 2469-9950

ID: CaltechAUTHORS:20190816-100424619

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Abstract: We examine the question of whether a π junction can spontaneously form in a Josephson junction between two topological superconductors. We study a junction between two time-reversal-invariant topological superconductors and show this system goes through a series of multiple transitions between a 0-junction phase, where the free energy has its minimum for a superconducting phase difference of zero, and a π-junction phase, where the free energy has its minimum for a superconducting phase difference of π. These transitions occur in the absence of a Coulomb blockade or magnetic impurities. Rather, they are driven by the spin-orbit coupling in the junction, and can be probed, for example, by measuring the tunneling density of states or the critical current as a function of the junction's length or its Fermi velocity.

Publication: Physical Review B Vol.: 100 No.: 6 ISSN: 2469-9950

ID: CaltechAUTHORS:20190429-075854330

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Abstract: Fracton topological phases host fractionalized topological quasiparticles with restricted mobility, with promising applications to fault-tolerant quantum computation. While a variety of exactly solvable fracton models have been proposed, there is a need for platforms to realize them experimentally. We show that a rich set of fracton phases emerges in interacting Majorana band models whose building blocks are within experimental reach. Specifically, our Majorana constructions overcome a principal obstacle, namely, the implementation of the complicated spin cluster interactions underlying fracton stabilizer codes. The basic building blocks of the proposed constructions include Coulomb blockaded Majorana islands and weak interisland Majorana hybridizations. This setting produces a wide variety of fracton states and promises numerous opportunities for probing and controlling fracton phases experimentally. Our approach also reveals the relation between fracton phases and Majorana fermion codes and further generates a hierarchy of fracton spin liquids.

Publication: Physical Review Research Vol.: 1 No.: 1 ISSN: 2643-1564

ID: CaltechAUTHORS:20190816-101048239

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Abstract: We consider a model of an acoustic black hole formed by a quasi-one dimensional Bose–Einstein condensate with a step-like horizon. This system is analyzed by solving the corresponding Bogoliubov–de Gennes equation with an appropriate matching condition at the jump. When the step is between a subsonic and supersonic flow, a sonic horizon develops and in addition to the scattering coefficients we compute the distribution of the accompanying analogue Hawking radiation. Additionally, in response to the abrupt variation in flow and non-linear Bogoliubov dispersion relation, evanescent solutions of the Bogoliubov–de Gennes equation also appear and decay out from the horizon. We bound this decay length and show that these modes produce a modulation of observables outside the event horizon by their interference with outgoing Hawking flux. We go further and find specific superpositions of ingoing eigenmodes which exhibit coherent cancellation of the Hawking flux outside the horizon but nevertheless have evanescent support outside the black hole. We conclude by speculating that when quasiparticle interactions are included, evanescent modes may yield a leakage of information across the event horizon via interactions between the real outgoing Hawking flux and the virtual evanescent modes, and that we may expect this as a generic feature of models which break Lorentz invariance at the UV (Planck) scale.

Publication: Annals of Physics Vol.: 407ISSN: 0003-4916

ID: CaltechAUTHORS:20190426-161745452

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Abstract: Quantum memories for light are important components for future long-distance quantum networks. We present on-chip quantum storage of telecommunication-band light at the single-photon level in an ensemble of erbium-167 ions in an yttrium orthosilicate photonic crystal nanobeam resonator. Storage times of up to 10 μ s are demonstrated with an all-optical atomic-frequency-comb protocol in a dilution refrigerator under a magnetic field of 380 mT. We show this quantum-storage platform to have high bandwidth, high fidelity, and multimode capacity, and we outline a path toward an efficient erbium-167 quantum memory for light.

Publication: Physical Review Applied Vol.: 12 No.: 2 ISSN: 2331-7019

ID: CaltechAUTHORS:20190904-142554756

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Abstract: Matthew Fisher recently postulated a mechanism by which quantum phenomena could influence cognition: Phosphorus nuclear spins may resist decoherence for long times. The spins would serve as biological qubits. The qubits may resist decoherence longer when in Posner molecules. We imagine that Fisher postulates correctly. How adroitly could biological systems process quantum information (QI)? We establish a framework for answering. Additionally, we construct applications of biological qubits to quantum error correction, quantum communication, and quantum computation. First, we posit how the QI encoded by the spins transforms as Posner molecules form. The transformation points to a natural computational basis for qubits in Posner molecules. From the basis, we construct a quantum code that detects arbitrary single-qubit errors. Each molecule encodes one qutrit. Shifting from information storage to computation, we define the model of Posner quantum computation. To illustrate the model’s quantum-communication ability, we show how it can teleport information incoherently: A state’s weights are teleported. Dephasing results from the entangling operation’s simulation of a coarse-grained Bell measurement. Whether Posner quantum computation is universal remains an open question. However, the model’s operations can efficiently prepare a Posner state usable as a resource in universal measurement-based quantum computation. The state results from deforming the Affleck–Kennedy–Lieb–Tasaki (AKLT) state and is a projected entangled-pair state (PEPS). Finally, we show that entanglement can affect molecular-binding rates, boosting a binding probability from 33.6% to 100% in an example. This work opens the door for the QI-theoretic analysis of biological qubits and Posner molecules.

Publication: Annals of Physics Vol.: 407ISSN: 0003-4916

ID: CaltechAUTHORS:20171122-084552130

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Abstract: In magnetically doped thin-film topological insulators, aligning the magnetic moments generates a quantum anomalous Hall phase supporting a single chiral edge state. We show that as the system demagnetizes, disorder from randomly oriented magnetic moments can produce a “quantum anomalous parity Hall” phase with helical edge modes protected by a unitary reflection symmetry. We further show that introducing superconductivity, combined with selective breaking of reflection symmetry by a gate, allows for creation and manipulation of Majorana zero modes via purely electrical means and at zero applied magnetic field.

Publication: Physical Review Letters Vol.: 123 No.: 4 ISSN: 0031-9007

ID: CaltechAUTHORS:20190426-083534979

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Abstract: Over 50 years ago, Anderson and Blount proposed that ferroelectric-like structural phase transitions may occur in metals, despite the expected screening of the Coulomb interactions that often drive polar transitions. Recently, theoretical treatments have suggested that such transitions require the itinerant electrons be decoupled from the soft transverse optical phonons responsible for polar order. However, this decoupled electron mechanism (DEM) has yet to be experimentally observed. Here we utilize ultrafast spectroscopy to uncover evidence of the DEM in LiOsO_3, the first known band metal to undergo a thermally driven polar phase transition (T_c ≈ 140 K). We demonstrate that intra-band photo-carriers relax by selectively coupling to only a subset of the phonon spectrum, leaving as much as 60% of the lattice heat capacity decoupled. This decoupled heat capacity is shown to be consistent with a previously undetected and partially displacive TO polar mode, indicating the DEM in LiOsO_3.

Publication: Nature Communications Vol.: 10ISSN: 2041-1723

ID: CaltechAUTHORS:20190719-102955020

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Abstract: Coupling a normal-metal wire to a superconductor induces an excitation gap Δ_(ind) in the normal metal. In the absence of disorder, the induced excitation gap is strongly suppressed by finite-size effects if the thickness D_S of the superconductor is much smaller than the thickness D_N of the normal metal and the superconducting coherence length ξ. We show that the presence of disorder, either in the bulk or at the exposed surface of the superconductor, significantly enhances the magnitude of Δ_(ind), such that Δ_(ind) approaches the superconducting gap Δ in the limit of strong disorder. We also discuss the shift of energy bands inside the normal-metal wire as a result of the coupling to the superconducting shell.

Publication: Physical Review B Vol.: 100 No.: 3 ISSN: 2469-9950

ID: CaltechAUTHORS:20190722-092305481

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Abstract: Majorana zero modes are a promising platform for topologically protected quantum information processing. Their non-Abelian nature, which is key for performing quantum gates, is most prominently exhibited through braiding. While originally formulated for two-dimensional systems, it has been shown that braiding can also be realized using one-dimensional wires by forming an essentially two-dimensional network. Here, we show that in driven systems far from equilibrium, one can do away with the second spatial dimension altogether by instead using quasienergy as the second dimension. To realize this, we use a Floquet topological superconductor which can exhibit Majorana modes at two special eigenvalues of the evolution operator, 0 and π, and thus can realize four Majorana modes in a single, driven quantum wire. We describe and numerically evaluate a protocol that realizes a topologically protected exchange of two Majorana zero modes in a single wire by adiabatically modulating the Floquet drive and using the π modes as auxiliary degrees of freedom.

Publication: Physical Review B Vol.: 100 No.: 4 ISSN: 2469-9950

ID: CaltechAUTHORS:20190429-083156058

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Abstract: We propose a new cellular automaton (CA), the sweep rule, which generalizes Toom’s rule to any locally Euclidean lattice. We use the sweep rule to design a local decoder for the toric code in d ≥ 3 dimensions, the sweep decoder, and rigorously establish a lower bound on its performance. We also numerically estimate the sweep decoder threshold for the three-dimensional toric code on the cubic and body-centered cubic lattices for phenomenological phase-flip noise. Our results lead to new CA decoders with provable error-correction thresholds for other topological quantum codes including the color code.

Publication: Physical Review Letters Vol.: 123 No.: 2 ISSN: 0031-9007

ID: CaltechAUTHORS:20190201-155942835

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Abstract: We consider the scaling of entanglement entropy in random Projected Entangled Pairs States (PEPS) with an internal symmetry given by a finite group G. We systematically demonstrate a correspondence between this entanglement entropy and the difference of free energies of a classical Ising model with an addition non-local term. This non-local term counts the number of domain walls in a particular configuration of the classical spin model. We argue that for that overwhelming majority of such states, this gives rise to an area law scaling with well-defined topological entanglement entropy. The topological entanglement entropy is shown to be log|G| for a simply connected region A and which manifests as a difference in the number of domain walls of ground state energies for the two spin models.

Publication: arXiv
ID: CaltechAUTHORS:20190801-134548265

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Abstract: Chaotic dynamics in quantum many-body systems scrambles local information so that at late times it can no longer be accessed locally. This is reflected quantitatively in the out-of-time-ordered correlator of local operators, which is expected to decay to 0 with time. However, for systems of finite size, out-of-time-ordered correlators do not decay exactly to 0 and in this paper we show that the residual value can provide useful insights into the chaotic dynamics. When energy is conserved, the late-time saturation value of the out-of-time-ordered correlator of generic traceless local operators scales as an inverse polynomial in the system size. This is in contrast to the inverse exponential scaling expected for chaotic dynamics without energy conservation. We provide both analytical arguments and numerical simulations to support this conclusion.

Publication: Physical Review Letters Vol.: 123 No.: 1 ISSN: 0031-9007

ID: CaltechAUTHORS:20170726-091047115

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Abstract: We propose a systematic way of constructing Floquet second-order topological insulators (SOTIs) based on time-glide symmetry, a nonsymmorphic space-time symmetry that is unique in Floquet systems. In particular, we are able to show that the static enlarged Hamiltonian in the frequency domain acquires reflection symmetry, which is inherited from the time-glide symmetry of the original system. As a consequence, one can construct a variety of time-glide symmetric Floquet SOTIs using the knowledge of static SOTIs. Moreover, the time-glide symmetry only needs to be implemented approximately in practice, enhancing the prospects of experimental realizations. We consider two examples, a 2D system in class AIII and a 3D system in class A, to illustrate our ideas, and then present a general recipe for constructing Floquet SOTIs in all symmetry classes.

Publication: Physical Review Letters Vol.: 123 No.: 1 ISSN: 0031-9007

ID: CaltechAUTHORS:20190409-112427983

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Abstract: In the context of quantum theories of spacetime, one overarching question is how quantum information in the bulk spacetime is encoded holographically in boundary degrees of freedom. It is particularly interesting to understand the correspondence between bulk subregions and boundary subregions in order to address the emergence of locality in the bulk quantum spacetime. For the AdS/CFT correspondence, it is known that this bulk information is encoded redundantly on the boundary in the form of an error-correcting code. Having access only to a subregion of the boundary is as if part of the holographic code has been damaged by noise and rendered inaccessible. In quantum-information science, the problem of recovering information from a damaged code is addressed by the theory of universal recovery channels. We apply and extend this theory to address the problem of relating bulk and boundary subregions in AdS/CFT, focusing on a conjecture known as entanglement wedge reconstruction. Existing work relies on the exact equivalence between bulk and boundary relative entropies, but these are only approximately equal in bulk effective field theory, and in similar situations it is known that predictions from exact entropic equalities can be qualitatively incorrect. We show that the framework of universal recovery channels provides a robust demonstration of the entanglement wedge reconstruction conjecture as well as new physical insights. Most notably, we find that a bulk operator acting in a given boundary region’s entanglement wedge can be expressed as the response of the boundary region’s modular Hamiltonian to a perturbation of the bulk state in the direction of the bulk operator. This formula can be interpreted as a noncommutative version of Bayes’s rule that attempts to undo the noise induced by restricting to only a portion of the boundary. To reach these conclusions, we extend the theory of universal recovery channels to finite-dimensional operator algebras and demonstrate that recovery channels approximately preserve the multiplicative structure of the operator algebra.

Publication: Physical Review X Vol.: 9 No.: 3 ISSN: 2160-3308

ID: CaltechAUTHORS:20190724-150856685

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Abstract: Interfacing superconducting qubits with optical photons require noise-free microwave-to-optical transducers, a technology currently not realized at the single-photon level. We propose to use four-wave mixing in an ensemble of cold ytterbium (Yb) atoms prepared in the metastable “clock” state. The parametric process uses two high-lying Rydberg states for bidirectional conversion between a 10 GHz microwave photon and an optical photon in the telecommunication E-band. To avoid noise photons due to spontaneous emission, we consider continuous operation far detuned from the intermediate states. We use an input-output formalism to predict conversion efficiencies of ≈50% with bandwidths of ≈100 kHz.

Publication: Physical Review A Vol.: 100 No.: 1 ISSN: 2469-9926

ID: CaltechAUTHORS:20190528-083651745

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Abstract: We introduce NetKet, a comprehensive open source framework for the study of many-body quantum systems using machine learning techniques. The framework is built around a general and flexible implementation of neural-network quantum states, which are used as a variational ansatz for quantum wavefunctions. NetKet provides algorithms for several key tasks in quantum many-body physics and quantum technology, namely quantum state tomography, supervised learning from wavefunction data, and ground state searches for a wide range of customizable lattice models. Our aim is to provide a common platform for open research and to stimulate the collaborative development of computational methods at the interface of machine learning and many-body physics.

Publication: SoftwareX Vol.: 10ISSN: 2352-7110

ID: CaltechAUTHORS:20190827-093549272

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Abstract: We introduce a driven-dissipative two-mode bosonic system whose reservoir causes simultaneous loss of two photons in each mode and whose steady states are superpositions of pair-coherent/Barut-Girardello coherent states. We show how quantum information encoded in a steady-state subspace of this system is exponentially immune to phase drifts (cavity dephasing) in both modes. Additionally, it is possible to protect information from arbitrary photon loss in either (but not simultaneously both) of the modes by continuously monitoring the difference between the expected photon numbers of the logical states. Despite employing more resources, the two-mode scheme enjoys two advantages over its one-mode cat-qubit counterpart with regards to implementation using current circuit QED technology. First, monitoring the photon number difference can be done without turning off the currently implementable dissipative stabilizing process. Second, a lower average photon number per mode is required to enjoy a level of protection at least as good as that of the cat-codes. We discuss circuit QED proposals to stabilize the code states, perform gates, and protect against photon loss via either active syndrome measurement or an autonomous procedure. We introduce quasiprobability distributions allowing us to represent two-mode states of fixed photon number difference in a two-dimensional complex plane, instead of the full four-dimensional two-mode phase space. The two-mode codes are generalized to multiple modes in an extension of the stabilizer formalism to non-diagonalizable stabilizers. The M-mode codes can protect against either arbitrary photon losses in up to M − 1 modes or arbitrary losses and gains in any one mode.

Publication: Quantum Science and Technology Vol.: 4 No.: 3 ISSN: 2058-9565

ID: CaltechAUTHORS:20190207-153140844

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Abstract: We present a two-dimensional (2D) photonic crystal system for interacting with cold cesium (Cs) atoms. The band structures of the 2D photonic crystals are predicted to produce unconventional atom-light interaction behaviors, including anisotropic emission, suppressed spontaneous decay and photon mediated atom-atom interactions controlled by the position of the atomic array relative to the photonic crystal. An optical conveyor technique is presented for continuously loading atoms into the desired trapping positions with optimal coupling to the photonic crystal. The device configuration also enables application of optical tweezers for controlled placement of atoms. Devices can be fabricated reliably from a 200nm silicon nitride device layer using a lithography-based process, producing predicted optical properties in transmission and reflection measurements. These 2D photonic crystal devices can be readily deployed to experiments for many-body physics with neutral atoms, and engineering of exotic quantum matter.

Publication: Proceedings of the National Academy of Sciences of the United States of America Vol.: 116 No.: 26 ISSN: 0027-8424

ID: CaltechAUTHORS:20190426-091633868

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Abstract: This work derives an analytical formula for the asymptotic state---the quantum state resulting from an infinite number of applications of a general quantum channel on some initial state. For channels admitting multiple fixed or rotating points, conserved quantities---the left fixed/rotating points of the channel---determine the dependence of the asymptotic state on the initial state. The formula stems from a Noether-like theorem stating that, for any channel admitting a full-rank fixed point, conserved quantities commute with that channel’s Kraus operators up to a phase. The formula is applied to adiabatic transport of the fixed-point space of channels, revealing cases where the dissipative/spectral gap can close during any segment of the adiabatic path. The formula is also applied to calculate expectation values of noninjective matrix product states (MPS) in the thermodynamic limit, revealing that those expectation values can also be calculated using an MPS with reduced bond dimension and a modified boundary.

Publication: Quantum Vol.: 3ISSN: 2521-327X

ID: CaltechAUTHORS:20190208-122111876

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Abstract: Recently, topological superconductors based on Josephson junctions in two-dimensional electron gases with strong Rashba spin-orbit coupling have been proposed as attractive alternatives to wire-based setups. Here, we elucidate how phase-controlled Josephson junctions based on quantum wells with [001] growth direction and an arbitrary combination of Rashba and Dresselhaus spin-orbit coupling can also host Majorana bound states for a wide range of parameters as long as the magnetic field is oriented appropriately. Hence, Majorana bound states based on Josephson junctions can appear in a wide class of two-dimensional electron gases. We study the effect of spin-orbit coupling, the Zeeman energies, and the superconducting phase difference to create a full topological phase diagram and find the optimal stability region to observe Majorana bound states in narrow junctions. Surprisingly, for equal Rashba and Dresselhaus spin-orbit coupling, well localized Majorana bound states can appear only for phase differences ϕ ≠ π as the topological gap protecting the Majorana bound states vanishes at ϕ = π . Our results show that the ratio between Rashba and Dresselhaus spin-orbit coupling or the choice of the in-plane crystallographic axis along which the superconducting phase bias is applied offer additional tunable knobs to test Majorana bound states in these systems. Finally, we discuss signatures of Majorana bound states that could be probed experimentally by tunneling conductance measurements at the edge of the junction.

Publication: Physical Review B Vol.: 99 No.: 21 ISSN: 2469-9950

ID: CaltechAUTHORS:20190612-140920221

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Abstract: We show that any language solvable in nondeterministic time exp( exp(⋯exp(n))), where the number of iterated exponentials is an arbitrary function R(n), can be decided by a multiprover interactive proof system with a classical polynomial-time verifier and a constant number of quantum entangled provers, with completeness 1 and soundness 1 − exp(−Cexp(⋯exp(n))), where the number of iterated exponentials is R(n)−1 and C>0 is a universal constant. The result was previously known for R=1 and R=2; we obtain it for any time-constructible function R. The result is based on a compression technique for interactive proof systems with entangled provers that significantly simplifies and strengthens a protocol compression result of Ji (STOC’17). As a separate consequence of this technique we obtain a different proof of Slofstra’s recent result on the uncomputability of the entangled value of multiprover games (Forum of Mathematics, Pi 2019). Finally, we show that even minor improvements to our compression result would yield remarkable consequences in computational complexity theory and the foundations of quantum mechanics: first, it would imply that the class MIP* contains all computable languages; second, it would provide a negative resolution to a multipartite version of Tsirelson’s problem on the relation between the commuting operator and tensor product models for quantum correlations.

Publication: arXiv
ID: CaltechAUTHORS:20190204-112657116

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Abstract: It has long been recognized that atomic emission of radiation is not an immutable property of an atom, but is instead dependent on the electromagnetic environment and, in the case of ensembles, also on the collective interactions between the atoms. In an open radiative environment, the hallmark of collective interactions is enhanced spontaneous emission—super-radiance—with non-dissipative dynamics largely obscured by rapid atomic decay. Here we observe the dynamical exchange of excitations between a single artificial atom and an entangled collective state of an atomic array through the precise positioning of artificial atoms realized as superconducting qubits along a one-dimensional waveguide. This collective state is dark, trapping radiation and creating a cavity-like system with artificial atoms acting as resonant mirrors in the otherwise open waveguide. The emergent atom–cavity system is shown to have a large interaction-to-dissipation ratio (cooperativity exceeding 100), reaching the regime of strong coupling, in which coherent interactions dominate dissipative and decoherence effects. Achieving strong coupling with interacting qubits in an open waveguide provides a means of synthesizing multi-photon dark states with high efficiency and paves the way for exploiting correlated dissipation and decoherence-free subspaces of quantum emitter arrays at the many-body level.

Publication: Nature Vol.: 569 No.: 7758 ISSN: 0028-0836

ID: CaltechAUTHORS:20190225-095611254

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Abstract: Thermodynamics imposes restrictions on what state transformations are possible. In the macroscopic limit of asymptotically many independent copies of a state—as for instance in the case of an ideal gas—the possible transformations become reversible and are fully characterized by the free energy. In this Letter, we present a thermodynamic resource theory for quantum processes that also becomes reversible in the macroscopic limit, a property that is especially rare for a resource theory of quantum channels. We identify a unique single-letter and additive quantity, the thermodynamic capacity, that characterizes the “thermodynamic value” of a quantum channel, in the sense that the work required to simulate many repetitions of a quantum process employing many repetitions of another quantum process becomes equal to the difference of the respective thermodynamic capacities. On a technical level, we provide asymptotically optimal constructions of universal implementations of quantum processes. A challenging aspect of this construction is the apparent necessity to coherently combine thermal engines that would run in different thermodynamic regimes depending on the input state. Our results have applications in quantum Shannon theory by providing a generalized notion of quantum typical subspaces and by giving an operational interpretation to the entropy difference of a channel.

Publication: Physical Review Letters Vol.: 122 No.: 20 ISSN: 0031-9007

ID: CaltechAUTHORS:20190211-152656438

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Abstract: We consider two-dimensional states of matter satisfying a uniform area law for entanglement. We show that the topological entanglement entropy is equal to the minimum relative entropy distance from the reduced state to the set of thermal states of local models. The argument is based on strong subadditivity of quantum entropy. For states with zero topological entanglement entropy, in particular, the formula gives locality of the states at the boundary of a region as thermal states of local Hamiltonians. It also implies that the entanglement spectrum of a two-dimensional region is equal to the spectrum of a one-dimensional local thermal state on the boundary of the region.

Publication: Physical Review B Vol.: 99 No.: 19 ISSN: 2469-9950

ID: CaltechAUTHORS:20180620-190843167

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Abstract: We propose a realization of chiral Majorana modes propagating on the hinges of a 3D antiferromagnetic topological insulator, which was recently theoretically predicted and experimentally confirmed in the tetradymite-type MnBi_2Te_4-related ternary chalgogenides. These materials consist of ferromagnetically ordered 2D layers, whose magnetization direction alternates between neighboring layers, forming an antiferromagnetic order. Besides surfaces with a magnetic gap, there also exist gapless surfaces with a single Dirac cone, which can be gapped out when proximity coupled to an s-wave superconductor. On the sharing edges between the two types of gapped surfaces, the chiral Majorana modes emerge. We further propose experimental signatures of these Majoana hinge modes in terms of two-terminal conductance measurements.

Publication: Physical Review B Vol.: 99 No.: 19 ISSN: 2469-9950

ID: CaltechAUTHORS:20181129-150354355

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Abstract: In this work we demonstrate that nonrandom mechanisms that lead to single-particle localization may also lead to many-body localization, even in the absence of disorder. In particular, we consider interacting spins and fermions in the presence of a linear potential. In the noninteracting limit, these models show the well-known Wannier–Stark localization. We analyze the fate of this localization in the presence of interactions. Remarkably, we find that beyond a critical value of the potential gradient these models exhibit nonergodic behavior as indicated by their spectral and dynamical properties. These models, therefore, constitute a class of generic nonrandom models that fail to thermalize. As such, they suggest new directions for experimentally exploring and understanding the phenomena of many-body localization. We supplement our work by showing that by using machine-learning techniques the level statistics of a system may be calculated without generating and diagonalizing the Hamiltonian, which allows a generation of large statistics.

Publication: Proceedings of the National Academy of Sciences of the United States of America Vol.: 116 No.: 19 ISSN: 0027-8424

ID: CaltechAUTHORS:20180821-144923153

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Abstract: We demonstrate single-atom resolved imaging with a survival probability of 0.99932(8) and a fidelity of 0.99991(1), enabling us to perform repeated high-fidelity imaging of single atoms in tweezers for thousands of times. We further observe lifetimes under laser cooling of more than seven minutes, an order of magnitude longer than in previous tweezer studies. Experiments are performed with strontium atoms in 813.4 nm tweezer arrays, which is at a magic wavelength for the clock transition. Tuning to this wavelength is enabled by off-magic Sisyphus cooling on the intercombination line, which lets us choose the tweezer wavelength almost arbitrarily. We find that a single not retro-reflected cooling beam in the radial direction is sufficient for mitigating recoil heating during imaging. Moreover, this cooling technique yields temperatures below 5 μK, as measured by release and recapture. Finally, we demonstrate clock-state resolved detection with average survival probability of 0.996(1) and average state detection fidelity of 0.981(1). Our work paves the way for atom-by-atom assembly of large defect-free arrays of alkaline-earth atoms, in which repeated interrogation of the clock transition is an imminent possibility.

Publication: Physical Review Letters Vol.: 122 No.: 17 ISSN: 0031-9007

ID: CaltechAUTHORS:20190123-112141969

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Abstract: A recent experiment in the Rydberg atom chain observed unusual oscillatory quench dynamics with a charge density wave initial state, and theoretical works identified a set of many-body “scar states” showing nonthermal behavior in the Hamiltonian as potentially responsible for the atypical dynamics. In the same nonintegrable Hamiltonian, we discover several eigenstates at an infinite temperature that can be represented exactly as matrix product states with a finite bond dimension, for both periodic boundary conditions (two exact E = 0 states) and open boundary conditions (two E = 0 states and one each E = ±√2). This discovery explicitly demonstrates the violation of the strong eigenstate thermalization hypothesis in this model and uncovers exact quantum many-body scar states. These states show signatures of translational symmetry breaking with a period-2 bond-centered pattern, despite being in one dimension at an infinite temperature. We show that the nearby many-body scar states can be well approximated as “quasiparticle excitations” on top of our exact E = 0 scar states and propose a quasiparticle explanation of the strong oscillations observed in experiments.

Publication: Physical Review Letters Vol.: 122 No.: 17 ISSN: 0031-9007

ID: CaltechAUTHORS:20181203-095532141

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Abstract: Finding optimal correction of errors in generic stabilizer codes is a computationally hard problem, even for simple noise models. While this task can be simplified for codes with some structure, such as topological stabilizer codes, developing good and efficient decoders still remains a challenge. In our paper, we systematically study a very versatile class of decoders based on feedforward neural networks. To demonstrate adaptability, we apply neural decoders to the triangular color and toric codes under various noise models with realistic features, such as spatially correlated errors. We report that neural decoders provide a significant improvement over leading efficient decoders in terms of the error-correction threshold. In particular, the neural decoder threshold for the two-dimensional color code is very close to the toric code threshold. Using neural networks simplifies the design of decoders and does not require prior knowledge of the underlying noise.

Publication: Physical Review A Vol.: 99 No.: 5 ISSN: 2469-9926

ID: CaltechAUTHORS:20190212-153409929

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Abstract: Recent experiments with strongly interacting, driven Rydberg ensembles have introduced a promising setup for the study of self-organized criticality (SOC) in cold atom systems. Based on this setup, we theoretically propose a control mechanism for the paradigmatic avalanche dynamics of SOC in the form of a time-dependent drive amplitude. This gives access to a variety of avalanche dominated, self-organization scenarios, prominently including self-organized criticality, as well as sub- and supercritical dynamics. We analyze the dependence of the dynamics on external scales and spatial dimensionality. It demonstrates the potential of driven Rydberg systems as a playground for the exploration of an extended SOC phenomenology and their relation to other common scenarios of SOC, such as, e.g., in neural networks and on graphs.

Publication: Physical Review A Vol.: 99 No.: 5 ISSN: 2469-9926

ID: CaltechAUTHORS:20190520-090739781

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Abstract: The goal of this note is to explore the behavior of effective action in the SYK model with general continuous global symmetries. A global symmetry will decompose the whole Hamiltonian of a many-body system to several single charge sectors. For the SYK model, the effective action near the saddle point is given as the free product of the Schwarzian action part and the free action of the group element moving in the group manifold. With a detailed analysis in the free sigma model, we prove a modified version of Peter-Weyl theorem that works for generic spin structure. As a conclusion, we could make a comparison between the thermodynamics and the spectral form factors between the whole theory and the single charge sector, to make predictions on the SYK model and see how symmetry affects the chaotic behavior in certain timescales.

Publication: Journal of High Energy Physics Vol.: 2019 No.: 5 ISSN: 1126-6708

ID: CaltechAUTHORS:20190520-103300835

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Abstract: Current techniques in quantum process tomography typically return a single point estimate of an unknown process based on a finite albeit large amount of measurement data. Due to statistical fluctuations, however, other processes close to the point estimate can also produce the observed data with near certainty. Unless appropriate error bars can be constructed, the point estimate does not carry any sound operational interpretation. Here, we provide a solution to this problem by constructing a confidence region estimator for quantum processes. Our method enables reliable estimation of essentially any figure of merit for quantum processes on few qubits, including the diamond distance to a specific noise model, the entanglement fidelity, and the worst-case entanglement fidelity, by identifying error regions which contain the true state with high probability. We also provide a software package, QPtomographer, implementing our estimator for the diamond norm and the worst-case entanglement fidelity. We illustrate its usage and performance with several simulated examples. Our tools can be used to reliably certify the performance of, e.g., error correction codes, implementations of unitary gates, or more generally any noise process affecting a quantum system.

Publication: Physical Review A Vol.: 99 No.: 5 ISSN: 2469-9926

ID: CaltechAUTHORS:20190208-123849148

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Abstract: The dynamics of a nearly-AdS_2 spacetime with boundaries is reduced to that of two particles in the anti-de Sitter space. We determine the class of physically meaningful wavefunctions, and prescribe the statistical mechanics of a black hole. We demonstrate how wavefunctions for a two-sided black hole and a regularized notion of trace can be used to construct thermal partition functions, and more generally, arbitrary density matrices. We also obtain correlation functions of external operators.

Publication: Journal of High Energy Physics Vol.: 2019 No.: 5 ISSN: 1126-6708

ID: CaltechAUTHORS:20190529-161258314

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Abstract: In privacy amplification, two mutually trusted parties aim to amplify the secrecy of an initial shared secret X in order to establish a shared private key K by exchanging messages over an insecure communication channel. If the channel is authenticated the task can be solved in a single round of communication using a strong randomness extractor; choosing a quantum-proof extractor allows one to establish security against quantum adversaries. In the case that the channel is not authenticated, this simple solution is no longer secure. Nevertheless, Dodis and Wichs (STOC’09) showed that the problem can be solved in two rounds of communication using a non-malleable extractor, a stronger pseudo-random construction than a strong extractor. We give the first construction of a non-malleable extractor that is secure against quantum adversaries. The extractor is based on a construction by Li (FOCS’12), and is able to extract from source of min-entropy rates larger than 1 / 2. Combining this construction with a quantum-proof variant of the reduction of Dodis and Wichs, due to Cohen and Vidick (unpublished) we obtain the first privacy amplification protocol secure against active quantum adversaries.

Publication: arXiv No.: 11477
ID: CaltechAUTHORS:20190320-102401828

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Abstract: The problem of reliably certifying the outcome of a computation performed by a quantum device is rapidly gaining relevance. We present two protocols for a classical verifier to verifiably delegate a quantum computation to two non-communicating but entangled quantum provers. Our protocols have near-optimal complexity in terms of the total resources employed by the verifier and the honest provers, with the total number of operations of each party, including the number of entangled pairs of qubits required of the honest provers, scaling as O(g\log g) for delegating a circuit of size g. This is in contrast to previous protocols, whose overhead in terms of resources employed, while polynomial, is far beyond what is feasible in practice. Our first protocol requires a number of rounds that is linear in the depth of the circuit being delegated, and is blind, meaning neither prover can learn the circuit or its input. The second protocol is not blind, but requires only a constant number of rounds of interaction. Our main technical innovation is an efficient rigidity theorem which allows a verifier to test that two entangled provers perform measurements specified by an arbitrary m-qubit tensor product of single-qubit Clifford observables on their respective halves of m shared EPR pairs, with a robustness that is independent of m. Our two-prover classical-verifier delegation protocols are obtained by combining this rigidity theorem with a single-prover quantum-verifier protocol for the verifiable delegation of a quantum computation, introduced by Broadbent.

Publication: arXiv No.: 11478
ID: CaltechAUTHORS:20190320-123759874

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Abstract: We perform a numerical study of a spin-1/2 model with ℤ_2 × ℤ_2 symmetry in one dimension which demonstrates an interesting similarity to the physics of two-dimensional deconfined quantum critical points (DQCP). Specifically, we investigate the quantum phase transition between Ising ferromagnetic and valence bond solid (VBS) symmetry-breaking phases. Working directly in the thermodynamic limit using uniform matrix product states, we find evidence for a direct continuous phase transition that lies outside of the Landau-Ginzburg-Wilson paradigm. In our model, the continuous transition is found everywhere on the phase boundary. We find that the magnetic and VBS correlations show very close power-law exponents, which is expected from the self-duality of the parton description of this DQCP. Critical exponents vary continuously along the phase boundary in a manner consistent with the predictions of the field theory for this transition. We also find a regime where the phase boundary splits, as suggested by the theory, introducing an intermediate phase of coexisting ferromagnetic and VBS order parameters. Interestingly, we discover a transition involving this coexistence phase which is similar to the DQCP, being also disallowed by the Landau-Ginzburg-Wilson symmetry-breaking theory.

Publication: Physical Review B Vol.: 99 No.: 16 ISSN: 2469-9950

ID: CaltechAUTHORS:20190429-143530475

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Abstract: Foliated fracton order is a qualitatively new kind of phase of matter. It is similar to topological order, but with the fundamental difference that a layered structure, referred to as a foliation, plays an essential role and determines the mobility restrictions of the topological excitations. In this work, we introduce a new kind of field theory to describe these phases: a foliated field theory. We also introduce a new lattice model and string-membrane-net condensation picture of these phases, which is analogous to the string-net condensation picture of topological order.

Publication: SciPost Physics Vol.: 6 No.: 4 ISSN: 2542-4653

ID: CaltechAUTHORS:20190416-074932870

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Abstract: Quantum phase transitions (QPTs) involve transformations between different states of matter that are driven by quantum fluctuations1. These fluctuations play a dominant part in the quantum critical region surrounding the transition point, where the dynamics is governed by the universal properties associated with the QPT. Although time-dependent phenomena associated with classical, thermally driven phase transitions have been extensively studied in systems ranging from the early Universe to Bose–Einstein condensates, understanding critical real-time dynamics in isolated, non-equilibrium quantum systems remains a challenge. Here we use a Rydberg atom quantum simulator with programmable interactions to study the quantum critical dynamics associated with several distinct QPTs. By studying the growth of spatial correlations when crossing the QPT, we experimentally verify the quantum Kibble–Zurek mechanism (QKZM) for an Ising-type QPT, explore scaling universality and observe corrections beyond QKZM predictions. This approach is subsequently used to measure the critical exponents associated with chiral clock models, providing new insights into exotic systems that were not previously understood and opening the door to precision studies of critical phenomena, simulations of lattice gauge theories and applications to quantum optimization.

Publication: Nature Vol.: 568 No.: 7751 ISSN: 0028-0836

ID: CaltechAUTHORS:20190123-110710682

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Abstract: Magneto-elastic distortions are commonly detected across magnetic long-range ordering (LRO) transitions. In principle, they are also induced by the magnetic short-range ordering (SRO) that precedes a LRO transition, which contains information about short-range correlations and energetics that are essential for understanding how LRO is established. However these distortions are difficult to resolve because the associated atomic displacements are exceedingly small and do not break symmetry. Here we demonstrate high-multipole nonlinear optical polarimetry as a sensitive and mode selective probe of SRO induced distortions using CrSiTe_3 as a testbed. This compound is composed of weakly bonded sheets of nearly isotropic ferromagnetically interacting spins that, in the Heisenberg limit, would individually be impeded from LRO by the Mermin-Wagner theorem. Our results show that CrSiTe_3 evades this law via a two-step crossover from two- to three-dimensional magnetic SRO, manifested through two successive and previously undetected totally symmetric distortions above its Curie temperature.

Publication: Nature Communications Vol.: 10ISSN: 2041-1723

ID: CaltechAUTHORS:20190410-093027160

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Abstract: Based on several previous examples, we summarize explicitly the general procedure to gauge models with subsystem symmetries, which are symmetries with generators that have support within a sub-manifold of the system. The gauging process can be applied to any local quantum model on a lattice that is invariant under the subsystem symmetry. We focus primarily on simple 3D paramagnetic states with planar symmetries. For these systems, the gauged theory may exhibit foliated fracton order and we find that the species of symmetry charges in the paramagnet directly determine the resulting foliated fracton order. Moreover, we find that gauging linear subsystem symmetries in 2D or 3D models results in a self-duality similar to gauging global symmetries in 1D.

Publication: SciPost Physics Vol.: 6 No.: 4 ISSN: 2542-4653

ID: CaltechAUTHORS:20181023-140032523

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Abstract: In this chapter we address the topic of quantum thermodynamics in the presence of additional observables beyond the energy of the system. In particular we discuss the special role that the generalized Gibbs ensemble plays in this theory, and derive this state from the perspectives of a micro-canonical ensemble, dynamical typicality and a resource-theory formulation. A notable obstacle occurs when some of the observables do not commute, and so it is impossible for the observables to simultaneously take on sharp microscopic values. We show how this can be circumvented, discuss information-theoretic aspects of the setting, and explain how thermodynamic costs can be traded between the different observables. Finally, we discuss open problems and future directions for the topic.

Publication: arXiv No.: 195
ID: CaltechAUTHORS:20190213-103051707

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Abstract: Thermodynamics can be formulated in either of two approaches, the phenomenological approach, which refers to the macroscopic properties of systems, and the statistical approach, which describes systems in terms of their microscopic constituents. We establish a connection between these two approaches by means of a new axiomatic framework that can take errors and imprecisions into account. This link extends to systems of arbitrary sizes including very small systems, for which the treatment of imprecisions is pertinent to any realistic situation. Based on this, we identify the quantities that characterise whether certain thermodynamic processes are possible with entropy measures from information theory. In the error-tolerant case, these entropies are so-called smooth min and max entropies. Our considerations further show that in an appropriate macroscopic limit there is a single entropy measure that characterises which state transformations are possible. In the case of many independent copies of a system (the so-called i.i.d. regime), the relevant quantity is the von Neumann entropy. Transformations among microcanonical states are characterised by the Boltzmann entropy.

Publication: arXiv No.: 195
ID: CaltechAUTHORS:20190211-151339114

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Abstract: π/8 phase gates (magic gates or T gates) are crucial to augment topological systems based on Majorana zero modes to full quantum universality. We present a scheme based on a combination of projective measurements and nonadiabatic evolution that effectively cancels smooth control errors when implementing phase gates in Majorana-based systems. Previous schemes based on adiabatic evolution are susceptible to problems arising from small but finite dynamical phases that are generically present in topologically unprotected gates. A measurement-only approach eliminates dynamical phases. For nonprotected gates, however, forced-measurement schemes are no longer effective, which leads to low success probabilities of obtaining the right succession of measurement outcomes in a measurement-only implementation. We show how to obtain a viable measurement-based scheme which dramatically increases the success probabilities by evolving the system nonadiabatically with respect to the degenerate subspace in between measurements. We outline practical applications of our scheme in recently proposed quantum computing designs based on Majorana tetrons and hexons.

Publication: Physical Review B Vol.: 99 No.: 14 ISSN: 2469-9950

ID: CaltechAUTHORS:20190424-142039996

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Abstract: Gaussian thermal loss channels are of particular importance to quantum communication theory since they model realistic optical communication channels. Except for special cases, the quantum capacity of Gaussian thermal loss channels is not yet quantified completely. In this paper, we provide improved upper bounds of the Gaussian thermal loss channel capacity, both in energy-constrained and unconstrained scenarios. We briefly review Gottesman-Kitaev-Preskill (GKP) codes and discuss their experimental implementation. We then prove, in the energyunconstrained case, that a family of GKP codes achieves the quantum capacity of Gaussian thermal loss channels up to at most a constant gap from the improved upper bound. In the energy-constrained case, we formulate a biconvex encoding and decoding optimization problem to maximize entanglement fidelity. Then, we solve the biconvex optimization heuristically by an alternating semidefinite programming (SDP) method and report that, starting from Haar random initial codes, our numerical optimization yields a hexagonal GKP code as an optimal encoding in a practically relevant regime.

Publication: IEEE Transactions on Information Theory Vol.: 65 No.: 4 ISSN: 0018-9448

ID: CaltechAUTHORS:20181011-133942418

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Abstract: Recent technical developments in the fields of quantum electromechanics and optomechanics have spawned nanoscale mechanical transducers with the sensitivity to measure mechanical displacements at the femtometre scale and the ability to convert electromagnetic signals at the single photon level. A key challenge in this field is obtaining strong coupling between motion and electromagnetic fields without adding additional decoherence. Here we present an electromechanical transducer that integrates a high-frequency (0.42 GHz) hypersonic phononic crystal with a superconducting microwave circuit. The use of a phononic bandgap crystal enables quantum-level transduction of hypersonic mechanical motion and concurrently eliminates decoherence caused by acoustic radiation. Devices with hypersonic mechanical frequencies provide a natural pathway for integration with Josephson junction quantum circuits, a leading quantum computing technology, and nanophotonic systems capable of optical networking and distributing quantum information.

Publication: Nature Nanotechnology Vol.: 14ISSN: 1748-3387

ID: CaltechAUTHORS:20190107-154636309

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Abstract: Majorana bound states are zero-energy modes localized at the ends of a one-dimensional (1D) topological superconductor. Introducing disorder usually increases the Majorana localization length, until eventually inducing a topological phase transition to a trivial phase. In this work we show that in some cases weak disorder causes the Majorana localization length to decrease, making the topological phase more robust. Increasing the disorder further eventually leads to a change of trend and to a phase transition to a trivial phase. Interestingly the transition occurs at ξ_0 ≫ l, where l is the disorder mean-free path and ξ_0 is the localization length in the clean limit. Our results are particularly relevant to a 1D topological superconductors formed in planar Josephson junctions.

Publication: Physical Review Letters Vol.: 122 No.: 12 ISSN: 0031-9007

ID: CaltechAUTHORS:20181105-091729626

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Abstract: In this work, we show that the checkerboard model exhibits the phenomenon of foliated fracton order. We introduce a renormalization-group transformation for the model that utilizes toric code bilayers as an entanglement resource and show how to extend the model to general three-dimensional manifolds. Furthermore, we use universal properties distilled from the structure of fractional excitations and ground-state entanglement to characterize the foliated fracton phase and find that it is the same as two copies of the X-cube model. Indeed, we demonstrate that the checkerboard model can be transformed into two copies of the X-cube model via an adiabatic deformation.

Publication: Physical Review B Vol.: 99 No.: 11 ISSN: 2469-9950

ID: CaltechAUTHORS:20181023-135513684

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Abstract: Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg limit, which can be achieved for noiseless quantum systems, but is not achievable in general for systems subject to noise. Here we study how measurement precision can be enhanced through quantum error correction, a general method for protecting a quantum system from the damaging effects of noise. We find a necessary and sufficient condition for achieving the Heisenberg limit using quantum probes subject to Markovian noise, assuming that noiseless ancilla systems are available, and that fast, accurate quantum processing can be performed. When the sufficient condition is satisfied, the quantum error-correcting code achieving the best possible precision can be found by solving a semidefinite program. We also show that noiseless ancilla are not needed when the signal Hamiltonian and the error operators commute. Finally we provide two explicit, archetypal examples of quantum sensors: qubits undergoing dephasing and a lossy bosonic mode.

No.: 10934
ID: CaltechAUTHORS:20190606-092443914

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Abstract: Recent work [Martin et al., Phys. Rev. X 7, 041008 (2017)] shows that a spin coupled to two externally supplied circularly polarized electromagnetic modes can effectuate a topological, quantized transfer of photons from one mode to the other. Here, we study the effect in the case when only one of the modes is externally provided, while the other is a dynamical quantum mechanical cavity mode. Focusing on the signatures and stability under experimentally accessible conditions, we show that the effect persists down to the few-photon quantum limit and that it can be used to generate highly entangled “cat states” of cavity and spin. By tuning the strength of the external drive to a “sweet spot,” the quantized pumping can arise starting from an empty (zero-photon) cavity state. We also find that inclusion of external noise and dissipation does not suppress but rather stabilizes the conversion effect, even after multiple cavity modes are taken into account.

Publication: Physical Review B Vol.: 99 No.: 9 ISSN: 2469-9950

ID: CaltechAUTHORS:20190325-132537557

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Abstract: Proving that the parent Hamiltonian of a Projected Entangled Pair State (PEPS) is gapped remains an important open problem. We take a step forward in solving this problem by showing two results: first, we identify an approximate factorization condition on the boundary state of rectangular subregions that is sufficient to prove that the parent Hamiltonian of the bulk 2D PEPS has a constant gap in the thermodynamic limit; second, we then show that Gibbs state of a local, finite-range Hamiltonian satisfy such condition. The proof applies to the case of injective and MPO-injective PEPS, employs the martingale method of nearly commuting projectors, and exploits a result of Araki (Commun Math Phys 14(2):120–157, 1969) on the robustness of one dimensional Gibbs states. Our result provides one of the first rigorous connections between boundary theories and dynamical properties in an interacting many body system.

Publication: Communications in Mathematical Physics Vol.: 366 No.: 3 ISSN: 0010-3616

ID: CaltechAUTHORS:20190311-132254669

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Abstract: Wavelengths in the telecommunication window (approximately 1.25–1.65 μm) are ideal for quantum communication due to low transmission loss in fiber networks. To realize quantum networks operating at these wavelengths, long-lived quantum memories that couple to telecom-band photons with high efficiency need to be developed. We propose coupling neutral ytterbium atoms, which have a strong telecom-wavelength transition, to a silicon photonic crystal cavity. Specifically, we consider the ^3P_0↔^3D_1 transition in neutral ^(171)Yb to interface its long-lived nuclear spin in the metastable ^3P_0 “clock” state with a telecom-band photon at 1.4μm. We show that Yb atoms can be trapped using a short-wavelength (approximately 470 nm) tweezer at a distance of 350 nm from the silicon photonic crystal cavity. At this distance, due to the slowly decaying evanescent cavity field at a longer wavelength, we obtain a single-photon Rabi frequency of g/2π ≈ 100 MHz and a cooperativity of C ≈ 47 while maintaining a high photon collection efficiency into a single mode fiber. The combination of high system efficiency, telecom-band operation, and long coherence times makes this platform well suited for quantum optics on a silicon chip and long-distance quantum communication.

Publication: Physical Review Applied Vol.: 11 No.: 3 ISSN: 2331-7019

ID: CaltechAUTHORS:20181203-111424788

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Abstract: We study the 6j symbol for the conformal group, and its appearance in three seemingly unrelated contexts: the SYK model, conformal representation theory, and perturbative amplitudes in AdS. The contribution of the planar Feynman diagrams to the three-point function of the bilinear singlets in SYK is shown to be a 6j symbol. We generalize the computation of these and other Feynman diagrams to d dimensions. The 6j symbol can be viewed as the crossing kernel for conformal partial waves, which may be computed using the Lorentzian inversion formula. We provide closed-form expressions for 6j symbols in d = 1, 2, 4. In AdS, we show that the 6j symbol is the Lorentzian inversion of a crossing-symmetric tree-level exchange amplitude, thus efficiently packaging the doubletrace OPE data. Finally, we consider one-loop diagrams in AdS with internal scalars and external spinning operators, and show that the triangle diagram is a 6j symbol, while one-loop n-gon diagrams are built out of 6j symbols.

Publication: Journal of High Energy Physics Vol.: 2019 No.: 3 ISSN: 1029-8479

ID: CaltechAUTHORS:20190314-092752423

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Abstract: Device-independent security is the gold standard for quantum cryptography: not only is security based entirely on the laws of quantum mechanics, but it holds irrespective of any a priori assumptions on the quantum devices used in a protocol, making it particularly applicable in a quantum-wary environment. While the existence of device-independent protocols for tasks such as randomness expansion and quantum key distribution has recently been established, the underlying proofs of security remain very challenging, yield rather poor key rates, and demand very high quality quantum devices, thus making them all but impossible to implement in practice. We introduce a technique for the analysis of device-independent cryptographic protocols. We provide a flexible protocol and give a security proof that provides quantitative bounds that are asymptotically tight, even in the presence of general quantum adversaries. At a high level our approach amounts to establishing a reduction to the scenario in which the untrusted device operates in an identical and independent way in each round of the protocol. This is achieved by leveraging the sequential nature of the protocol and makes use of a newly developed tool, the “entropy accumulation theorem” of Dupuis, Fawzi, and Renner [Entropy Accumulation, preprint, 2016]. As concrete applications we give simple and modular security proofs for device-independent quantum key distribution and randomness expansion protocols based on the CHSH inequality. For both tasks, we establish essentially optimal asymptotic key rates and noise tolerance. In view of recent experimental progress, which has culminated in loophole-free Bell tests, it is likely that these protocols can be practically implemented in the near future.

Publication: SIAM Journal on Computing Vol.: 48 No.: 1 ISSN: 0097-5397

ID: CaltechAUTHORS:20190206-150209557

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Abstract: We study a one-dimensional (1D) system that shows many analogies to proposed two-dimensional (2D) deconfined quantum critical points (DQCP). Our system is a translationally invariant spin-1/2 chain with onsite Z_2×Z_2 symmetry and time-reversal symmetry. It undergoes a direct continuous transition from a ferromagnet (FM), where one of the Z2 symmetries and the time reversal are broken, to a valence bond solid (VBS), where all onsite symmetries are restored while the translation symmetry is broken. The other Z_2 symmetry remains unbroken throughout, but its presence is crucial for both the direct transition (via specific Berry phase effect on topological defects, also related to a Lieb-Schultz-Mattis–type theorem) and the precise characterization of the VBS phase (which has crystalline-symmetry-protected-topological–like property). The transition has a description in terms of either two domain-wall species that “fractionalize” the VBS order parameter or in terms of two partons that “fractionalize” the FM order parameter, with each picture having its own Z_2 gauge theory structure. The two descriptions are dual to each other and, at long wavelengths, take the form of a self-dual gauged Ashkin-Teller model, reminiscent of the self-dual easy-plane noncompact CP^1 model that arises in the description of the 2D easy-plane DQCP. We also find an exact reformulation of the transition that leads to a simple field-theory description that explicitly unifies the FM and VBS order parameters; this reformulation can be interpreted as a new parton approach that does not attempt to fractionalize either of the FM and VBS order parameters but instead encodes them in instanton operators. Aside from providing explicit realizations of many ideas proposed in the context of the 2D DQCP, here in the simpler and fully tractable 1D setting with continuous transition, our study also suggests a possible line of approach to the 2D DQCP.

Publication: Physical Review B Vol.: 99 No.: 7 ISSN: 2469-9950

ID: CaltechAUTHORS:20181105-090225094

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Abstract: A method for the implementation of a universal set of fault-tolerant logical gates is presented using homological product codes. In particular, it is shown that one can fault-tolerantly map between different encoded representations of a given logical state, enabling the application of different classes of transversal gates belonging to the underlying quantum codes. This allows for the circumvention of no-go results pertaining to universal sets of transversal gates and provides a general scheme for fault-tolerant computation while keeping the stabilizer generators of the code sparse.

Publication: Quantum Vol.: 3ISSN: 2521-327X

ID: CaltechAUTHORS:20190212-154658098

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Abstract: Out-of-time-ordered correlators (OTOCs) have received considerable recent attention as qualitative witnesses of information scrambling in many-body quantum systems. Theoretical discussions of OTOCs typically focus on closed systems, raising the question of their suitability as scrambling witnesses in realistic open systems. We demonstrate empirically that the nonclassical negativity of the quasiprobability distribution (QPD) behind the OTOC is a more sensitive witness for scrambling than the OTOC itself. Nonclassical features of the QPD evolve with timescales that are robust with respect to decoherence and are immune to false positives caused by decoherence. To reach this conclusion, we numerically simulate spin-chain dynamics and three measurement protocols (the interferometric, quantum-clock, and weak-measurement schemes) for measuring OTOCs. We target experiments based on quantum-computing hardware such as superconducting qubits and trapped ions.

Publication: Physical Review Letters Vol.: 122 No.: 4 ISSN: 0031-9007

ID: CaltechAUTHORS:20190201-111654680

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Abstract: We present an exact solution of Einstein’s equation that describes the gravitational shockwave of a massless particle on the horizon of a Kerr–Newman black hole. The backreacted metric is of the generalized Kerr–Schild form and is Type II in the Petrov classification. We show that if the background frame is aligned with shear-free null geodesics, and if the background Ricci tensor satisfies a simple condition, then all nonlinearities in the perturbation will drop out of the curvature scalars. We make heavy use of the method of spin coefficients (the Newman–Penrose formalism) in its compacted form (the Geroch–Held–Penrose formalism).

Publication: General Relativity and Gravitation Vol.: 51 No.: 2 ISSN: 0001-7701

ID: CaltechAUTHORS:20190204-101752686

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Abstract: We derive an identity relating the growth exponent of early-time OTOCs, the pre-exponential factor, and a third number called “branching time”. The latter is defined within the dynamical mean-field framework, namely, in terms of the retarded kernel. This identity can be used to calculate stringy effects in the SYK and similar models; we also explicitly define “strings” in this context. As another application, we consider an SYK chain. If the coupling strength βJ is above a certain threshold and nonlinear (in the magnitude of OTOCs) effects are ignored, the exponent in the butterfly wavefront is exactly 2π/β.

Publication: Journal of High Energy Physics Vol.: 2019 No.: 2 ISSN: 1126-6708

ID: CaltechAUTHORS:20190220-075207560

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Abstract: The properties of coupled emitters can differ dramatically from those of their individual constituents. Canonical examples include sub- and super-radiance, wherein the decay rate of a collective excitation is reduced or enhanced due to correlated interactions with the environment. Here, we systematically study the properties of collective excitations for regularly spaced arrays of quantum emitters coupled to a one-dimensional waveguide. We find that, for low excitation numbers, the modal properties are well-characterized by spin waves with a definite wavevector. Moreover, the decay rate of the most subradiant modes obeys a universal scaling with a cubic suppression in the number of emitters. Multi-excitation subradiant eigenstates can be built from fermionic combinations of single excitation eigenstates; such 'fermionization' results in multiple excitations that spatially repel one another. We put forward a method to efficiently create and measure such subradiant states, which can be realized with superconducting qubits. These measurement protocols probe both real-space correlations (using on-site dispersive readout) and temporal correlations in the emitted field (using photon correlation techniques).

Publication: New Journal of Physics Vol.: 21 No.: 2 ISSN: 1367-2630

ID: CaltechAUTHORS:20180313-154705927

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Abstract: Experiments and numerical simulations are described that develop quantitative understanding of atomic motion near the surfaces of nanoscopic photonic crystal waveguides (PCWs). Ultracold atoms are delivered from a moving optical lattice into the PCW. Synchronous with the moving lattice, transmission spectra for a guided-mode probe field are recorded as functions of lattice transport time and frequency detuning of the probe beam. By way of measurements such as these, we have been able to validate quantitatively our numerical simulations, which are based upon detailed understanding of atomic trajectories that pass around and through nanoscopic regions of the PCW under the influence of optical and surface forces. The resolution for mapping atomic motion is roughly 50 nm in space and 100 ns in time. By introducing auxiliary guided-mode (GM) fields that provide spatially varying AC Stark shifts, we have, to some degree, begun to control atomic trajectories, such as to enhance the flux into the central vacuum gap of the PCW at predetermined times and with known AC Stark shifts. Applications of these capabilities include enabling high fractional filling of optical trap sites within PCWs, calibration of optical fields within PCWs, and utilization of the time-dependent, optically dense atomic medium for novel nonlinear optical experiments.

Publication: Proceedings of the National Academy of Sciences of the United States of America Vol.: 116 No.: 2 ISSN: 0027-8424

ID: CaltechAUTHORS:20190102-070829348

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Abstract: Chaotic dynamics in closed local quantum systems scrambles quantum information, which is manifested quantitatively in the decay of the out-of-time-ordered correlators (OTOC) of local operators. How is information scrambling affected when the system is coupled to the environment and suffers from dissipation? In this paper, we address this question by defining a dissipative version of OTOC and numerically study its behavior in a prototypical chaotic quantum chain in the presence of dissipation. We find that dissipation leads to not only the overall decay of the scrambled information due to leaking but also structural changes so that the ‘information light cone’ can only reach a finite distance even when the effect of overall decay is removed. Based on this observation we conjecture a modified version of the Lieb-Robinson bound in dissipative systems.

Publication: Physical Review B Vol.: 99 No.: 1 ISSN: 2469-9950

ID: CaltechAUTHORS:20190109-090932499

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Abstract: Many-body-localized (MBL) systems do not thermalize under their intrinsic dynamics. The athermality of MBL, we propose, can be harnessed for thermodynamic tasks. We illustrate this ability by formulating an Otto engine cycle for a quantum many-body system. The system is ramped between a strongly localized MBL regime and a thermal (or weakly localized) regime. The difference between the energy-level correlations of MBL systems and of thermal systems enables mesoscale engines to run in parallel in the thermodynamic limit, enhances the engine's reliability, and suppresses worst-case trials. We estimate analytically and calculate numerically the engine's efficiency and per-cycle power. The efficiency mirrors the efficiency of the conventional thermodynamic Otto engine. The per-cycle power scales linearly with the system size and inverse-exponentially with a localization length. This work introduces a thermodynamic lens onto MBL, which, having been studied much recently, can now be considered for use in thermodynamic tasks.

Publication: Physical Review B Vol.: 99 No.: 2 ISSN: 2469-9950

ID: CaltechAUTHORS:20171004-143754557

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Abstract: Floquet engineering offers tantalizing opportunities for controlling the dynamics of quantum many-body systems and realizing new nonequilibrium phases of matter. However, this approach faces a major challenge: generic interacting Floquet systems absorb energy from the drive, leading to uncontrolled heating which washes away the sought-after behavior. How to achieve and control a nontrivial nonequilibrium steady state is therefore of crucial importance. In this work, we study the dynamics of an interacting one-dimensional periodically driven electronic system coupled to a phonon heat bath. Using the Floquet-Boltzmann equation (FBE) we show that the electronic populations of the Floquet eigenstates can be controlled by the dissipation. We find the regime in which the steady state features an insulator-like filling of the Floquet bands, with a low density of additional excitations. Furthermore, we develop a simple rate equation model for the steady state excitation density that captures the behavior obtained from the numerical solution of the FBE over a wide range of parameters.

Publication: Physical Review B Vol.: 99 No.: 1 ISSN: 2469-9950

ID: CaltechAUTHORS:20180710-135957911

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Abstract: Preparing quantum thermal states on a quantum computer is in general a difficult task. We provide a procedure to prepare a thermal state on a quantum computer with a logarithmic depth circuit of local quantum channels assuming that the thermal state correlations satisfy the following two properties: (i) the correlations between two regions are exponentially decaying in the distance between the regions, and (ii) the thermal state is an approximate Markov state for shielded regions. We require both properties to hold for the thermal state of the Hamiltonian on any induced subgraph of the original lattice. Assumption (ii) is satisfied for all commuting Gibbs states, while assumption (i) is satisfied for every model above a critical temperature. Both assumptions are satisfied in one spatial dimension. Moreover, both assumptions are expected to hold above the thermal phase transition for models without any topological order at finite temperature. As a building block, we show that exponential decay of correlation (for thermal states of Hamiltonians on all induced subgraphs) is sufficient to efficiently estimate the expectation value of a local observable. Our proof uses quantum belief propagation, a recent strengthening of strong sub-additivity, and naturally breaks down for states with topological order.

Publication: Communications in Mathematical Physics Vol.: 365 No.: 1 ISSN: 0010-3616

ID: CaltechAUTHORS:20170726-092817023

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Abstract: The equivalence principle is a perennial subject of controversy, especially in connection with radiation by a uniformly accelerated classical charge, or a freely falling charge observed by a supported detector. Recently, related issues have been raised in connection with the Unruh radiation associated with accelerated detectors (including two-level atoms and resonant cavities). A third type of system, very easy to analyze because of conformal invariance, is a two-dimensional scalar field interacting with perfectly reflecting boundaries (mirrors). After reviewing the issues for atoms and cavities, we investigate a stationary mirror from the point of view of an accelerated detector in 'Rindler space'. In keeping with the conclusions of earlier authors about the electromagnetic problem, we find that a radiative effect is indeed observed; from an inertial point of view, the process arises from a collision of the negative vacuum energy of Rindler space with the mirror. There is a qualitative symmetry under interchange of accelerated and inertial subsystems (a vindication of the equivalence principle), but it hinges on the accelerated detector's being initially in its own 'Rindler vacuum'. This observation is consistent with the recent work on the Unruh problem.

Publication: Physica Scripta Vol.: 94 No.: 1 ISSN: 0031-8949

ID: CaltechAUTHORS:20181126-133133488

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Abstract: In systems governed by “chaotic” local Hamiltonians, we conjecture the universality of eigenstate entanglement (defined as the average entanglement entropy of all eigenstates) by proposing an exact formula for its dependence on the subsystem size. This formula is derived from an analytical argument based on a plausible assumption, and is supported by numerical simulations.

Publication: Nuclear Physics B Vol.: 938ISSN: 0550-3213

ID: CaltechAUTHORS:20181009-103946710

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Abstract: Fracton models exhibit a variety of exotic properties and lie beyond the conventional framework of gapped topological order. In a previous work, we generalized the notion of gapped phase to one of foliated fracton phase by allowing the addition of layers of gapped two-dimensional resources in the adiabatic evolution between gapped three-dimensional models. Moreover, we showed that the X-cube model is a fixed point of one such phase. In this paper, according to this definition, we look for universal properties of such phases which remain invariant throughout the entire phase. We propose multi-partite entanglement quantities, generalizing the proposal of topological entanglement entropy designed for conventional topological phases. We present arguments for the universality of these quantities and show that they attain non-zero constant value in non-trivial foliated fracton phases.

Publication: SciPost Physics Vol.: 6 No.: 1 ISSN: 2542-4653

ID: CaltechAUTHORS:20180924-141823095

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Abstract: We revisit the corner transfer matrix renormalization group (CTMRG) method of Nishino and Okunishi for contracting two-dimensional (2D) tensor networks and demonstrate that its performance can be substantially improved by determining the tensors using an eigenvalue solver as opposed to the power method used in CTMRG. We also generalize the variational uniform matrix product state (VUMPS) ansatz for diagonalizing 1D quantum Hamiltonians to the case of 2D transfer matrices and discuss similarities with the corner methods. These two new algorithms will be crucial to improving the performance of variational infinite projected entangled pair state (PEPS) methods.

Publication: Physical Review B Vol.: 98 No.: 23 ISSN: 2469-9950

ID: CaltechAUTHORS:20180626-152653715

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Abstract: Matrix product representation provides a useful formalism to study not only entangled states but also entangled operators in one dimension. In this paper, we focus on unitary transformations and show that matrix product operators that are unitary provide a necessary and sufficient representation of one-dimensional (1D) unitaries that preserve locality. That is, we show that matrix product operators that are unitary are guaranteed to preserve locality by mapping local operators to local operators, while at the same time all locality-preserving unitaries can be represented in a matrix product way. Moreover, we show that matrix product representation gives a straightforward way to extract the index defined by Gross, Nesme, Vogts, and Werner in [D. Gross et al., Commun. Math. Phys. 310, 419 (2012)] for classifying 1D locality-preserving unitaries. The key to our discussion is a set of “fixed-point” conditions which characterize the form of the matrix product unitary operators after blocking sites. Finally, we show that if the unitary condition is only required for certain system sizes, then matrix product formalism allows more possibilities. In particular, we give an example of a simple matrix product operator which is unitary only for odd system sizes, does not preserve locality, and carries a “fractional” index.

Publication: Physical Review B Vol.: 98 No.: 24 ISSN: 2469-9950

ID: CaltechAUTHORS:20171108-141516563

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Abstract: We study thermal states of strongly interacting quantum spin chains and prove that those can be represented in terms of convex combinations of matrix product states. Apart from revealing new features of the entanglement structure of Gibbs states, our results provide a theoretical justification for the use of White's algorithm of minimally entangled typical thermal states. Furthermore, we shed new light on time dependent matrix product state algorithms which yield hydrodynamical descriptions of the underlying dynamics.

Publication: Physical Review B Vol.: 98 No.: 23 ISSN: 2469-9950

ID: CaltechAUTHORS:20190102-092233446

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Abstract: The Quantum Approximate Optimization Algorithm, QAOA, uses a shallow depth quantum circuit to produce a parameter dependent state. For a given combinatorial optimization problem instance, the quantum expectation of the associated cost function is the parameter dependent objective function of the QAOA. We demonstrate that if the parameters are fixed and the instance comes from a reasonable distribution then the objective function value is concentrated in the sense that typical instances have (nearly) the same value of the objective function. This applies not just for optimal parameters as the whole landscape is instance independent. We can prove this is true for low depth quantum circuits for instances of MaxCut on large 3-regular graphs. Our results generalize beyond this example. We support the arguments with numerical examples that show remarkable concentration. For higher depth circuits the numerics also show concentration and we argue for this using the Law of Large Numbers. We also observe by simulation that if we find parameters which result in good performance at say 10 bits these same parameters result in good performance at say 24 bits. These findings suggest ways to run the QAOA that reduce or eliminate the use of the outer loop optimization and may allow us to find good solutions with fewer calls to the quantum computer.

Publication: arXiv
ID: CaltechAUTHORS:20190801-134537838

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Abstract: Time-quasiperiodic Majoranas are generalizations of Floquet Majoranas in time-quasiperiodic superconducting systems. We show that in a system driven at d mutually irrational frequencies, there are up to 2^d types of such Majoranas, coexisting despite spatial overlap and lack of time-translational invariance. Although the quasienergy spectrum is dense in such systems, the time-quasiperiodic Majoranas can be stable and robust against resonances due to localization in periodic-drive-induced synthetic dimensions. This is demonstrated in a time-quasiperiodic Kitaev chain driven at two frequencies. We further relate the existence of multiple Majoranas in a time-quasiperiodic system to the time-quasicrystal phase introduced recently. These time-quasiperiodic Majoranas open a possibility for braiding which will be pursued in the future.

Publication: Physical Review B Vol.: 98 No.: 22 ISSN: 2469-9950

ID: CaltechAUTHORS:20180521-093207551

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Abstract: Dark states are stationary states of a dissipative, Lindblad-type time evolution with zero von Neumann entropy, therefore representing examples of pure steady states. Nonequilibrium dynamics featuring a dark state recently gained a lot of attraction since their implementation in the context of driven-open quantum systems represents a viable possibility to engineer unique, pure states. Inspired by recent experimental progress with ultracold Rydberg ensembles, we analyze a driven many-body spin system, which displays a mean-field bistability between a dark steady state and a mixed steady state. As a function of the driving strength one observes a discontinuous phase transition that connects the zero entropy (dark) state with a finite entropy (mixed) state. The transition is characterized by a jump of the von Neumann entropy from zero to a finite value, which is of genuine nonequilibrium character. We analyze the relevant long wavelength fluctuations driving this transition by means of the renormalization group. This allows us to approach the nonequilibrium dark-state transition and identify similarities and clear differences to common, equilibrium phase transitions, to establish the phenomenology for a first-order dark-state phase transition, and to relate it to the dynamics in driven dissipative Rydberg ensembles.

Publication: Physical Review A Vol.: 98 No.: 6 ISSN: 2469-9926

ID: CaltechAUTHORS:20190102-092233550

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Abstract: Forthcoming exascale digital computers will further advance our knowledge of quantum chromodynamics, but formidable challenges will remain. In particular, Euclidean Monte Carlo methods are not well suited for studying real-time evolution in hadronic collisions, or the properties of hadronic matter at nonzero temperature and chemical potential. Digital computers may never be able to achieve accurate simulations of such phenomena in QCD and other strongly-coupled field theories; quantum computers will do so eventually, though I'm not sure when. Progress toward quantum simulation of quantum field theory will require the collaborative efforts of quantumists and field theorists, and though the physics payoff may still be far away, it's worthwhile to get started now. Today's research can hasten the arrival of a new era in which quantum simulation fuels rapid progress in fundamental physics.

ID: CaltechAUTHORS:20190122-113145453

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Abstract: When two two-dimensional electron gas layers, each at Landau-level filling factor ν=1/2, are sufficiently close together, a condensate of interlayer excitons emerges at low temperature. Although the excitonic phase is qualitatively well understood, the incoherent phase just above the critical layer separation is not. Using a combination of tunneling spectroscopy and conventional transport, we explore the incoherent phase in samples both near the phase boundary and further from it. In the more closely spaced bilayers we find the electronic spectral functions narrower and the Fermi energy of the ν=1/2 composite fermion metal smaller than in the more widely separated bilayers. We attribute these effects to a softening of the intralayer Coulomb interaction due to interlayer screening.

Publication: Physical Review B Vol.: 98 No.: 20 ISSN: 2469-9950

ID: CaltechAUTHORS:20181009-080813831

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Abstract: In this work we address the physics of individual three-dimensional Weyl nodes subject to a moderate concentration of disorder. Previous analysis indicates the presence of a quantum phase transition below which disorder becomes irrelevant and the integrity of sharp nodal points of vanishing spectral density is preserved in this system. This statement appears to be at variance with the inevitable presence of statistically rare fluctuations which cannot be considered as weak and must have strong influence on the system's spectrum, no matter how small the average concentration. We here reconcile the two pictures by demonstrating that rare fluctuation potentials in the Weyl system generate a peculiar type of resonances which carry spectral density in any neighborhood of zero energy, but never at zero. In this way, the vanishing of the DoS for weak disorder survives the inclusion of rare events. We demonstrate this feature by considering three different models of disorder, each emphasizing specific aspects of the problem: a simplistic box potential model, a model with Gaussian distributed disorder, and one with a finite number of s-wave scatterers. Our analysis also explains why the protection of the nodal DoS may be difficult to see in simulations of finite size lattices.

Publication: Physical Review B Vol.: 98 No.: 20 ISSN: 2469-9950

ID: CaltechAUTHORS:20181112-072756668

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Abstract: We show that edge-state transport in semiconductor-based quantum spin Hall systems is unexpectedly robust to magnetic fields. The origin for this robustness lies in an intrinsic suppression of the edge-state g-factor and the fact that the edge-state Dirac point is typically hidden in the valence band. A detailed k⋅p band-structure analysis reveals that both InAs/GaSb and HgTe/CdTe quantum wells exhibit such buried Dirac points for a wide range of well thicknesses. By simulating transport in a disordered system described within an effective model, we demonstrate that edge-state transport remains nearly quantized up to large magnetic fields, consistent with recent experiments.

Publication: Physical Review B Vol.: 98 No.: 20 ISSN: 2469-9950

ID: CaltechAUTHORS:20171004-145628173

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Abstract: We show that the minimal rate of noise needed to catalytically erase the entanglement in a bipartite quantum state is given by the regularized relative entropy of entanglement. This offers a solution to the central open question raised in [Groisman et al., Phys. Rev. A 72, 032317 (2005)] and complements their main result that the minimal rate of noise needed to erase all correlations is given by the quantum mutual information. We extend our discussion to the tripartite setting where we show that an asymptotic rate of noise given by the regularized relative entropy of recovery is sufficient to catalytically transform the state to a locally recoverable version of the state.

Publication: Physical Review Letters Vol.: 121 No.: 19 ISSN: 0031-9007

ID: CaltechAUTHORS:20170817-105927636

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Abstract: Photon-mediated interactions between quantum systems are essential for realizing quantum networks and scalable quantum information processing. We demonstrate such interactions between pairs of silicon-vacancy (SiV) color centers coupled to a diamond nanophotonic cavity. When the optical transitions of the two color centers are tuned into resonance, the coupling to the common cavity mode results in a coherent interaction between them, leading to spectrally-resolved superradiant and subradiant states. We use the electronic spin degrees of freedom of the SiV centers to control these optically-mediated interactions. Such controlled interactions will be crucial in developing cavity-mediated quantum gates between spin qubits and for realizing scalable quantum network nodes.

Publication: Science Vol.: 362 No.: 6415 ISSN: 0036-8075

ID: CaltechAUTHORS:20180920-124019346

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Abstract: We demonstrate optical probing of spectrally resolved single Nd^(3+) rare-earth ions in yttrium orthovanadate. The ions are coupled to a photonic crystal resonator and show strong enhancement of the optical emission rate via the Purcell effect, resulting in near radiatively limited single photon emission. The measured high coupling cooperativity between a single photon and the ion allows for the observation of coherent optical Rabi oscillations. This could enable optically controlled spin qubits, quantum logic gates, and spin-photon interfaces for future quantum networks.

Publication: Physical Review Letters Vol.: 121 No.: 18 ISSN: 0031-9007

ID: CaltechAUTHORS:20181031-132501305

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Abstract: Realization of the quantum spin Hall effect in graphene devices has remained an outstanding challenge dating back to the inception of the field of topological insulators. Graphene’s exceptionally weak spin-orbit coupling—stemming from carbon’s low mass—poses the primary obstacle. We experimentally and theoretically study artificially enhanced spin-orbit coupling in graphene via random decoration with dilute Bi_2Te_3 nanoparticles. Multiterminal resistance measurements suggest the presence of helical edge states characteristic of a quantum spin Hall phase; the magnetic field and temperature dependence of the resistance peaks, x-ray photoelectron spectra, scanning tunneling spectroscopy, and first-principles calculations further support this scenario. These observations highlight a pathway to spintronics and quantum information applications in graphene-based quantum spin Hall platforms.

Publication: Science Advances Vol.: 4 No.: 11 ISSN: 2375-2548

ID: CaltechAUTHORS:20180710-140608150

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Abstract: Characterizing quantum processes is a key task in the development of quantum technologies, especially at the noisy intermediate scale of today’s devices. One method for characterizing processes is randomized benchmarking, which is robust against state preparation and measurement errors and can be used to benchmark Clifford gates. Compressed sensing techniques achieve full tomography of quantum channels essentially at optimal resource efficiency. In this Letter, we show that the favorable features of both approaches can be combined. For characterizing multiqubit unitary gates, we provide a rigorously guaranteed and practical reconstruction method that works with an essentially optimal number of average gate fidelities measured with respect to random Clifford unitaries. Moreover, for general unital quantum channels, we provide an explicit expansion into a unitary 2-design, allowing for a practical and guaranteed reconstruction also in that case. As a side result, we obtain a new statistical interpretation of the unitarity—a figure of merit characterizing the coherence of a process.

Publication: Physical Review Letters Vol.: 121 No.: 17 ISSN: 0031-9007

ID: CaltechAUTHORS:20181025-104453537

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Abstract: This is a collection of notes about spectral form factors of standard ensembles in random matrix theory, written for the practical usage of the current study of late time quantum chaos. More precisely, we consider the Gaussian unitary ensemble, the Gaussian orthogonal ensemble, the Gaussian symplectic ensemble, the Wishart-Laguerre unitary ensemble, the Wishart-Laguerre orthogonal ensemble, and the Wishart-Laguerre symplectic ensemble. These results and their physics applications cover a threefold classification of late time quantum chaos in terms of spectral form factors.

Publication: Physical Review D Vol.: 98 No.: 8 ISSN: 2470-0010

ID: CaltechAUTHORS:20180620-153751182

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Abstract: We study out-of-time-ordered correlators (OTOCs) in hard-core boson models with short-range and long-range hopping and compare the results to the OTOCs in the Luttinger-liquid model. For density-density correlations, a related expectation value of the squared commutator starts at zero and decays back to zero after the passage of the wavefront in all three models, while the wavefront broadens as t^(1/3) in the short-range model and shows no broadening in the long-range model and the Luttinger-liquid model. For the boson creation operator, the corresponding commutator function shows saturation inside the light cone in all three models, with similar wavefront behavior as in the density-density commutator function, despite the presence of a nonlocal string in terms of Jordan-Wigner fermions. For the long-range model and the Luttinger-liquid model, the commutator function decays as a power law outside the light cone in the long-time regime when following different fixed-velocity rays. In all cases, the OTOCs approach their long-time values in a power-law fashion, with different exponents for different observables and short-range versus long-range cases. Our long-range model appears to capture exponents in the Luttinger-liquid model (which are found to be independent of the Luttinger parameter in the model). This conclusion also comes to bear on the OTOC calculations in conformal field theories, which we propose correspond to long-ranged models.

Publication: Physical Review B Vol.: 98 No.: 13 ISSN: 2469-9950

ID: CaltechAUTHORS:20180821-145330708

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Abstract: We give a protocol for producing certifiable randomness from a single untrusted quantum device that is polynomial-time bounded. The randomness is certified to be statistically close to uniform from the point of view of any computationally unbounded quantum adversary, that may share entanglement with the quantum device. The protocol relies on the existence of post-quantum secure trapdoor claw-free functions, and introduces a new primitive for constraining the power of an untrusted quantum device. We then show how to construct this primitive based on the hardness of the learning with errors (LWE) problem. The randomness protocol can also be used as the basis for an efficiently verifiable "quantum supremacy" proposal, thus answering an outstanding challenge in the field.

ID: CaltechAUTHORS:20190201-143229032

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Abstract: We demonstrate single-shot imaging and narrow-line cooling of individual alkaline-earth atoms in optical tweezers; specifically, strontium trapped in 515.2−nm light. Our approach enables high-fidelity detection of single atoms by imaging photons from the broad singlet transition while cooling on the narrow intercombination line, and we extend this technique to highly uniform two-dimensional tweezer arrays with 121 sites. Cooling during imaging is based on a previously unobserved narrow-line Sisyphus mechanism, which we predict to be applicable in a wide variety of experimental situations. Further, we demonstrate optically resolved sideband cooling of a single atom to near the motional ground state of a tweezer, which is tuned to a magic-trapping configuration achieved by elliptical polarization. Finally, we present calculations, in agreement with our experimental results, that predict a linear-polarization and polarization-independent magic crossing at 520(2) nm and 500.65(50) nm, respectively. Our results pave the way for a wide range of novel experimental avenues based on individually controlled alkaline-earth atoms in tweezers—from fundamental experiments in atomic physics to quantum computing, simulation, and metrology.

Publication: Physical Review X Vol.: 8 No.: 4 ISSN: 2160-3308

ID: CaltechAUTHORS:20181203-104933854

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Abstract: We define the deconstruction cost of a tripartite quantum state on systems ABE as the minimum rate of noise needed to apply to the AE systems, such that there is negligible disturbance to the marginal state on the BE systems, while the system A of the resulting state is locally recoverable from the E system alone. We refer to such actions as deconstruction operations and protocols implementing them as state deconstruction protocols. State deconstruction generalizes Landauer erasure of a single-party quantum state as well the erasure of correlations of a two-party quantum state. We find that the deconstruction cost of a tripartite quantum state on systems ABE is equal to its conditional quantum mutual information (CQMI) I(A;B|E), thus giving the CQMI an operational interpretation in terms of a state deconstruction protocol. We also define a related task called conditional erasure, in which the goal is to apply noise to systems AE in order to decouple system A from systems BE, while causing negligible disturbance to the marginal state of systems BE. We find that the optimal rate of noise for conditional erasure is also equal to the CQMI I(A;B|E). State deconstruction and conditional erasure lead to operational interpretations of the quantum discord and squashed entanglement, which are quantum correlation measures based on the CQMI. We find that the quantum discord is equal to the cost of simulating einselection, the process by which a quantum system interacts with an environment, resulting in selective loss of information in the system. The squashed entanglement is equal to half the minimum rate of noise needed for deconstruction and/or conditional erasure if Alice has available the best possible system E to help in the deconstruction and/or conditional erasure task.

Publication: Physical Review A Vol.: 98 No.: 4 ISSN: 2469-9926

ID: CaltechAUTHORS:20170726-092810091

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Abstract: We relate the amount of entanglement required to play linear system non-local games near-optimally to the hyperlinear profile of finitely presented groups. By calculating the hyperlinear profile of a certain group, we give an example of a finite non-local game for which the amount of entanglement required to play ϵ-optimally is at least Ω(1/ϵ^k), f or some k > 0. Since this function approaches infinity as ϵ approaches zero, this provides a quantitative version of a theorem of the first author.

Publication: Annales Henri Poincaré Vol.: 19 No.: 10 ISSN: 1424-0637

ID: CaltechAUTHORS:20180926-132554192

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Abstract: We show that given an explicit description of a multiplayer game, with a classical verifier and a constant number of players, it is QMA-hard, under randomized reductions, to distinguish between the cases when the players have a strategy using entanglement that succeeds with probability 1 in the game, or when no such strategy succeeds with probability larger than 1/2. This proves the “games quantum PCP conjecture” of Fitzsimons and the second author (ITCS'15), albeit under randomized reductions. The core component in our reduction is a construction of a family of two-player games for testing n-qubit maximally entangled states. For any integer n ≥ 2, we give such a game in which questions from the verifier are O(log n) bits long, and answers are poly(loglogn) bits long. We show that for any constant ε ≥ 0, any strategy that succeeds with probability at least 1 - ε in the test must use a state that is within distance δ(ε) = O(ε c ) from a state that is locally equivalent to a maximally entangled state on n qubits, for some universal constant c > 0. The construction is based on the classical plane-vs-point test for multivariate low-degree polynomials of Raz and Safra (STOC'97). We extend the classical test to the quantum regime by executing independent copies of the test in the generalized Pauli X and Z bases over Fq, where q is a sufficiently large prime power, and combine the two through a test for the Pauli twisted commutation relations. Our main complexity-theoretic result is obtained by combining this family of games with techniques from the classical PCP literature. More specifically, we use constructions of PCPs of proximity introduced by Ben-Sasson et al. (CCC'05), and crucially rely on a linear property of such PCPs. Another consequence of our results is a deterministic reduction from the games quantum PCP conjecture to a suitable formulation of the constraint satisfaction quantum PCP conjecture.

ID: CaltechAUTHORS:20190201-143229217

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Abstract: Waveguide quantum electrodynamics studies photon-mediated interactions of quantum emitters in a one-dimensional radiation channel. Although signatures of such interactions have been observed previously in a variety of physical systems, observation of coherent cooperative dynamics has been obscured by radiative decay of atoms into the waveguide. Employing transmon qubits as artificial atoms coupled to a microwave coplanar waveguide, here we observe dynamical oscillations in an open system where a designated probe qubit interacts with an entangled dark state of an array of qubits which effectively traps radiation as an atomic cavity. The qubit-cavity system is shown to achieve a large cooperativity of C=172 due to collective enhancement of photon-mediated interactions, entering the strong coupling regime. The quantum coherence of the dark state cavity is also explored through its nonlinear response at the single-excitation level. With realistic refinements, this system is suitable for studying the many-body dynamics of large (N>10) quantum spin chains, synthesizing highly non-classical radiation fields on demand, and implementing universal quantum logic operations with high fidelity on information encoded within decoherence-free subspaces.

Publication: arXiv
ID: CaltechAUTHORS:20190108-091005866

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Abstract: Feynman's circuit-to-Hamiltonian construction connects quantum computation and ground states of many-body quantum systems. Kitaev applied this construction to demonstrate QMA-completeness of the local Hamiltonian problem, and Aharanov et al. used it to show the equivalence of adiabatic computation and the quantum circuit model. In this work, we analyze the low energy properties of a class of modified circuit Hamiltonians, which include features like complex weights and branching transitions. For history states with linear clocks and complex weights, we develop a method for modifying the circuit propagation Hamiltonian to implement any desired distribution over the time steps of the circuit in a frustration-free ground state, and show that this can be used to obtain a constant output probability for universal adiabatic computation while retaining the Ω(T^(−2))Ω scaling of the spectral gap, and without any additional overhead in terms of numbers of qubits. Furthermore, we establish limits on the increase in the ground energy due to input and output penalty terms for modified tridiagonal clocks with non-uniform distributions on the time steps by proving a tight O(T^(−2)) upper bound on the product of the spectral gap and ground state overlap with the endpoints of the computation. Using variational techniques which go beyond the Ω(T^(−3)) scaling that follows from the usual geometrical lemma, we prove that the standard Feynman-Kitaev Hamiltonian already saturates this bound. We review the formalism of unitary labeled graphs which replace the usual linear clock by graphs that allow branching and loops, and we extend the O(T^(−2)) bound from linear clocks to this more general setting. In order to achieve this, we apply Chebyshev polynomials to generalize an upper bound on the spectral gap in terms of the graph diameter to the context of arbitrary Hermitian matrices.

Publication: Quantum Vol.: 2ISSN: 2521-327X

ID: CaltechAUTHORS:20171102-114342542

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Abstract: We derive an effective equation of motion within the steady-state subspace of a large family of Markovian open systems (i.e., Lindbladians) due to perturbations of their Hamiltonians and system-bath couplings. Under mild and realistic conditions, competing dissipative processes destructively interfere without the need for fine-tuning and produce no dissipation within the steady-state subspace. In quantum error-correction, these effects imply that continuously error-correcting Lindbladians are robust to calibration errors, including miscalibrations consisting of operators undetectable by the code. A similar interference is present in more general systems if one implements a particular Hamiltonian drive, resulting in a coherent cancellation of dissipation. On the opposite extreme, we provide a simple implementation of universal Lindbladian simulation.

Publication: arXiv
ID: CaltechAUTHORS:20190208-121222483

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Abstract: A topological superconductor is characterized by having a pairing gap in the bulk and gapless self-hermitian Majorana modes at its boundary. In one dimension, these are zero-energy modes bound to the ends, while in two dimensions these are chiral gapless modes traveling along the edge. Majorana modes have attracted a lot of interest due to their exotic properties, which include non-abelian exchange statistics. Progress in realizing topological superconductivity has been made by combining spin-orbit coupling, conventional superconductivity, and magnetism. The existence of protected Majorana modes, however, does not inherently require the breaking of time-reversal symmetry by magnetic fields. Indeed, pairs of Majorana modes can reside at the boundary of a \emph{time-reversal-invariant} topological superconductor (TRITOPS). It is the time-reversal symmetry which then protects this so-called Majorana Kramers' pair from gapping out. This is analogous to the case of the two-dimensional topological insulator, with its pair of helical gapless boundary modes, protected by time-reversal symmetry. Realizing the TRITOPS phase will be a major step in the study of topological phases of matter. In this paper we describe the physical properties of the TRITOPS phase, and review recent proposals for engineering and detecting them in condensed matter systems, in one and two spatial dimensions. We mostly focus on extrinsic superconductors, where superconductivity is introduced through the proximity effect. We emphasize the role of interplay between attractive and repulsive electron-electron interaction as an underlying mechanism. When discussing the detection of the TRITOPS phase, we focus on the physical imprint of Majorana Kramers' pairs, and review proposals of transport measurement which can reveal their existence.

ID: CaltechAUTHORS:20181105-101425533

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Abstract: The tensor network representation of many-body quantum states, given by local tensors, provides a promising numerical tool for the study of strongly correlated topological phases in two dimensions. However, the representation may be vulnerable to instabilities caused by small variations in the local tensors. For example, the topological order in the tensor network representations of the toric code ground state has been shown in Chen, Zeng, Gu, Chuang, and Wen, Phys. Rev. B 82, 165119 (2010)to be unstable if the variations break certain Z_2 symmetry of the tensor. In this work, we ask whether other types of topological orders suffer from similar kinds of instability and if so, what is the underlying physical mechanism and whether we can protect the order by enforcing certain symmetries on the tensor. We answer these questions by showing that the tensor network representations of all string-net models are indeed unstable, but the matrix product operator (MPO) symmetries of the tensors identified in Şahinoğlu, Williamson, Bultinck, Mariën, Haegeman, Schuch, and Verstraete, arXiv:1409.2150 can help to protect the order. In particular, we show that a subset of variations that break the MPO symmetries lead to instability by inducing the condensation of bosonic quasiparticles, which destroys the topological order in the wave function. Therefore such variations must be forbidden for the encoded topological order to be reliably extracted from the local tensors. On the other hand, if a tensor network based variational algorithm is used to simulate the phase transition due to boson condensation, such variation directions may prove important to access the continuous transition correctly.

Publication: Physical Review B Vol.: 98 No.: 12 ISSN: 2469-9950

ID: CaltechAUTHORS:20161107-095433292

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Abstract: Embedding tunable quantum emitters in a photonic bandgap structure enables control of dissipative and dispersive interactions between emitters and their photonic bath. Operation in the transmission band, outside the gap, allows for studying waveguide quantum electrodynamics in the slow-light regime. Alternatively, tuning the emitter into the bandgap results in finite-range emitter–emitter interactions via bound photonic states. Here, we couple a transmon qubit to a superconducting metamaterial with a deep sub-wavelength lattice constant (λ/60). The metamaterial is formed by periodically loading a transmission line with compact, low-loss, low-disorder lumped-element microwave resonators. Tuning the qubit frequency in the vicinity of a band-edge with a group index of n_g = 450, we observe an anomalous Lamb shift of −28 MHz accompanied by a 24-fold enhancement in the qubit lifetime. In addition, we demonstrate selective enhancement and inhibition of spontaneous emission of different transmon transitions, which provide simultaneous access to short-lived radiatively damped and long-lived metastable qubit states.

Publication: Nature Communications Vol.: 9ISSN: 2041-1723

ID: CaltechAUTHORS:20180313-154248544

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Abstract: Time-reversal symmetry suppresses electron backscattering in a quantum-spin-Hall edge, yielding quantized conductance at zero temperature. Understanding the dominant corrections in finite-temperature experiments remains an unsettled issue. We study a novel mechanism for conductance suppression: backscattering caused by incoherent electromagnetic noise. Specifically, we show that an electric potential fluctuating randomly in time can backscatter electrons inelastically without constraints faced by electron-electron interactions. We quantify noise-induced corrections to the dc conductance in various regimes and propose an experiment to test this scenario.

Publication: Physical Review Letters Vol.: 121 No.: 10 ISSN: 0031-9007

ID: CaltechAUTHORS:20180906-130214378

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Abstract: Bell-inequality violations establish that two systems share some quantum entanglement. We give a simple test to certify that two systems share an asymptotically large amount of entanglement, n EPR states. The test is efficient: unlike earlier tests that play many games, in sequence or in parallel, our test requires only one or two CHSH games. One system is directed to play a CHSH game on a random specified qubit i, and the other is told to play games on qubits {i,j}, without knowing which index is i. The test is robust: a success probability within delta of optimal guarantees distance O(n^{5/2} sqrt{delta}) from n EPR states. However, the test does not tolerate constant delta; it breaks down for delta = Omega~(1/sqrt{n}). We give an adversarial strategy that succeeds within delta of the optimum probability using only O~(delta^{-2}) EPR states.

Publication: Quantum Vol.: 2ISSN: 2521-327X

ID: CaltechAUTHORS:20171108-142443122

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Abstract: In this paper, we present an exactly solvable model for two-dimensional topological superconductors with helical Majorana edge modes protected by time-reversal symmetry. Our construction is based on the idea of decorated domain walls and makes use of the Kasteleyn orientation on a two-dimensional lattice, which was used for the construction of the symmetry protected fermion phase with Z_2 symmetry by Tarantino et al. and Ware et al. By decorating the time-reversal domain walls with spinful Majorana chains, we are able to construct a commuting projector Hamiltonian with zero correlation length ground state wave function that realizes a strongly interacting version of the two-dimensional topological superconductor. From our construction, it can be seen that the T_2 = −1 transformation rule for the fermions is crucial for the existence of such a nontrivial phase; with T_2 = 1, our construction does not work.

Publication: Physical Review B Vol.: 98 No.: 9 ISSN: 2469-9950

ID: CaltechAUTHORS:20171023-101545053

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Abstract: We examine theoretically how dipole-dipole interactions arising from multiple photon scattering lead to a modified distribution of ground-state populations in a driven, ordered one-dimensional array of multilevel atoms. Specifically, we devise a level configuration in which a ground-state population accumulated solely due to dipole-dipole interactions can be up to 20% in regimes accessible to current experiments with neutral atom arrays. For much larger systems, the steady state can consist of an equal distribution of population across the ground-state manifold. Our results illustrate how dipole-dipole interactions can be accentuated through interference, and regulated by the geometry of ordered atom arrays. More generally, control techniques for multilevel atoms that can be degraded by multiple scattering, such as optical pumping, will benefit from an improved understanding and control of dipole-dipole interactions available in ordered arrays.

Publication: Physical Review A Vol.: 98 No.: 3 ISSN: 2469-9926

ID: CaltechAUTHORS:20180913-133202972

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Abstract: We show that a quantum many-body system may be controlled by means of Floquet engineering, i.e., their properties may be controlled and manipulated by employing periodic driving. We present a concrete driving scheme that allows control over the nature of mobile units and the amount of diffusion in generic many-body systems. We demonstrate these ideas for the Fermi-Hubbard model, where the drive renders doubly occupied sites (doublons) the mobile excitations in the system. In particular, we show that the amount of diffusion in the system and the level of fermion-pairing may be controlled and understood solely in terms of the doublon dynamics. We find that under certain circumstances the diffusion in the system may be eliminated completely. We conclude our work by generalizing these ideas to generic many-body systems.

Publication: SciPost Physics Vol.: 5ISSN: 2542-4653

ID: CaltechAUTHORS:20180620-195305259

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Abstract: Parafermion zero modes are generalizations of Majorana modes that underlie comparatively rich non-Abelian-anyon properties. We introduce exact mappings that connect parafermion chains, which can emerge in two-dimensional fractionalized media, to strictly one-dimensional fermionic systems. In particular, we show that parafermion zero modes in the former setting translate into symmetry-enriched Majorana modes that intertwine with a bulk order parameter—yielding braiding and fusion properties that are impossible in standard Majorana platforms. Fusion characteristics of symmetry-enriched Majorana modes are directly inherited from the associated parafermion setup and can be probed via two kinds of anomalous pumping cycles that we construct. Most notably, our mappings relate ℤ_4 parafermions to conventional electrons with time-reversal symmetry. In this case, one of our pumping protocols entails fairly minimal experimental requirements: Cycling a weakly correlated wire between a trivial phase and time-reversal-invariant topological superconducting state produces an edge magnetization with quadrupled periodicity. Our work highlights new avenues for exploring beyond-Majorana physics in experimentally relevant one-dimensional electronic platforms, including proximitized ferromagnetic chains.

Publication: Physical Review B Vol.: 98 No.: 8 ISSN: 2469-9950

ID: CaltechAUTHORS:20180827-094621499

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Abstract: We numerically assess model wave functions for the recently proposed particle-hole-symmetric Pfaffian (“PH-Pfaffian”) topological order, a phase consistent with the recently reported thermal Hall conductance [M. Banerjee et al., Nature 559, 205 (2018)] at the ever enigmatic ν = 5/2 quantum Hall plateau. We find that the most natural Moore-Read-inspired trial state for the PH-Pfaffian, when projected into the lowest Landau level, exhibits a remarkable numerical similarity on accessible system sizes with the corresponding (compressible) composite Fermi liquid. Consequently, this PH-Pfaffian trial state performs reasonably well energetically in the half-filled lowest Landau level, but is likely not a good starting point for understanding the ν = 5/2 ground state. Our results suggest that the PH-Pfaffian model wave function either encodes anomalously weak p-wave pairing of composite fermions or fails to represent a gapped, incompressible phase altogether.

Publication: Physical Review B Vol.: 98 No.: 8 ISSN: 2469-9950

ID: CaltechAUTHORS:20180810-093237801

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Abstract: Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future. Quantum computers with 50-100 qubits may be able to perform tasks which surpass the capabilities of today's classical digital computers, but noise in quantum gates will limit the size of quantum circuits that can be executed reliably. NISQ devices will be useful tools for exploring many-body quantum physics, and may have other useful applications, but the 100-qubit quantum computer will not change the world right away - we should regard it as a significant step toward the more powerful quantum technologies of the future. Quantum technologists should continue to strive for more accurate quantum gates and, eventually, fully fault-tolerant quantum computing.

Publication: Quantum Vol.: 2ISSN: 2521-327X

ID: CaltechAUTHORS:20180521-094354257

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Abstract: The Berry curvature of a Bloch band can be interpreted as a local magnetic field in reciprocal space. This analogy can be extended by defining an electric field analog in reciprocal space which arises from the time-dependent Berry connection. We explore the term in the semiclassical equation of motion that gives rise to this phenomenon, and show that it can lead to anomalous drift in wave-packet motion. A similar effect arises from changes in the band population due to periodic driving, where the resulting drift depends on the nature of the drive and can be expressed in terms of a shift vector. Finally, these effects can be combined to build a pump with a net anomalous drift during a cyclic evolution in momentum space.

Publication: Physical Review B Vol.: 98 No.: 6 ISSN: 2469-9950

ID: CaltechAUTHORS:20180521-092304073

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Abstract: We propose the use of recurrent neural networks for classifying phases of matter based on the dynamics of experimentally accessible observables. We demonstrate this approach by training recurrent networks on the magnetization traces of two distinct models of one-dimensional disordered and interacting spin chains. The obtained phase diagram for a well-studied model of the many-body localization transition shows excellent agreement with previously known results obtained from time-independent entanglement spectra. For a periodically driven model featuring an inherently dynamical time-crystalline phase, the phase diagram that our network traces coincides with an order parameter for its expected phases.

Publication: Physical Review B Vol.: 98 No.: 6 ISSN: 2469-9950

ID: CaltechAUTHORS:20180723-093013664

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Abstract: The search for exotic quantum spin liquid states in simple yet realistic spin models remains a central challenge in the field of frustrated quantum magnetism. Here we consider the canonical nearest-neighbor kagome Heisenberg antiferromagnet restricted to a quasi-one-dimensional strip consisting entirely of corner-sharing triangles. Using large-scale density matrix renormalization group calculations, we identify in this model an extended gapless quantum phase characterized by central charge c = 2 and power-law decaying spin and bond-energy correlations which oscillate at tunably incommensurate wave vectors. We argue that this intriguing spin liquid phase can be understood as a marginal instability of a two-band spinon Fermi surface coupled to an emergent U(1) gauge field, an interpretation which we substantiate via bosonization analysis and Monte Carlo calculations on model Gutzwiller variational wave functions. Our results represent one of the first numerical demonstrations of emergent fermionic spinons in a simple SU(2) invariant nearest-neighbor Heisenberg model beyond the strictly one-dimensional (Bethe chain) limit.

Publication: Physical Review B Vol.: 98 No.: 5 ISSN: 2469-9950

ID: CaltechAUTHORS:20180827-094621388

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Abstract: A major application for atomic ensembles consists of a quantum memory for light, in which an optical state can be reversibly converted to a collective atomic excitation on demand. There exists a well-known fundamental bound on the storage error, when the ensemble is describable by a continuous medium governed by the Maxwell–Bloch equations. However, these equations are semi-phenomenological, as they treat emission of the atoms into other directions other than the mode of interest as being independent. On the other hand, in systems such as dense, ordered atomic arrays, atoms interact with each other strongly and spatial interference of the emitted light might be exploited to suppress emission into unwanted directions, thereby enabling improved error bounds. Here, we develop a general formalism that fully accounts for spatial interference, and which finds the maximum storage efficiency for a single photon with known spatial input mode into a collection of atoms with discrete, known positions. As an example, we apply this technique to study a finite two-dimensional square array of atoms. We show that such a system enables a storage error that scales with atom number N_a like ~(log N_a)^2/N_a^2, and that, remarkably, an array of just 4 × 4 atoms in principle allows for an error of less than 1%, which is comparable to a disordered ensemble with an optical depth of around 600.

Publication: New Journal of Physics Vol.: 20 No.: 8 ISSN: 1367-2630

ID: CaltechAUTHORS:20180912-135435506

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Abstract: It is conjectured that in the geometric formulation of quantum computing, one can study quantum complexity through classical entropy of statistical ensembles established non-relativistically in the group manifold of unitary operators. The kinetic and positional decompositions of statistical entropy are conjectured to correspond to the Kolmogorov complexity and computational complexity, respectively, of corresponding quantum circuits. In this paper, we claim that by applying the virial theorem to the group manifold, one can derive a generic relation between Kolmogorov complexity and computational complexity in the thermal equilibrium.

Publication: Journal of High Energy Physics Vol.: 2018 No.: 8 ISSN: 1126-6708

ID: CaltechAUTHORS:20180823-140218375

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Abstract: Insights from quantum information theory show that correlation measures based on quantum entropy are fundamental tools that reveal the entanglement structure of multipartite states. In that spirit, Groisman, Popescu, and Winter [Phys. Rev. A 72, 032317 (2005)] showed that the quantum mutual information I(A;B) quantifies the minimal rate of noise needed to erase the correlations in a bipartite state of quantum systems AB. Here, we investigate correlations in tripartite systems ABE. In particular, we are interested in the minimal rate of noise needed to apply to the systems AE in order to erase the correlations between A and B given the information in system E, in such a way that there is only negligible disturbance on the marginal BE. We present two such models of conditional decoupling, called deconstruction and conditional erasure cost of tripartite states ABE. Our main result is that both are equal to the conditional quantum mutual information I(A;B|E)—establishing it as an operational measure for tripartite quantum correlations.

Publication: Physical Review Letters Vol.: 121 No.: 4 ISSN: 0031-9007

ID: CaltechAUTHORS:20180727-091530188

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Abstract: We study the dynamics of Majorana zero modes that are shuttled via local tuning of the electrochemical potential in a superconducting wire. By performing time-dependent simulations of microscopic lattice models, we show that diabatic corrections associated with the moving Majorana modes are quantitatively captured by a simple Landau-Zener description. We further simulate a Rabi-oscillation protocol in a specific qubit design with four Majorana zero modes in a single wire and quantify constraints on the timescales for performing qubit operations in this setup. Our simulations utilize a Majorana representation of the system, which greatly simplifies simulations of superconductors at the mean-field level.

Publication: SciPost Physics Vol.: 5 No.: 1 ISSN: 2542-4653

ID: CaltechAUTHORS:20190521-132353909

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Abstract: Fractons are gapped pointlike excitations in d=3 topological ordered phases whose motion is constrained. They have been discovered in several gapped models but a unifying physical mechanism for generating them is still missing. It has been noticed that in symmetric-tensor U(1) gauge theories, charges are fractons and cannot move freely due to, for example, the conservation of not only the charge but also the dipole moment. To connect these theories with fully gapped fracton models, we study Higgs and partial confinement mechanisms in rank-2 symmetric-tensor gauge theories, where charges or magnetic excitations, respectively, are condensed. Specifically, we describe two different routes from the rank-2 U(1) scalar charge theory to the X-cube fracton topological order, finding that a combination of Higgs and partial confinement mechanisms is necessary to obtain the fully gapped fracton model. On the other hand, the rank-2 Z_2 scalar charge theory, which is obtained from the former theory upon condensing charge-2 matter, is equivalent to four copies of the d=3 toric code and does not support fracton excitations. We also explain how the checkerboard fracton model can be viewed as a rank-2 Z_2 gauge theory with two different Gauss' law constraints on different lattice sites.

Publication: Physical Review B Vol.: 98 No.: 3 ISSN: 2469-9950

ID: CaltechAUTHORS:20180710-075128971

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Abstract: We studied the in-plane dynamic and static charge conductivity of electron doped Sr_2IrO_4 using optical spectroscopy and DC transport measurements. The optical conductivity indicates that the pristine material is an indirect semiconductor with a direct Mott gap of 0.55 eV. Upon substitution of 2% La per formula unit the Mott gap is suppressed except in a small fraction of the material (15%) where the gap survives, and overall the material remains insulating. Instead of a zero energy mode (or Drude peak) we observe a soft collective mode (SCM) with a broad maximum at 40 meV. Doping to 10% increases the strength of the SCM, and a zero-energy mode occurs together with metallic DC conductivity. Further increase of the La substitution doesn't change the spectral weight integral up to 3 eV. It does however result in a transfer of the SCM spectral weight to the zero-energy mode, with a corresponding reduction of the DC resistivity for all temperatures from 4 to 300 K. The presence of a zero-energy mode signals that at least part of the Fermi surface remains ungapped at low temperatures, whereas the SCM appears to be caused by pinning a collective frozen state involving part of the doped electrons.

Publication: Physical Review B Vol.: 98 No.: 4 ISSN: 2469-9950

ID: CaltechAUTHORS:20180705-153353866

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Abstract: Heat transport studies of fractional quantum Hall systems provide evidence for a new phase of matter with potential applications in fault-tolerant quantum computation.

Publication: Physics Vol.: 11ISSN: 1943-2879

ID: CaltechAUTHORS:20180709-130559395

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Abstract: We present two techniques that can greatly reduce the number of gates required to realize an energy measurement, with application to ground state preparation in quantum simulations. The first technique realizes that to prepare the ground state of some Hamiltonian, it is not necessary to implement the time-evolution operator: any unitary operator which is a function of the Hamiltonian will do. We propose one such unitary operator which can be implemented exactly, circumventing any Taylor or Trotter approximation errors. The second technique is tailored to lattice models, and is targeted at reducing the use of generic single-qubit rotations, which are very expensive to produce by standard fault tolerant techniques. In particular, the number of generic single-qubit rotations used by our method scales with the number of parameters in the Hamiltonian, which contrasts with a growth proportional to the lattice size required by other techniques.

Publication: Physical Review Letters Vol.: 121 No.: 1 ISSN: 0031-9007

ID: CaltechAUTHORS:20180705-150616687

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Abstract: Rare-earth ions in crystals are a proven solid-state platform for quantum technologies in the ensemble regime and attractive for new opportunities at the single-ion level. Among the trivalent rare earths, ^(171)Yb^(3+) is unique in that it possesses a single 4f excited-state manifold and is the only paramagnetic isotope with a nuclear spin of 1/2. In this work, we present measurements of the optical and spin properties of ^(171)Yb^(3+):YVO_4 to assess whether this distinct energy-level structure can be harnessed for quantum interfaces. The material was found to possess large optical absorption compared to other rare-earth-doped crystals owing to the combination of narrow inhomogeneous broadening and a large transition oscillator strength. In moderate magnetic fields, we measure optical linewidths less than 3 kHz and nuclear spin linewidths less than 50 Hz. We characterize the excited-state hyperfine and Zeeman interactions in this system, which enables the engineering of a Λ system and demonstration of all-optical coherent control over the nuclear-spin ensemble. Given these properties, ^(171)Yb^(3+):YVO_4 has significant potential for building quantum interfaces such as ensemble-based memories, microwave-to-optical transducers, and optically addressable single rare-earth-ion spin qubits.

Publication: Physical Review B Vol.: 98 No.: 2 ISSN: 2469-9950

ID: CaltechAUTHORS:20180705-152507349

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Abstract: This Colloquium describes a new paradigm for creating strong quantum interactions of light and matter by way of single atoms and photons in nanoscopic lattices. Beyond the possibilities for quantitative improvements for familiar phenomena in atomic physics and quantum optics, there is a growing research community that is exploring novel quantum phases and phenomena that arise from atom-photon interactions in one- and two-dimensional nanophotonic lattices. Nanophotonic structures offer the intriguing possibility to control atom-photon interactions by engineering the medium properties through which they interact. An important aspect of these new research lines is that they have become possible only by pushing the state-of-the-art capabilities in nanophotonic device fabrication and by the integration of these capabilities into the realm of ultracold atoms. This Colloquium attempts to inform a broad physics community of the emerging opportunities in this new field on both theoretical and experimental fronts. The research is inherently multidisciplinary, spanning the fields of nanophotonics, atomic physics, quantum optics, and condensed matter physics.

Publication: Reviews of Modern Physics Vol.: 90 No.: 3 ISSN: 0034-6861

ID: CaltechAUTHORS:20180801-135418489

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Abstract: Fracton models, a collection of exotic gapped lattice Hamiltonians recently discovered in three spatial dimensions, contain some “topological” features: They support fractional bulk excitations (dubbed fractons) and a ground-state degeneracy that is robust to local perturbations. However, because previous fracton models have been defined and analyzed only on a cubic lattice with periodic boundary conditions, it is unclear to what extent a notion of topology is applicable. In this paper, we demonstrate that the X-cube model, a prototypical type-I fracton model, can be defined on general three-dimensional manifolds. Our construction revolves around the notion of a singular compact total foliation of the spatial manifold, which constructs a lattice from intersecting stacks of parallel surfaces called leaves. We find that the ground-state degeneracy depends on the topology of the leaves and the pattern of leaf intersections. We further show that such a dependence can be understood from a renormalization group transformation for the X-cube model, wherein the system size can be changed by adding or removing 2D layers of topological states. Our results lead to an improved definition of fracton phase and bring to the fore the topological nature of fracton orders.

Publication: Physical Review X Vol.: 8 No.: 3 ISSN: 2160-3308

ID: CaltechAUTHORS:20180829-095556028

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Abstract: For systems of controllable qubits, we provide a method for experimentally obtaining a useful class of multitime correlators using sequential generalized measurements of arbitrary strength. Specifically, if a correlator can be expressed as an average of nested (anti)commutators of operators that square to the identity, then that correlator can be determined exactly from the average of a measurement sequence. As a relevant example, we provide quantum circuits for measuring multiqubit out-of-time-order correlators using optimized control-Z or ZX-90 two-qubit gates common in superconducting transmon implementations.

Publication: Physical Review A Vol.: 98 No.: 1 ISSN: 2469-9926

ID: CaltechAUTHORS:20180725-074911293

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Abstract: Holographic states that have a well-defined geometric dual in AdS/CFT are not faithfully represented by Haar-typical states in finite-dimensional models. As such, trying to apply principles and lessons from Haar-random ensembles of states to holographic states can lead to apparent puzzles and contradictions. We point out a handful of these pitfalls.

Publication: SciPost Physics Vol.: 4 No.: 6 ISSN: 2542-4653

ID: CaltechAUTHORS:20190521-131432519

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Abstract: We show that dimerization of an optomechanical crystal lattice, which leads to folding of the band diagram, can couple flexural mechanical modes to optical fields within the unit cell via radiation pressure. When compared to currently realized crystals, a substantial improvement in the coupling between photons and phonons is found. For experimental verification, we implement a dimerized lattice in a silicon optomechanical nanobeam cavity and measure a vacuum coupling rate of g_0/2π= 1.7 MHz between an optical resonance at λ_c = 1545 nm and a mechanical resonance at 1.14 GHz.

Publication: Applied Physics Letters Vol.: 112 No.: 25 ISSN: 0003-6951

ID: CaltechAUTHORS:20180619-130930341

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Abstract: We introduce a family of commuting-projector Hamiltonians whose degrees of freedom involve ℤ_3 parafermion zero modes residing in a parent fractional-quantum-Hall fluid. These commuting-projector models inherit nontrivial Hall conductance from the parent quantum-Hall states in which they are defined, and thus can describe chiral topological phases. The two simplest models in this family emerge from dressing Ising-paramagnet and toric-code spin models with parafermions; we study their edge properties, anyonic excitations, and ground-state degeneracy. We show that the first model realizes a symmetry-enriched topological phase (SET) for which ℤ_2 spin-flip symmetry from the Ising paramagnet permutes the anyons. Interestingly, the interface between this SET and the parent quantum-Hall phase realizes symmetry-enforced ℤ_3 parafermion criticality with no fine-tuning required. The second model exhibits a non-Abelian phase that is consistent with SU(2)_4 topological order, and can be accessed by gauging the ℤ_2 symmetry in the SET. Employing Levin-Wen string-net models with ℤ_2-graded structure, we generalize this picture to construct a large class of commuting-projector models for ℤ_2 SETs and non-Abelian topological orders exhibiting the same relation. Our construction provides the first commuting-projector-Hamiltonian realization of chiral bosonic non-Abelian topological order.

Publication: Physical Review B Vol.: 97 No.: 24 ISSN: 2469-9950

ID: CaltechAUTHORS:20180626-130432855

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Abstract: We theoretically study the topological robustness of the surface physics induced by Weyl Fermi-arc surface states in the presence of short-ranged quenched disorder and surface-bulk hybridization. This is investigated with numerically exact calculations on a lattice model exhibiting Weyl Fermi arcs. We find that the Fermi-arc surface states, in addition to having a finite lifetime from disorder broadening, hybridize with nonperturbative bulk rare states making them no longer bound to the surface (i.e., they lose their purely surface spectral character). Thus, we provide strong numerical evidence that the Weyl Fermi arcs are not topologically protected from disorder. Nonetheless, the surface chiral velocity is robust and survives in the presence of strong disorder, persisting all the way to the Anderson-localized phase by forming localized current loops that live within the localization length of the surface. Thus, the Weyl semimetal is not topologically robust to the presence of disorder, but the surface chiral velocity is.

Publication: Physical Review B Vol.: 97 No.: 23 ISSN: 2469-9950

ID: CaltechAUTHORS:20180607-103545257

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Abstract: Robust electronic edge or surface modes play key roles in the fascinating quantized responses exhibited by topological materials. Even in trivial materials, topological bands and edge states can be induced dynamically by a time-periodic drive. Such Floquet topological insulators (FTIs) inherently exist out of equilibrium; the extent to which they can host quantized transport, which depends on the steady-state population of their dynamically induced edge states, remains a crucial question. In this work, we obtain the steady states of two-dimensional FTIs in the presence of the natural dissipation mechanisms present in solid state systems. We give conditions under which the steady-state distribution resembles that of a topological insulator in the Floquet basis. In this state, the distribution in the Floquet edge modes exhibits a sharp feature akin to a Fermi level, while the bulk hosts a small density of excitations. We determine the regimes where topological edge-state transport persists and can be observed in FTIs.

Publication: Physical Review B Vol.: 97 No.: 24 ISSN: 2469-9950

ID: CaltechAUTHORS:20180606-094237198

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Abstract: On-chip nanophotonic cavities will advance quantum information science and measurement because they enable efficient interaction between photons and long-lived solid-state spins, such as those associated with rare-earth ions in crystals. The enhanced photon-ion interaction creates new opportunities for all-optical control using the ac Stark shift. Toward this end, we characterize the ac Stark interaction between off-resonant optical fields and Nd^(3+)-ion dopants in a photonic crystal resonator fabricated from yttrium orthovanadate (YVO_4). Using photon echo techniques, at a detuning of 160 MHz we measure a maximum ac Stark shift of 2π × 12.3 MHz per intracavity photon, which is large compared to both the homogeneous linewidth (Γ_h = 84 kHz) and characteristic width of isolated spectral features created through optical pumping (Γ_f ≈ 3 MHz). The photon-ion interaction strength in the device is sufficiently large to control the frequency and phase of the ions for quantum information processing applications. In particular, we discuss and assess the use of the cavity enhanced ac Stark shift to realize all-optical quantum memory and detection protocols. Our results establish the ac Stark shift as a powerful added control in rare-earth ion quantum technologies.

Publication: Physical Review A Vol.: 97 No.: 6 ISSN: 2469-9926

ID: CaltechAUTHORS:20180627-161133893

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Abstract: Summoning retrieves quantum information, prepared somewhere in spacetime, at another specified point in spacetime, but this task is limited by the quantum no-cloning principle and the speed-of-light bound. We develop a thorough mathematical framework for summoning quantum information in a relativistic system and formulate a quantum summoning protocol for any valid configuration of causal diamonds in spacetime. For single-qubit summoning, we present a protocol based on a Calderbank–Shor–Steane code that decreases the space complexity for encoding by a factor of two compared to the previous best result and reduces the gate complexity from scaling as the cube to the square of the number of causal diamonds. Our protocol includes decoding whose gate complexity scales linearly with the number of causal diamonds. Our thorough framework for quantum summoning enables full specification of the protocol, including spatial and temporal implementation and costs, which enables quantum summoning to be a well posed protocol for relativistic quantum communication purposes.

Publication: New Journal of Physics Vol.: 20 No.: 6 ISSN: 1367-2630

ID: CaltechAUTHORS:20180629-103232818

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Abstract: We show that for any ε > 0 there is an XOR game G = G(ε) with Θ(ε^(−1/5)) inputs for one player and Θ(ε^(−2/5)) inputs for the other player such that Ω(ε^(−1/5)) ebits are required for any strategy achieving bias that is at least a multiplicative factor (1−ε) from optimal. This gives an exponential improvement in both the number of inputs or outputs and the noise tolerance of any previously-known self-test for highly entangled states. Up to the exponent −1/5 the scaling of our bound with ε is tight: for any XOR game there is an ε-optimal strategy using ⌈ε^(−1)⌉ ebits, irrespective of the number of questions in the game.

Publication: Quantum Information and Computation Vol.: 18 No.: 7-8 ISSN: 1533-7146

ID: CaltechAUTHORS:20180926-101512002

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Abstract: Most experimental protocols for measuring scrambling require time evolution with a Hamiltonian and with the Hamiltonian's negative counterpart (backward time evolution). Engineering controllable quantum many-body systems for which such forward and backward evolution is possible is a significant experimental challenge. Furthermore, if the system of interest is quantum chaotic, one might worry that any small errors in the time reversal will be rapidly amplified, obscuring the physics of scrambling. This paper undermines this expectation: We exhibit a renormalization protocol that extracts nearly ideal out-of-time-ordered-correlator measurements from imperfect experimental measurements. We analytically and numerically demonstrate the protocol's effectiveness, up to the scrambling time, in a variety of models and for sizable imperfections. The scheme extends to errors from decoherence by an environment.

Publication: Physical Review A Vol.: 97 No.: 6 ISSN: 2469-9926

ID: CaltechAUTHORS:20180614-080416976

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Abstract: We show that Araki and Masuda’s weighted non-commutative vector-valued L_p-spaces (Araki and Masuda in Publ Res Inst Math Sci Kyoto Univ 18:339–411, 1982) correspond to an algebraic generalization of the sandwiched Rényi divergences with parameter α = p/2. Using complex interpolation theory, we prove various fundamental properties of these divergences in the setup of von Neumann algebras, including a data-processing inequality and monotonicity in α. We thereby also give new proofs for the corresponding finite-dimensional properties. We discuss the limiting cases α → {1/2,1,∞} leading to minus the logarithm of Uhlmann’s fidelity, Umegaki’s relative entropy, and the max-relative entropy, respectively. As a contribution that might be of independent interest, we derive a Riesz–Thorin theorem for Araki–Masuda L_p-spaces and an Araki–Lieb–Thirring inequality for states on von Neumann algebras.

Publication: Annales Henri Poincaré Vol.: 19 No.: 6 ISSN: 1424-0637

ID: CaltechAUTHORS:20170817-111159578

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Abstract: We show that it is NP-hard to approximate, to within an additive constant, the maximum success probability of players sharing quantum entanglement in a two-player game with classical questions of logarithmic length and classical answers of constant length. As a corollary, the inclusion NEXP subseteq MIP^*, first shown by Ito and Vidick (FOCS'12) with three provers, holds with two provers only. The proof is based on a simpler, improved analysis of the low-degree test of Raz and Safra (STOC'97) against two entangled provers.

Publication: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany
ID: CaltechAUTHORS:20180822-141142977

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Abstract: We propose and analyze a novel realization of a solid-state quantum network, where separated silicon-vacancy centers are coupled via the phonon modes of a quasi-one-dimensional diamond waveguide. In our approach, quantum states encoded in long-lived electronic spin states can be converted into propagating phonon wave packets and be reabsorbed efficiently by a distant defect center. Our analysis shows that under realistic conditions, this approach enables the implementation of high-fidelity, scalable quantum communication protocols within chip-scale spin-qubit networks. Apart from quantum information processing, this setup constitutes a novel waveguide QED platform, where strong-coupling effects between solid-state defects and individual propagating phonons can be explored at the quantum level.

Publication: Physical Review Letters Vol.: 120 No.: 21 ISSN: 0031-9007

ID: CaltechAUTHORS:20180525-090858291

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Abstract: We present a field-theoretic treatment of an adiabatic quantum motor. We explicitly discuss a motor called the Thouless motor which is based on a Thouless pump operating in reverse. When a sliding periodic potential is considered to be the motor degree of freedom, a bias voltage applied to the electron channel sets the motor in motion. We investigate a Thouless motor whose electron channel is modeled as a Luttinger liquid. Interactions increase the gap opened by the periodic potential. For an infinite Luttinger liquid the coupling-induced friction is enhanced by electron-electron interactions. When the Luttinger liquid is ultimately coupled to Fermi liquid reservoirs, the dissipation reduces to its value for a noninteracting electron system for a constant motor velocity. Our results can also be applied to a motor based on a nanomagnet coupled to a quantum spin Hall edge.

Publication: Physical Review B Vol.: 97 No.: 19 ISSN: 2469-9950

ID: CaltechAUTHORS:20180509-110549288

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Abstract: Quantum indistinguishability plays a crucial role in many low-energy physical phenomena, from quantum fluids to molecular spectroscopy. It is, however, typically ignored in most high-temperature processes, particularly for ionic coordinates, implicitly assumed to be distinguishable, incoherent, and thus well approximated classically. We explore enzymatic chemical reactions involving small symmetric molecules and argue that in many situations a full quantum treatment of collective nuclear degrees of freedom is essential. Supported by several physical arguments, we conjecture a “quantum dynamical selection” (QDS) rule for small symmetric molecules that precludes chemical processes that involve direct transitions from orbitally nonsymmetric molecular states. As we propose and discuss, the implications of the QDS rule include (i) a differential chemical reactivity of para- and orthohydrogen, (ii) a mechanism for inducing intermolecular quantum entanglement of nuclear spins, (iii) a mass-independent isotope fractionation mechanism, (iv) an explanation of the enhanced chemical activity of “reactive oxygen species”, (v) illuminating the importance of ortho-water molecules in modulating the quantum dynamics of liquid water, and (vi) providing the critical quantum-to-biochemical linkage in the nuclear spin model of the (putative) quantum brain, among others.

Publication: Proceedings of the National Academy of Sciences of the United States of America Vol.: 115 No.: 20 ISSN: 0027-8424

ID: CaltechAUTHORS:20180430-145931994

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Abstract: We control the electronic structure of the silicon-vacancy (SiV) color-center in diamond by changing its static strain environment with a nano-electro-mechanical system. This allows deterministic and local tuning of SiV optical and spin transition frequencies over a wide range, an essential step towards multiqubit networks. In the process, we infer the strain Hamiltonian of the SiV revealing large strain susceptibilities of order 1 PHz/strain for the electronic orbital states. We identify regimes where the spin-orbit interaction results in a large strain susceptibility of order 100 THz/strain for spin transitions, and propose an experiment where the SiV spin is strongly coupled to a nanomechanical resonator.

Publication: Physical Review B Vol.: 97 No.: 20 ISSN: 2469-9950

ID: CaltechAUTHORS:20180529-090727339

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Abstract: Methylammonium lead iodide perovskite (MAPbI_3) exhibits long charge carrier lifetimes that are linked to its high efficiency in solar cells. Yet, the mechanisms governing these unusual carrier dynamics are not completely understood. A leading hypothesis—disproved in this work—is that a large, static bulk Rashba effect slows down carrier recombination. Here, using second harmonic generation rotational anisotropy measurements on MAPbI_3 crystals, we demonstrate that the bulk structure of tetragonal MAPbI_3 is centrosymmetric with I4/mcmspace group. Our calculations show that a significant Rashba splitting in the bandstructure requires a non-centrosymmetric lead iodide framework, and that incorrect structural relaxations are responsible for the previously predicted large Rashba effect. The small Rashba splitting allows us to compute effective masses in excellent agreement with experiment. Our findings rule out the presence of a large static Rashba effect in bulk MAPbI_3, and our measurements find no evidence of dynamic Rashba effects.

Publication: Nature Communications Vol.: 9ISSN: 2041-1723

ID: CaltechAUTHORS:20180508-105825258

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Abstract: Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the storage threshold error rates for bit-flip and phase-flip noise in the 3D color code (3DCC) on the body-centered cubic lattice, assuming perfect syndrome measurements. In particular, by exploiting a connection between error correction and statistical mechanics, we estimate the threshold for 1D stringlike and 2D sheetlike logical operators to be p^((1))_(3DCC) ≃ 1.9% and p^((2))_(3DCC) ≃ 27.6%. We obtain these results by using parallel tempering Monte Carlo simulations to study the disorder-temperature phase diagrams of two new 3D statistical-mechanical models: the four- and six-body random coupling Ising models.

Publication: Physical Review Letters Vol.: 120 No.: 18 ISSN: 0031-9007

ID: CaltechAUTHORS:20171004-145219476

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Abstract: The nonunity quantum efficiency (QE) in photodiodes (PD) causes deterioration of signal quality in quantum optical experiments due to photocurrent loss as well as the introduction of vacuum fluctuations into the measurement. In this paper, we report that the external QE enhancement of a PD was demonstrated by recycling the reflected photons. The external QE for an InGaAs PD was increased by 0.01–0.06 from 0.86–0.92 over a wide range of incident angles. Moreover, we confirmed that this technique does not increase backscattered light when the recycled beam is properly misaligned.

Publication: Applied Optics Vol.: 57 No.: 13 ISSN: 0003-6935

ID: CaltechAUTHORS:20171112-131948306

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Abstract: Given an entanglement measure E, the entanglement of a quantum channel is defined as the largest amount of entanglement E that can be generated from the channel, if the sender and receiver are not allowed to share a quantum state before using the channel. The amortized entanglement of a quantum channel is defined as the largest net amount of entanglement E that can be generated from the channel, if the sender and receiver are allowed to share an arbitrary state before using the channel. Our main technical result is that amortization does not enhance the entanglement of an arbitrary quantum channel, when entanglement is quantified by the max-Rains relative entropy. We prove this statement by employing semi-definite programming (SDP) duality and SDP formulations for the max-Rains relative entropy and a channel's max-Rains information, found recently in Wang et al (arXiv:1709.00200). The main application of our result is a single-letter, strong converse, and efficiently computable upper bound on the capacity of a quantum channel for transmitting qubits when assisted by positive-partial-transpose preserving (PPT-P) channels between every use of the channel. As the class of local operations and classical communication (LOCC) is contained in PPT-P, our result establishes a benchmark for the LOCC-assisted quantum capacity of an arbitrary quantum channel, which is relevant in the context of distributed quantum computation and quantum key distribution.

Publication: New Journal of Physics Vol.: 20 No.: 5 ISSN: 1367-2630

ID: CaltechAUTHORS:20180518-131642361

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Abstract: We use random matrix theory to explore late-time chaos in supersymmetric quantum mechanical systems. Motivated by the recent study of supersymmetric SYK models and their random matrix classification, we consider the Wishart-Laguerre unitary ensemble and compute the spectral form factors and frame potentials to quantify chaos and randomness. Compared to the Gaussian ensembles, we observe the absence of a dip regime in the form factor and a slower approach to Haar-random dynamics. We find agreement between our random matrix analysis and predictions from the supersymmetric SYK model, and discuss the implications for supersymmetric chaotic systems.

Publication: Journal of High Energy Physics Vol.: 2018 No.: 5 ISSN: 1126-6708

ID: CaltechAUTHORS:20180601-081711482

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Abstract: Single- and two-mode multiphoton states are the cornerstone of many quantum technologies, e.g., metrology. In the optical regime, these states are generally obtained combining heralded single photons with linear optics tools and post-selection, leading to inherent low success probabilities. In a recent paper [A. González-Tudela et al., Phys. Rev. Lett. 118, 213601 (2017)], we design several protocols that harness the long-range atomic interactions induced in waveguide QED to improve fidelities and protocols of single-mode multiphoton emission. Here, we give full details of these protocols, revisit them to simplify some of their requirements, and also extend them to generate two-mode multiphoton states, such as Yurke or NOON states.

Publication: Physical Review A Vol.: 97 No.: 5 ISSN: 2469-9926

ID: CaltechAUTHORS:20180313-161114247

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Abstract: Thermodynamics describes large-scale, slowly evolving systems. Two modern approaches generalize thermodynamics: fluctuation theorems, which concern finite-time nonequilibrium processes, and one-shot statistical mechanics, which concerns small scales and finite numbers of trials. Combining these approaches, we calculate a one-shot analog of the average dissipated work defined in fluctuation contexts: the cost of performing a protocol in finite time instead of quasistatically. The average dissipated work has been shown to be proportional to a relative entropy between phase-space densities, to a relative entropy between quantum states, and to a relative entropy between probability distributions over possible values of work. We derive one-shot analogs of all three equations, demonstrating that the order-infinity Rényi divergence is proportional to the maximum possible dissipated work in each case. These one-shot analogs of fluctuation-theorem results contribute to the unification of these two toolkits for small-scale, nonequilibrium statistical physics.

Publication: Physical Review E Vol.: 97 No.: 5 ISSN: 2470-0045

ID: CaltechAUTHORS:20150622-113733758

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Abstract: For many years, quasicrystals were observed only as solid-state metallic alloys, yet current research is now actively exploring their formation in a variety of soft materials, including systems of macromolecules, nanoparticles and colloids. Much effort is being invested in understanding the thermodynamic properties of these soft-matter quasicrystals in order to predict and possibly control the structures that form, and hopefully to shed light on the broader yet unresolved general questions of quasicrystal formation and stability. Moreover, the ability to control the self-assembly of soft quasicrystals may contribute to the development of novel photonics or other applications based on self-assembled metamaterials. Here a path is followed, leading to quantitative stability predictions, that starts with a model developed two decades ago to treat the formation of multiple-scale quasiperiodic Faraday waves (standing wave patterns in vibrating fluid surfaces) and which was later mapped onto systems of soft particles, interacting via multiple-scale pair potentials. The article reviews, and substantially expands, the quantitative predictions of these models, while correcting a few discrepancies in earlier calculations, and presents new analytical methods for treating the models. In so doing, a number of new stable quasicrystalline structures are found with octagonal, octadecagonal and higher-order symmetries, some of which may, it is hoped, be observed in future experiments.

Publication: International Union of Crystallography Journal Vol.: 5 No.: 3 ISSN: 2052-2525

ID: CaltechAUTHORS:20180220-092159661

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Abstract: Experimental control over ultracold quantum gases has made it possible to investigate low-dimensional systems of both bosonic and fermionic atoms. In closed one-dimensional systems there are many similarities in the dynamics of local quantities for spinless fermions and strongly interacting “hard-core” bosons, which on a lattice can be formalized via a Jordan-Wigner transformation. In this study, we analyze the similarities and differences for spinless fermions and hard-core bosons on a lattice in the presence of particle loss. The removal of a single fermion causes differences in local quantities compared with the bosonic case because of the different particle exchange symmetry in the two cases. We identify deterministic and probabilistic signatures of these dynamics in terms of local particle density, which could be measured in ongoing experiments with quantum gas microscopes.

Publication: Physical Review A Vol.: 97 No.: 5 ISSN: 2469-9926

ID: CaltechAUTHORS:20180521-090406352

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Abstract: We show that for three dimensional gravity with higher genus boundary conditions, if the theory possesses a sufficiently light scalar, there is a second order phase transition where the scalar field condenses. This three dimensional version of the holographic superconducting phase transition occurs even though the pure gravity solutions are locally AdS3. This is in addition to the first order Hawking-Page-like phase transitions between different locally AdS3 handlebodies. This implies that the Rényi entropies of holographic CFTs will undergo phase transitions as the Rényi parameter is varied, as long as the theory possesses a scalar operator which is lighter than a certain critical dimension. We show that this critical dimension has an elegant mathematical interpretation as the Hausdorff dimension of the limit set of a quotient group of AdS3, and use this to compute it, analytically near the boundary of moduli space and numerically in the interior of moduli space. We compare this to a CFT computation generalizing recent work of Belin, Keller and Zadeh, bounding the critical dimension using higher genus conformal blocks, and find a surprisingly good match.

Publication: Journal of High Energy Physics Vol.: 2018 No.: 5 ISSN: 1126-6708

ID: CaltechAUTHORS:20180606-103432482

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Abstract: The representation of discrete, compact wavelet transformations (WTs) as circuits of local unitary gates is discussed. We employ a similar formalism as used in the multiscale representation of quantum many-body wave functions using unitary circuits, further cementing the relation established in the literature between classical and quantum multiscale methods. An algorithm for constructing the circuit representation of known orthogonal, dyadic, discrete WTs is presented, and the explicit representation for Daubechies wavelets, coiflets, and symlets is provided. Furthermore, we demonstrate the usefulness of the circuit formalism in designing WTs, including various classes of symmetric wavelets and multiwavelets, boundary wavelets, and biorthogonal wavelets.

Publication: Physical Review A Vol.: 97 No.: 5 ISSN: 2469-9926

ID: CaltechAUTHORS:20161031-090659507

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Abstract: We give an exposition of the SYK model with several new results. A non-local correction to the Schwarzian effective action is found. The same action is obtained by integrating out the bulk degrees of freedom in a certain variant of dilaton gravity. We also discuss general properties of out-of-time-order correlators.

Publication: Journal of High Energy Physics Vol.: 2018 No.: 5 ISSN: 1126-6708

ID: CaltechAUTHORS:20180530-110303978

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Abstract: The classification of states of matter and their corresponding phase transitions is a special kind of machine-learning task, where physical data allow for the analysis of new algorithms, which have not been considered in the general computer-science setting so far. Here we introduce an unsupervised machine-learning scheme for detecting phase transitions with a pair of discriminative cooperative networks (DCNs). In this scheme, a guesser network and a learner network cooperate to detect phase transitions from fully unlabeled data. The new scheme is efficient enough for dealing with phase diagrams in two-dimensional parameter spaces, where we can utilize an active contour model—the snake—from computer vision to host the two networks. The snake, with a DCN “brain,” moves and learns actively in the parameter space, and locates phase boundaries automatically.

Publication: Physical Review Letters Vol.: 120 No.: 17 ISSN: 0031-9007

ID: CaltechAUTHORS:20180426-142653150

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Abstract: A defining feature of a symmetry protected topological phase (SPT) in one dimension is the degeneracy of the Schmidt values for any given bipartition. For the system to go through a topological phase transition separating two SPTs, the Schmidt values must either split or cross at the critical point in order to change their degeneracies. A renormalization group (RG) approach based on this splitting or crossing is proposed, through which we obtain an RG flow that identifies the topological phase transitions in the parameter space. Our approach can be implemented numerically in an efficient manner, for example, using the matrix product state formalism, since only the largest first few Schmidt values need to be calculated with sufficient accuracy. Using several concrete models, we demonstrate that the critical points and fixed points of the RG flow coincide with the maxima and minima of the entanglement entropy, respectively, and the method can serve as a numerically efficient tool to analyze interacting SPTs in the parameter space.

Publication: Physical Review B Vol.: 97 No.: 15 ISSN: 2469-9950

ID: CaltechAUTHORS:20180425-144715290

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Abstract: Magnetic adsorbates on superconductors induce local bound states within the superconducting gap. These Yu-Shiba-Rusinov (YSR) states decay slowly away from the impurity compared to atomic orbitals, even in 3D bulk crystals. Here, we use scanning tunneling spectroscopy to investigate their hybridization between two nearby magnetic Mn adatoms on a superconducting Pb(001) surface. We observe that the hybridization leads to the formation of symmetric and antisymmetric combinations of YSR states. We investigate how the structure of the dimer wave functions and the energy splitting depend on the shape of the underlying monomer orbitals and the orientation of the dimer with respect to the Pb lattice.

Publication: Physical Review Letters Vol.: 120 No.: 15 ISSN: 0031-9007

ID: CaltechAUTHORS:20180412-110335738

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Abstract: Out-of-time-ordered correlators (OTOC) have been proposed to characterize quantum chaos in generic systems. However, they can also show interesting behavior in integrable models, resembling the OTOC in chaotic systems in some aspects. Here we study the OTOC for different operators in the exactly-solvable one-dimensional quantum Ising spin chain. The OTOC for spin operators that are local in terms of the Jordan-Wigner fermions has a “shell-like” structure: After the wavefront passes, the OTOC approaches its original value in the long-time limit, showing no signature of scrambling; the approach is described by a t^(−1) power law at long time t. On the other hand, the OTOC for spin operators that are nonlocal in the Jordan-Wigner fermions has a “ball-like” structure, with its value reaching zero in the long-time limit, looking like a signature of scrambling; the approach to zero, however, is described by a slow power law t^(−1/4) for the Ising model at the critical coupling. These long-time power-law behaviors in the lattice model are not captured by conformal field theory calculations. The mixed OTOC with both local and nonlocal operators in the Jordan-Wigner fermions also has a “ball-like” structure, but the limiting values and the decay behavior appear to be nonuniversal. In all cases, we are not able to define a parametrically large window around the wavefront to extract the Lyapunov exponent.

Publication: Physical Review B Vol.: 97 No.: 14 ISSN: 2469-9950

ID: CaltechAUTHORS:20180418-093907947

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Abstract: Combining physical and synthetic dimensions allows a controllable realization and manipulation of high-dimensional topological states. In our work, we introduce two quasiperiodically driven one-dimensional systems which enable tunable topological energy conversion between different driving sources. Using three drives, we realize a four-dimensional quantum Hall state which allows energy conversion between two of the drives within the bulk of the one-dimensional system. With only two drives, we achieve energy conversion between the two at the edge of the chain. Both effects are a manifestation of the effective axion electrodynamics in a three-dimensional time-reversal-invariant topological insulator. Furthermore, we explore the effects of disorder and commensurability of the driving frequencies, and show the phenomena are robust. We propose two experimental platforms, based on semiconductor heterostructures and ultracold atoms in optical lattices, in order to observe the topological energy conversion.

Publication: Physical Review B Vol.: 97 No.: 13 ISSN: 2469-9950

ID: CaltechAUTHORS:20180416-135742666

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Abstract: Stabilizer codes are among the most successful quantum error-correcting codes, yet they have important limitations on their ability to fault tolerantly compute. Here, we introduce a new quantity, the disjointness of the stabilizer code, which, roughly speaking, is the number of mostly nonoverlapping representations of any given nontrivial logical Pauli operator. The notion of disjointness proves useful in limiting transversal gates on any error-detecting stabilizer code to a finite level of the Clifford hierarchy. For code families, we can similarly restrict logical operators implemented by constant-depth circuits. For instance, we show that it is impossible, with a constant-depth but possibly geometrically nonlocal circuit, to implement a logical non-Clifford gate on the standard two-dimensional surface code.

Publication: Physical Review X Vol.: 8 No.: 2 ISSN: 2160-3308

ID: CaltechAUTHORS:20180521-152345918

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Abstract: Information-theoretic approaches provide a promising avenue for extending the laws of thermodynamics to the nanoscale. Here, we provide a general fundamental lower limit, valid for systems with an arbitrary Hamiltonian and in contact with any thermodynamic bath, on the work cost for the implementation of any logical process. This limit is given by a new information measure—the coherent relative entropy—which accounts for the Gibbs weight of each microstate. The coherent relative entropy enjoys a collection of natural properties justifying its interpretation as a measure of information and can be understood as a generalization of a quantum relative entropy difference. As an application, we show that the standard first and second laws of thermodynamics emerge from our microscopic picture in the macroscopic limit. Finally, our results have an impact on understanding the role of the observer in thermodynamics: Our approach may be applied at any level of knowledge—for instance, at the microscopic, mesoscopic, or macroscopic scales—thus providing a formulation of thermodynamics that is inherently relative to the observer. We obtain a precise criterion for when the laws of thermodynamics can be applied, thus making a step forward in determining the exact extent of the universality of thermodynamics and enabling a systematic treatment of Maxwell-demon-like situations.

Publication: Physical Review X Vol.: 8 No.: 2 ISSN: 2160-3308

ID: CaltechAUTHORS:20171102-133438149

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Abstract: Two topics, evolving rapidly in separate fields, were combined recently: the out-of-time-ordered correlator (OTOC) signals quantum-information scrambling in many-body systems. The Kirkwood-Dirac (KD) quasiprobability represents operators in quantum optics. The OTOC was shown to equal a moment of a summed quasiprobability [Yunger Halpern, Phys. Rev. A 95, 012120 (2017)]. That quasiprobability, we argue, is an extension of the KD distribution. We explore the quasiprobability's structure from experimental, numerical, and theoretical perspectives. First, we simplify and analyze Yunger Halpern's weak-measurement and interference protocols for measuring the OTOC and its quasiprobability. We decrease, exponentially in system size, the number of trials required to infer the OTOC from weak measurements. We also construct a circuit for implementing the weak-measurement scheme. Next, we calculate the quasiprobability (after coarse graining) numerically and analytically: we simulate a transverse-field Ising model first. Then, we calculate the quasiprobability averaged over random circuits, which model chaotic dynamics. The quasiprobability, we find, distinguishes chaotic from integrable regimes. We observe nonclassical behaviors: the quasiprobability typically has negative components. It becomes nonreal in some regimes. The onset of scrambling breaks a symmetry that bifurcates the quasiprobability, as in classical-chaos pitchforks. Finally, we present mathematical properties. We define an extended KD quasiprobability that generalizes the KD distribution. The quasiprobability obeys a Bayes-type theorem, for example, that exponentially decreases the memory required to calculate weak values, in certain cases. A time-ordered correlator analogous to the OTOC, insensitive to quantum-information scrambling, depends on a quasiprobability closer to a classical probability. This work not only illuminates the OTOC's underpinnings, but also generalizes quasiprobability theory and motivates immediate-future weak-measurement challenges.

Publication: Physical Review A Vol.: 97 No.: 4 ISSN: 2469-9926

ID: CaltechAUTHORS:20171108-145509877

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Abstract: Cherently splitting a one-dimensional Bose gas provides an attractive, experimentally established platform to investigate many-body quantum dynamics. At short enough times, the dynamics is dominated by the dephasing of single quasiparticles, and well described by the relaxation towards a generalized Gibbs ensemble corresponding to the free Luttinger theory. At later times on the other hand, the approach to a thermal Gibbs ensemble is expected for a generic, interacting quantum system. Here, we go one step beyond the quadratic Luttinger theory and include the leading phonon-phonon interactions. By applying kinetic theory and nonequilibrium Dyson-Schwinger equations, we analyze the full relaxation dynamics beyond dephasing and determine the asymptotic thermalization process in the two-wire system for a symmetric splitting protocol. The major observables are the different phonon occupation functions and the experimentally accessible coherence factor, as well as the phase correlations between the two wires. We demonstrate that, depending on the splitting protocol, the presence of phonon collisions can have significant influence on the asymptotic evolution of these observables, which makes the corresponding thermalization dynamics experimentally accessible.

Publication: Physical Review A Vol.: 97 No.: 4 ISSN: 2469-9926

ID: CaltechAUTHORS:20180411-114458960

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Abstract: We consider a one-dimensional interacting spinless fermion model, which displays the well-known Luttinger liquid (LL) to charge density wave (CDW) transition as a function of the ratio between the strength of the interaction U and the hopping J . We subject this system to a spatially uniform drive which is ramped up over a finite time interval and becomes time periodic in the long-time limit. We show that by using a density matrix renormalization group approach formulated for infinite system sizes, we can access the large-time limit even when the drive induces finite heating. When both the initial and long-time states are in the gapless (LL) phase, the final state has power-law correlations for all ramp speeds. However, when the initial and final state are gapped (CDW phase), we find a pseudothermal state with an effective temperature that depends on the ramp rate, both for the Magnus regime in which the drive frequency is very large compared to other scales in the system and in the opposite limit where the drive frequency is less than the gap. Remarkably, quantum defects (instantons) appear when the drive tunes the system through the quantum critical point, in a realization of the Kibble-Zurek mechanism.

Publication: Physical Review Letters Vol.: 120 No.: 12 ISSN: 0031-9007

ID: CaltechAUTHORS:20180313-161721314

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Abstract: When a d-dimensional quantum system is subjected to a periodic drive, it may be treated as a (d+1)-dimensional system, where the extra dimension is a synthetic one. This approach, however, affords only a limited level of control of the effective potential along the synthetic direction. In this work, we introduce a new mean for controlling the Floquet synthetic dimension. We show that arbitrary potentials, as well as edges in the synthetic dimension, could be introduced using a memory component in the system’s dynamics. We demonstrate this principle by exploring topological edge states propagating normal to synthetic dimensions. Such systems may act as an optical isolator which allows the transmission of light in a directional way. Also, we suggest an experimental realization of the memory effect in spins coupled to nanofabricated Weyl semimetal surface states.

Publication: Physical Review Letters Vol.: 120 No.: 10 ISSN: 0031-9007

ID: CaltechAUTHORS:20171004-143507726

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Abstract: We prove, for any state in a conformal field theory defined on a set of boundary manifolds with corresponding classical holographic bulk geometry, that for any bipartition of the boundary into two non-clopen sets, the density matrix cannot be a tensor product of the reduced density matrices on each region of the bipartition. In particular, there must be entanglement across the bipartition surface. We extend this no-go theorem to general, arbitrary partitions of the boundary manifolds into non-clopen parts, proving that the density matrix cannot be a tensor product. This result gives a necessary condition for states to potentially correspond to holographic duals.

Publication: Europhysics Letters Vol.: 121 No.: 6 ISSN: 0295-5075

ID: CaltechAUTHORS:20170314-133758800

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Abstract: The early Gottesman, Kitaev, and Preskill (GKP) proposal for encoding a qubit in an oscillator has recently been followed by cat- and binomial-code proposals. Numerically optimized codes have also been proposed, and we introduce codes of this type here. These codes have yet to be compared using the same error model; we provide such a comparison by determining the entanglement fidelity of all codes with respect to the bosonic pure-loss channel (i.e., photon loss) after the optimal recovery operation. We then compare achievable communication rates of the combined encoding-error-recovery channel by calculating the channel's hashing bound for each code. Cat and binomial codes perform similarly, with binomial codes outperforming cat codes at small loss rates. Despite not being designed to protect against the pure-loss channel, GKP codes significantly outperform all other codes for most values of the loss rate. We show that the performance of GKP and some binomial codes increases monotonically with increasing average photon number of the codes. In order to corroborate our numerical evidence of the cat-binomial-GKP order of performance occurring at small loss rates, we analytically evaluate the quantum error-correction conditions of those codes. For GKP codes, we find an essential singularity in the entanglement fidelity in the limit of vanishing loss rate. In addition to comparing the codes, we draw parallels between binomial codes and discrete-variable systems. First, we characterize one- and two-mode binomial as well as multiqubit permutation-invariant codes in terms of spin-coherent states. Such a characterization allows us to introduce check operators and error-correction procedures for binomial codes. Second, we introduce a generalization of spin-coherent states, extending our characterization to qudit binomial codes and yielding a multiqudit code.

Publication: Physical Review A Vol.: 97 No.: 3 ISSN: 2469-9926

ID: CaltechAUTHORS:20180330-091105009

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Abstract: Thermodynamics, which describes vast systems, has been reconciled with small scales, relevant to single-molecule experiments, in resource theories. Resource theories have been used to model exchanges of energy and information. Recently, particle exchanges were modeled; and an umbrella family of thermodynamic resource theories was proposed to model diverse baths, interactions, and free energies. This paper motivates and details the family's structure and prospective applications. How to model electrochemical, gravitational, magnetic, and other thermodynamic systems is explained. Szilárd's engine and Landauer's Principle are generalized, as resourcefulness is shown to be convertible not only between information and gravitational energy, but also among diverse degrees of freedom. Extensive variables are associated with quantum operators that might fail to commute, introducing extra nonclassicality into thermodynamic resource theories. An early version of this paper partially motivated the later development of noncommutative thermalization. This generalization expands the theories' potential for modeling realistic systems with which small-scale statistical mechanics might be tested experimentally.

Publication: Journal of Physics A: Mathematical and Theoretical Vol.: 51 No.: 9 ISSN: 1751-8113

ID: CaltechAUTHORS:20180202-075245400

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Abstract: The eigenstate thermalization hypothesis is a compelling conjecture which strives to explain the apparent thermal behavior of generic observables in closed quantum systems. Although we are far from a complete analytic understanding, quantum chaos is often seen as a strong indication that the ansatz holds true. In this paper, we address the thermalization of energy eigenstates in the Sachdev-Ye-Kitaev model, a maximally chaotic model of strongly-interacting Majorana fermions. We numerically investigate eigenstate thermalization for specific few-body operators in the original SYK model as well as its N = 1 supersymmetric extension and find evidence that these models satisfy ETH. We discuss the implications of ETH for a gravitational dual and the quantum information-theoretic properties of SYK it suggests.

Publication: Journal of High Energy Physics Vol.: 2018 No.: 2 ISSN: 1126-6708

ID: CaltechAUTHORS:20171011-191649202

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Abstract: We prove that the asymptotic behavior of the recoupling coefficients of the symmetric group S_k is characterized by a quantum marginal problem: they decay polynomially in k if there exists a quantum state of three particles with given eigenvalues for their reduced density operators and exponentially otherwise. As an application, we deduce solely from symmetry considerations of the coefficients the strong subadditivity property of the von Neumann entropy, first proved by Lieb and Ruskai (J Math Phys 14:1938–1941, 1973). Our work may be seen as a non-commutative generalization of the representation-theoretic aspect of the recently found connection between the quantum marginal problem and the Kronecker coefficient of the symmetric group, which has applications in quantum information theory and algebraic complexity theory. This connection is known to generalize the correspondence between Weyl’s problem on the addition of Hermitian matrices and the Littlewood–Richardson coefficients of SU(d). In this sense, our work may also be regarded as a generalization of Wigner’s famous observation of the semiclassical behavior of the recoupling coefficients (here also known as 6j or Racah coefficients), which decay polynomially whenever a tetrahedron with given edge lengths exists. More precisely, we show that our main theorem contains a characterization of the possible eigenvalues of partial sums of Hermitian matrices thus presenting a representation-theoretic characterization of a generalization of Weyl’s problem. The appropriate geometric objects to SU(d) recoupling coefficients are thus tuples of Hermitian matrices and to S_k recoupling coefficients they are three-particle quantum states.

Publication: Annales Henri Poincaré Vol.: 19 No.: 2 ISSN: 1424-0637

ID: CaltechAUTHORS:20171215-104925515

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Abstract: Device-independent cryptography goes beyond conventional quantum cryptography by providing security that holds independently of the quality of the underlying physical devices. Device-independent protocols are based on the quantum phenomena of non-locality and the violation of Bell inequalities. This high level of security could so far only be established under conditions which are not achievable experimentally. Here we present a property of entropy, termed “entropy accumulation”, which asserts that the total amount of entropy of a large system is the sum of its parts. We use this property to prove the security of cryptographic protocols, including device-independent quantum key distribution, while achieving essentially optimal parameters. Recent experimental progress, which enabled loophole-free Bell tests, suggests that the achieved parameters are technologically accessible. Our work hence provides the theoretical groundwork for experimental demonstrations of device-independent cryptography.

Publication: Nature Communications Vol.: 9ISSN: 2041-1723

ID: CaltechAUTHORS:20180130-110708768

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Abstract: We have used a combination of ultrafast coherent phonon spectroscopy, ultrafast thermometry, and time-dependent Landau theory to study the inversion symmetry breaking phase transition at T_c=200 K in the strongly spin-orbit coupled correlated metal Cd_2Re_2O_7. We establish that the structural distortion at T_c is a secondary effect through the absence of any softening of its associated phonon mode, which supports a purely electronically driven mechanism. However, the phonon lifetime exhibits an anomalously strong temperature dependence that decreases linearly to zero near T_c. We show that this behavior naturally explains the spurious appearance of phonon softening in previous Raman spectroscopy experiments and should be a prevalent feature of correlated electron systems with linearly coupled order parameters.

Publication: Physical Review Letters Vol.: 120 No.: 4 ISSN: 0031-9007

ID: CaltechAUTHORS:20180131-160608890

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Abstract: We introduce a method “DMT” for approximating density operators of 1D systems that, when combined with a standard framework for time evolution (TEBD), makes possible simulation of the dynamics of strongly thermalizing systems to arbitrary times. We demonstrate that the method performs well for both near-equilibrium initial states (Gibbs states with spatially varying temperatures) and far-from-equilibrium initial states, including quenches across phase transitions and pure states.

Publication: Physical Review B Vol.: 97 No.: 3 ISSN: 2469-9950

ID: CaltechAUTHORS:20170925-082950649

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Abstract: We combine the density matrix renormalization group (DMRG) with matrix product state tangent space concepts to construct a variational algorithm for finding ground states of one-dimensional quantum lattices in the thermodynamic limit. A careful comparison of this variational uniform matrix product state algorithm (VUMPS) with infinite density matrix renormalization group (IDMRG) and with infinite time evolving block decimation (ITEBD) reveals substantial gains in convergence speed and precision. We also demonstrate that VUMPS works very efficiently for Hamiltonians with long-range interactions and also for the simulation of two-dimensional models on infinite cylinders. The new algorithm can be conveniently implemented as an extension of an already existing DMRG implementation.

Publication: Physical Review B Vol.: 97 No.: 4 ISSN: 2469-9950

ID: CaltechAUTHORS:20171103-134852714

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Abstract: We show that Ramsey spectroscopy of fermionic alkaline-earth atoms in a square-well trap provides an efficient and accurate estimate for the eigenspectrum of a density matrix whose n copies are stored in the nuclear spins of n such atoms. This spectrum estimation is enabled by the high symmetry of the interaction Hamiltonian, dictated, in turn, by the decoupling of the nuclear spin from the electrons and by the shape of the square-well trap. Practical performance of this procedure and its potential applications to quantum computing and time keeping with alkaline-earth atoms are discussed.

Publication: Physical Review Letters Vol.: 120 No.: 2 ISSN: 0031-9007

ID: CaltechAUTHORS:20170123-122232253

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Abstract: Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg limit, which can be achieved for noiseless quantum systems, but is not achievable in general for systems subject to noise. Here we study how measurement precision can be enhanced through quantum error correction, a general method for protecting a quantum system from the damaging effects of noise. We find a necessary and sufficient condition for achieving the Heisenberg limit using quantum probes subject to Markovian noise, assuming that noiseless ancilla systems are available, and that fast, accurate quantum processing can be performed. When the sufficient condition is satisfied, a quantum error-correcting code can be constructed that suppresses the noise without obscuring the signal; the optimal code, achieving the best possible precision, can be found by solving a semidefinite program.

Publication: Nature Communications Vol.: 9ISSN: 2041-1723

ID: CaltechAUTHORS:20170720-172112488

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Abstract: Recent work has shown that quantum computers can compute scattering probabilities in massive quantum field theories, with a run time that is polynomial in the number of particles, their energy, and the desired precision. Here we study a closely related quantum field-theoretical problem: estimating the vacuum-to-vacuum transition amplitude, in the presence of spacetime-dependent classical sources, for a massive scalar field theory in (1+1) dimensions. We show that this problem is BQP-hard; in other words, its solution enables one to solve any problem that is solvable in polynomial time by a quantum computer. Hence, the vacuum-to-vacuum amplitude cannot be accurately estimated by any efficient classical algorithm, even if the field theory is very weakly coupled, unless BQP=BPP. Furthermore, the corresponding decision problem can be solved by a quantum computer in a time scaling polynomially with the number of bits needed to specify the classical source fields, and this problem is therefore BQP-complete. Our construction can be regarded as an idealized architecture for a universal quantum computer in a laboratory system described by massive phi^4 theory coupled to classical spacetime-dependent sources.

Publication: Quantum Vol.: 2ISSN: 2521-327X

ID: CaltechAUTHORS:20170720-172919513

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Abstract: Conventional wisdom suggests that the long-time behavior of isolated interacting periodically driven (Floquet) systems is a featureless maximal-entropy state characterized by an infinite temperature. Efforts to thwart this uninteresting fixed point include adding sufficient disorder to realize a Floquet many-body localized phase or working in a narrow region of drive frequencies to achieve glassy nonthermal behavior at long time. Here we show that in clean systems the Floquet eigenstates can exhibit nonthermal behavior due to finite system size. We consider a one-dimensional system of spinless fermions with nearest-neighbor interactions where the interaction term is driven. Interestingly, even with no static component of the interaction, the quasienergy spectrum contains gaps and a significant fraction of the Floquet eigenstates, at all quasienergies, have nonthermal average doublon densities. We show that this nonthermal behavior arises due to emergent integrability at large interaction strength and discuss how the integrability breaks down with power-law dependence on system size.

Publication: Physical Review B Vol.: 97 No.: 1 ISSN: 2469-9950

ID: CaltechAUTHORS:20180130-143240205

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Abstract: At long times, residual couplings to the environment become relevant even in the most isolated experiments, a crucial difficulty for the study of fundamental aspects of many-body dynamics. A particular example is many-body localization in a cold-atom setting, where incoherent photon scattering introduces both dephasing and particle loss. Whereas dephasing has been studied in detail and is known to destroy localization already on the level of non-interacting particles, the effect of particle loss is less well understood. A difficulty arises due to the 'non-local' nature of the loss process, complicating standard numerical tools using matrix product decomposition. Utilizing symmetries of the Lindbladian dynamics, we investigate the particle loss on both the dynamics of observables, as well as the structure of the density matrix and the individual states. We find that particle loss in the presence of interactions leads to dissipation and a strong suppression of the (operator space) entanglement entropy. Our approach allows for the study of the interplay of dephasing and loss for pure and mixed initial states to long times, which is important for future experiments using controlled coupling of the environment.

Publication: Quantum Science and Technology Vol.: 3 No.: 1 ISSN: 2058-9565

ID: CaltechAUTHORS:20171215-092653893

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Abstract: We show how the snowflake phononic crystal structure, which recently has been realized experimentally, can be turned into a topological ins ulator for mechanical waves. This idea, based purely on simple geometrical modifications, could be readily implemented on the nanoscale.

Publication: Physical Review B Vol.: 97 No.: 2 ISSN: 2469-9950

ID: CaltechAUTHORS:20170427-154005220

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Abstract: We numerically construct translationally invariant quasiconserved operators with maximum range M, which best commute with a nonintegrable quantum spin chain Hamiltonian, up to M = 12. In the large coupling limit, we find that the residual norm of the commutator of the quasiconserved operator decays exponentially with its maximum range M at small M, and turns into a slower decay at larger M. This quasiconserved operator can be understood as a dressed total “spin-z” operator, by comparing with the perturbative Schrieffer-Wolff construction developed to high order reaching essentially the same maximum range. We also examine the operator inverse participation ratio of the operator, which suggests its localization in the operator Hilbert space. The operator also shows an almost exponentially decaying profile at short distance, while the long-distance behavior is not clear due to limitations of our numerical calculation. Further dynamical simulation confirms that the prethermalization-equilibrated values are described by a generalized Gibbs ensemble that includes such quasiconserved operator.

Publication: Physical Review B Vol.: 96 No.: 21 ISSN: 2469-9950

ID: CaltechAUTHORS:20171004-144618632

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Abstract: The success of polynomial-time tensor network methods for computing ground states of certain quantum local Hamiltonians has recently been given a sound theoretical basis by Arad et al. [Math. Phys. 356, 65 (2017)]. The convergence proof, however, relies on “rigorous renormalization group” (RRG) techniques which differ fundamentally from existing algorithms. We introduce a practical adaptation of the RRG procedure which, while no longer theoretically guaranteed to converge, finds matrix product state ansatz approximations to the ground spaces and low-lying excited spectra of local Hamiltonians in realistic situations. In contrast to other schemes, RRG does not utilize variational methods on tensor networks. Rather, it operates on subsets of the system Hilbert space by constructing approximations to the global ground space in a treelike manner. We evaluate the algorithm numerically, finding similar performance to density matrix renormalization group (DMRG) in the case of a gapped nondegenerate Hamiltonian. Even in challenging situations of criticality, large ground-state degeneracy, or long-range entanglement, RRG remains able to identify candidate states having large overlap with ground and low-energy eigenstates, outperforming DMRG in some cases.

Publication: Physical Review B Vol.: 96 No.: 21 ISSN: 2469-9950

ID: CaltechAUTHORS:20170627-090122309

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Abstract: We characterize surface-plasmon polaritons at lossy planar interfaces between one dispersive and one nondispersive linear isotropic homogeneous media, i.e. materials or metamaterials. Specifically, we solve Maxwell's equations to obtain strict bounds for the permittivity and permeability of these media, such that satisfying these bounds implies surface-plasmon polaritons successfully propagate at the interface, and violation of the bounds impedes propagation, i.e. the field delocalizes from the surface into the bulk. Our characterization of surface-plasmon polaritons is valuable for checking the viability of a proposed application, and, as an example, we employ our method to falsify a previous prediction that surface-plasmon propagation through a surface of a double-negative refractive index medium occurs for any permittivity and permeability; instead, we show that propagation can occur only for certain medium parameters.

Publication: Journal of Optics Vol.: 19 No.: 12 ISSN: 2040-8978

ID: CaltechAUTHORS:20171120-103930042

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Abstract: Understanding what distinguishes quantum mechanics from classical mechanics is crucial for quantum information processing applications. In this work, we consider two notions of non-classicality for quantum systems, negativity of the Wigner function and contextuality for Pauli measurements. We prove that these two notions are equivalent for multi-qudit systems with odd local dimension. For a single qudit, the equivalence breaks down. We show that there exist single qudit states that admit a non-contextual hidden variable model description and whose Wigner functions are negative.

Publication: New Journal of Physics Vol.: 19 No.: 12 ISSN: 1367-2630

ID: CaltechAUTHORS:20180102-134007465

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Abstract: Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistics that can be obtained from the respective quantum states. In contrast, Petz showed that the measured relative entropy, defined as a maximization of the Kullback–Leibler divergence over projective measurement statistics, is strictly smaller than Umegaki’s quantum relative entropy whenever the states do not commute. We extend this result in two ways. First, we show that Petz’ conclusion remains true if we allow general positive operator-valued measures. Second, we extend the result to Rényi relative entropies and show that for non-commuting states the sandwiched Rényi relative entropy is strictly larger than the measured Rényi relative entropy for α∈(1/2,∞) and strictly smaller for α∈[0,1/2). The latter statement provides counterexamples for the data processing inequality of the sandwiched Rényi relative entropy for α<1/2. Our main tool is a new variational expression for the measured Rényi relative entropy, which we further exploit to show that certain lower bounds on quantum conditional mutual information are superadditive.

Publication: Letters in Mathematical Physics Vol.: 107 No.: 12 ISSN: 0377-9017

ID: CaltechAUTHORS:20161024-110728241

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Abstract: In a recent work, Moshkovitz [FOCS'14] presented a transformation n two-player games called "fortification", and gave an elementary proof of an (exponential decay) parallel repetition theorem for fortified two-player projection games. In this paper, we give an analytic reformulation of Moshkovitz's fortification framework, which was originally cast in combinatorial terms. This reformulation allows us to expand the scope of the fortification method to new settings. First, we show any game (not just projection games) can be fortified, and give a simple proof of parallel repetition for general fortified games. Then, we prove parallel repetition and fortification theorems for games with players sharing quantum entanglement, as well as games with more than two players. This gives a new gap amplification method for general games in the quantum and multiplayer settings, which has recently received much interest. An important component of our work is a variant of the fortification transformation, called "ordered fortification", that preserves the entangled value of a game. The original fortification of Moshkovitz does not in general preserve the entangled value of a game, and this was a barrier to extending the fortification framework to the quantum setting.

No.: 67
ID: CaltechAUTHORS:20160321-071142064

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Abstract: One of the central challenges in the study of quantum many-body systems is the complexity of simulating them on a classical computer. A recent advance by Landau et al. gave a polynomial time algorithm to compute a succinct classical description for unique ground states of gapped 1D quantum systems. Despite this progress many questions remained unresolved, including whether there exist rigorous efficient algorithms when the ground space is degenerate (and poly(n) dimensional), or for the poly(n) lowest energy states for 1D systems, or even whether such states admit succinct classical descriptions or area laws. In this paper we give a new algorithm for finding low energy states for 1D systems, based on a rigorously justified renormalization group (RG)-type transformation. In the process we resolve some of the aforementioned open questions, including giving a polynomial time algorithm for poly(n) degenerate ground spaces and an n^(O(log n)) algorithm for the poly(n) lowest energy states for 1D systems (under a mild density condition). We note that for these classes of systems the existence of a succinct classical description and area laws were not rigorously proved before this work. The algorithms are natural and efficient, and for the case of finding unique ground states for frustration-free Hamiltonians the running time is O(nM(n)), where M(n) is the time required to multiply two n by n matrices.

Publication: Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany
ID: CaltechAUTHORS:20200804-100730896

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Abstract: Kitaev's quantum double models, including the toric code, are canonical examples of quantum topological models on a two-dimensional spin lattice. Their Hamiltonian defines the ground space by imposing an energy penalty to any nontrivial flux or charge, but does not distinguish among those. We generalize this construction by introducing a family of Hamiltonians made of commuting four-body projectors that provide an intricate splitting of the Hilbert space by discriminating among nontrivial charges and fluxes. Our construction highlights that anyons are not in one-to-one correspondence with energy eigenspaces, a feature already present in Kitaev's construction. This discrepancy is due to the presence of local degrees of freedom in addition to topological ones on a lattice.

Publication: Physical Review B Vol.: 96 No.: 19 ISSN: 2469-9950

ID: CaltechAUTHORS:20170605-083553920

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Abstract: Denef and Douglas have observed that in certain landscape models the problem of finding small values of the cosmological constant is a large instance of a problem that is hard for the complexity class NP (Nondeterministic Polynomial-time). The number of elementary operations (quantum gates) needed to solve this problem by brute force search exceeds the estimated computational capacity of the observable Universe. Here we describe a way out of this puzzling circumstance: despite being NP-hard, the problem of finding a small cosmological constant can be attacked by more sophisticated algorithms whose performance vastly exceeds brute force search. In fact, in some parameter regimes the average-case complexity is polynomial. We demonstrate this by explicitly finding a cosmological constant of order 10^(-120) in a randomly generated 10^9-dimensional Arkani-Hamed–Dimopoulos–Kachru landscape.

Publication: Physical Review D Vol.: 96 No.: 10 ISSN: 2470-0010

ID: CaltechAUTHORS:20171114-150959412

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Abstract: We study micromotion in two-dimensional periodically driven systems in which all bulk Floquet eigenstates are localized by disorder. We show that this micromotion gives rise to a quantized time-averaged orbital magnetization density in any region completely filled with fermions. The quantization of magnetization density has a topological origin, and reveals the physical nature of the new phase identified in P. Titum, E. Berg, M. S. Rudner, G. Refael, and N. H. Lindner [Phys. Rev. X 6, 021013 (2016)]. We thus establish that the topological index of this phase can be accessed directly in bulk measurements, and propose an experimental protocol to do so using interferometry in cold-atom-based realizations.

Publication: Physical Review Letters Vol.: 119 No.: 18 ISSN: 0031-9007

ID: CaltechAUTHORS:20171101-122220832

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Abstract: Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians and analytically compute out-of-time-ordered correlation functions (OTOCs) and frame potentials to quantify scrambling, Haar-randomness, and circuit complexity. While our random matrix analysis gives a qualitatively correct prediction of the late-time behavior of chaotic systems, we find unphysical behavior at early times including an O(1) scrambling time and the apparent breakdown of spatial and temporal locality. The salient feature of GUE Hamiltonians which gives us computational traction is the Haar-invariance of the ensemble, meaning that the ensemble-averaged dynamics look the same in any basis. Motivated by this property of the GUE, we introduce k-invariance as a precise definition of what it means for the dynamics of a quantum system to be described by random matrix theory. We envision that the dynamical onset of approximate k-invariance will be a useful tool for capturing the transition from early-time chaos, as seen by OTOCs, to late-time chaos, as seen by random matrix theory.

Publication: Journal of High Energy Physics Vol.: 2017 No.: 11 ISSN: 1126-6708

ID: CaltechAUTHORS:20171102-135408184

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Abstract: One of the central challenges in the study of quantum many-body systems is the complexity of simulating them on a classical computer. A recent advance (Landau et al. in Nat Phys, 2015) gave a polynomial time algorithm to compute a succinct classical description for unique ground states of gapped 1D quantum systems. Despite this progress many questions remained unsolved, including whether there exist efficient algorithms when the ground space is degenerate (and of polynomial dimension in the system size), or for the polynomially many lowest energy states, or even whether such states admit succinct classical descriptions or area laws. In this paper we give a new algorithm, based on a rigorously justified RG type transformation, for finding low energy states for 1D Hamiltonians acting on a chain of nparticles. In the process we resolve some of the aforementioned open questions, including giving a polynomial time algorithm for poly(n) degenerate ground spaces and an n^(O(log n)) algorithm for the poly(n) lowest energy states (under a mild density condition). For these classes of systems the existence of a succinct classical description and area laws were not rigorously proved before this work. The algorithms are natural and efficient, and for the case of finding unique ground states for frustration-free Hamiltonians the running time is Õ(nM(n)), where M(n) is the time required to multiply two n × n matrices.

Publication: Communications in Mathematical Physics Vol.: 356 No.: 1 ISSN: 0010-3616

ID: CaltechAUTHORS:20160321-072746620

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Abstract: Symmetry fractionalization describes the fascinating phenomena that excitations in a 2D topological system can transform under symmetry in a fractional way. For example in fractional quantum Hall systems, excitations can carry fractional charges while the electrons making up the system have charge one. An important question is to understand what symmetry fractionalization (SF) patterns are possible given different types of topological order and different global symmetries. A lot of progress has been made recently in classifying the SF patterns, providing deep insight into the strongly correlated experimental signatures of systems like spin liquids and topological insulators. We review recent developments on this topic. First, it was shown that the SF patterns need to satisfy some simple consistency conditions. More interestingly, it was realized that some seemingly consistent SF patterns are actually ‘anomalous’, i.e. they cannot be realized in strictly 2D systems. We review various methods that have been developed to detect such anomalies. Applying such an understanding to 2D spin liquid allows one to enumerate all potentially realizable SF patterns and propose numerical and experimental probing methods to distinguish them. On the other hand, the anomalous SF patterns were shown to exist on the surface of 3D systems and reflect the nontrivial order in the 3D bulk. We review examples of this kind where the bulk states are topological insulators, topological superconductors, or have other symmetry protected topological orders.

Publication: Reviews in Physics Vol.: 2ISSN: 2405-4283

ID: CaltechAUTHORS:20161107-083133279

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Abstract: The past decade has witnessed an explosion in the field of quantum materials, headlined by the predictions and discoveries of novel Landau-symmetry-broken phases in correlated electron systems, topological phases in systems with strong spin–orbit coupling, and ultra-manipulable materials platforms based on two-dimensional van der Waals crystals. Discovering pathways to experimentally realize quantum phases of matter and exert control over their properties is a central goal of modern condensed-matter physics, which holds promise for a new generation of electronic/photonic devices with currently inaccessible and likely unimaginable functionalities. In this Review, we describe emerging strategies for selectively perturbing microscopic interaction parameters, which can be used to transform materials into a desired quantum state. Particular emphasis will be placed on recent successes to tailor electronic interaction parameters through the application of intense fields, impulsive electromagnetic stimulation, and nanostructuring or interface engineering. Together these approaches outline a potential roadmap to an era of quantum phenomena on demand.

Publication: Nature Materials Vol.: 16 No.: 11 ISSN: 1476-1122

ID: CaltechAUTHORS:20170922-102739878

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Abstract: We propose a scheme to realize a topological insulator with optical-passive elements and analyze the effects of Kerr nonlinearities in its topological behavior. In the linear regime, our design gives rise to an optical spectrum with topological features and where the bandwidths and bandgaps are dramatically broadened. The resulting edge modes cover a very wide frequency range. We relate this behavior to the fact that the effective Hamiltonian describing the system’s amplitudes is long range. We also develop a method to analyze the scheme in the presence of a Kerr medium. We assess robustness and stability of the topological features and predict the presence of chiral squeezed fluctuations at the edges in some parameter regimes.

Publication: Proceedings of the National Academy of Sciences of the United States of America Vol.: 114 No.: 43 ISSN: 0027-8424

ID: CaltechAUTHORS:20170511-122552160

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Abstract: Nonreciprocal circuit elements form an integral part of modern measurement and communication systems. Mathematically they require breaking of time-reversal symmetry, typically achieved using magnetic materials and more recently using the quantum Hall effect, parametric permittivity modulation or Josephson nonlinearities. Here we demonstrate an on-chip magnetic-free circulator based on reservoir-engineered electromechanic interactions. Directional circulation is achieved with controlled phase-sensitive interference of six distinct electro-mechanical signal conversion paths. The presented circulator is compact, its silicon-on-insulator platform is compatible with both superconducting qubits and silicon photonics, and its noise performance is close to the quantum limit. With a high dynamic range, a tunable bandwidth of up to 30 MHz and an in situ reconfigurability as beam splitter or wavelength converter, it could pave the way for superconducting qubit processors with multiplexed on-chip signal processing and readout.

Publication: Nature Communications Vol.: 8ISSN: 2041-1723

ID: CaltechAUTHORS:20170707-144005259

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Abstract: When a physical system is subjected to a strong external multifrequency drive, its dynamics can be conveniently represented in the multidimensional Floquet lattice. The number of Floquet lattice dimensions equals the number of irrationally-related drive frequencies, and the evolution occurs in response to a built-in effective “electric” field, whose components are proportional to the corresponding drive frequencies. The mapping allows us to engineer and study temporal analogs of many real-space phenomena. Here, we focus on the specific example of a two-level system under a two-frequency drive that induces topologically nontrivial band structure in the 2D Floquet space. The observable consequence of such a construction is the quantized pumping of energy between the sources with frequencies ω_1 and ω_2. When the system is initialized into a Floquet band with the Chern number C, the pumping occurs at a rate P_(12)=−P_(21)=(C/2π)ℏω_1ω_2, an exact counterpart of the transverse current in a conventional topological insulator.

Publication: Physical Review X Vol.: 7 No.: 4 ISSN: 2160-3308

ID: CaltechAUTHORS:20171011-110835402

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Abstract: We construct a Hamiltonian whose dynamics simulate the dynamics of every other Hamiltonian up to exponentially long times in the system size. The Hamiltonian is time-independent, local, one-dimensional, and translation invariant. As a consequence, we show (under plausible computational complexity assumptions) that the circuit complexity of the unitary dynamics under this Hamiltonian grows steadily with time up to an exponential value in system size. This result makes progress on a recent conjecture by Susskind, in the context of the AdS/CFT correspondence, that the time evolution of the thermofield double state of two conformal fields theories with a holographic dual has a circuit complexity increasing linearly in time, up to exponential time.

Publication: arXiv
ID: CaltechAUTHORS:20190801-134530640

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Abstract: We give two quantum algorithms for solving semidefinite programs (SDPs) providing quantum speed-ups. We consider SDP instances with m constraint matrices, each of dimension n, rank at most r, and sparsity s. The first algorithm assumes access to an oracle to the matrices at unit cost. We show that it has run time Õ(s^2(√((mϵ)^(−10)) + √((nϵ)^(−12))), with ϵ the error of the solution. This gives an optimal dependence in terms of m, n and quadratic improvement over previous quantum algorithms when m ≈ n. The second algorithm assumes a fully quantum input model in which the matrices are given as quantum states. We show that its run time is Õ (√m + poly(r))⋅poly(log m,log n,B,ϵ^(−1)), with B an upper bound on the trace-norm of all input matrices. In particular the complexity depends only poly-logarithmically in n and polynomially in r. We apply the second SDP solver to learn a good description of a quantum state with respect to a set of measurements: Given m measurements and a supply of copies of an unknown state ρ with rank at most r, we show we can find in time √m⋅poly(log m,log n,r,ϵ^(−1)) a description of the state as a quantum circuit preparing a density matrix which has the same expectation values as ρ on the m measurements, up to error ϵ. The density matrix obtained is an approximation to the maximum entropy state consistent with the measurement data considered in Jaynes' principle from statistical mechanics. As in previous work, we obtain our algorithm by "quantizing" classical SDP solvers based on the matrix multiplicative weight method. One of our main technical contributions is a quantum Gibbs state sampler for low-rank Hamiltonians with a poly-logarithmic dependence on its dimension, which could be of independent interest.

Publication: arXiv
ID: CaltechAUTHORS:20190801-134527208

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Abstract: Recent work on a family of boson-fermion mappings has emphasized the interplay of symmetry and duality: Phases related by a particle-vortex duality of bosons (fermions) are related by time-reversal symmetry in their fermionic (bosonic) formulation. We present exact mappings for a number of concrete models that make this property explicit on the operator level. We illustrate the approach with one- and two-dimensional quantum Ising models and then similarly explore the duality web of complex bosons and Dirac fermions in (2+1) dimensions. We generalize the latter to systems with long-range interactions and discover a continuous family of dualities embedding the previously studied cases.

Publication: Physical Review X Vol.: 7 No.: 4 ISSN: 2160-3308

ID: CaltechAUTHORS:20170525-150801314

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Abstract: Optical quantum memories are essential elements in quantum networks for long distance distribution of quantum entanglement. Scalable development of quantum network nodes requires on-chip qubit storage functionality with control of its readout time. We demonstrate a high-fidelity nanophotonic quantum memory based on a mesoscopic neodymium ensemble coupled to a photonic crystal cavity. The nanocavity enables >95% spin polarization for efficient initialization of the atomic frequency comb memory, and time-bin-selective readout via enhanced optical Stark shift of the comb frequencies. Our solid-state memory is integrable with other chip-scale photon source and detector devices for multiplexed quantum and classical information processing at the network nodes.

Publication: Science Vol.: 357 No.: 6358 ISSN: 0036-8075

ID: CaltechAUTHORS:20170815-100238435

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Abstract: A central question in quantum computation is to identify the resources that are responsible for quantum speed-up. Quantum contextuality has been recently shown to be a resource for quantum computation with magic states for odd-prime dimensional qudits and two-dimensional systems with real wave functions. The phenomenon of state-independent contextuality poses a priori an obstruction to characterizing the case of regular qubits, the fundamental building block of quantum computation. Here, we establish contextuality of magic states as a necessary resource for a large class of quantum computation schemes on qubits. We illustrate our result with a concrete scheme related to measurement-based quantum computation.

Publication: Physical Review Letters Vol.: 119 No.: 12 ISSN: 0031-9007

ID: CaltechAUTHORS:20170922-074333096

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Abstract: Quantum hypothesis testing is one of the most basic tasks in quantum information theory and has fundamental links with quantum communication and estimation theory. In this paper, we establish a formula that characterizes the decay rate of the minimal type-II error probability in a quantum hypothesis test of two Gaussian states given a fixed constraint on the type-I error probability. This formula is a direct function of the mean vectors and covariance matrices of the quantum Gaussian states in question. We give an application to quantum illumination, which is the task of determining whether there is a low-reflectivity object embedded in a target region with a bright thermal-noise bath. For the asymmetric-error setting, we find that a quantum illumination transmitter can achieve an error probability exponent stronger than a coherent-state transmitter of the same mean photon number, and furthermore, that it requires far fewer trials to do so. This occurs when the background thermal noise is either low or bright, which means that a quantum advantage is even easier to witness than in the symmetric-error setting because it occurs for a larger range of parameters. Going forward from here, we expect our formula to have applications in settings well beyond those considered in this paper, especially to quantum communication tasks involving quantum Gaussian channels.

Publication: Physical Review Letters Vol.: 119 No.: 12 ISSN: 0031-9007

ID: CaltechAUTHORS:20170817-110500251

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Abstract: Fiber tapers provide a way to rapidly measure the spectra of many types of optical microcavities. Proper fabrication of the taper ensures that its width varies sufficiently slowly (adiabatically) along the length of the taper so as to maintain single spatial mode propagation. This is usually accomplished by monitoring the spectral transmission through the taper. In addition to this characterization method it is also helpful to know the taper width versus length. By developing a model of optical backscattering within the fiber taper, it is possible to use backscatter measurements to characterize the taper width versus length. The model uses the concept of a local taper numerical aperture to accurately account for varying backscatter collection along the length of the taper. In addition to taper profile information, the backscatter reflectometry method delineates locations along the taper where fluctuations in fiber core refractive index, cladding refractive index, and taper surface roughness each provide the dominant source of backscattering. Rayleigh backscattering coefficients are also extracted by fitting the data with the model and are consistent with the fiber manufacturer’s datasheet. The optical backscattering reflectometer is also used to observe defects resulting from microcracks and surface contamination. All of this information can be obtained before the taper is removed from its fabrication apparatus. The backscattering method should also be prove useful for characterization of nanofibers.

Publication: Optics Express Vol.: 25 No.: 19 ISSN: 1094-4087

ID: CaltechAUTHORS:20171012-143819083

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Abstract: The Sachdev-Ye-Kitaev (SYK) model describes a collection of randomly interacting Majorana fermions that exhibits profound connections to quantum chaos and black holes. We propose a solid-state implementation based on a quantum dot coupled to an array of topological superconducting wires hosting Majorana zero modes. Interactions and disorder intrinsic to the dot mediate the desired random Majorana couplings, while an approximate symmetry suppresses additional unwanted terms. We use random-matrix theory and numerics to show that our setup emulates the SYK model (up to corrections that we quantify) and discuss experimental signatures.

Publication: Physical Review B Vol.: 96 No.: 12 ISSN: 2469-9950

ID: CaltechAUTHORS:20170705-111144781

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Abstract: We use the Holevo information to estimate distinguishability of microstates of a black hole in anti-de Sitter space by measurements one can perform on a subregion of a Cauchy surface of the dual conformal field theory. We find that microstates are not distinguishable at all until the subregion reaches a certain size and that perfect distinguishability can be achieved before the subregion covers the entire Cauchy surface. We will compare our results with expectations from the entanglement wedge reconstruction, tensor network models, and the bit threads interpretation of the Ryu-Takayanagi formula.

Publication: Physical Review D Vol.: 96 No.: 6 ISSN: 2470-0010

ID: CaltechAUTHORS:20170918-091256373

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Abstract: We provide an explicit lattice model of bosons with two separately conserved boson species [U(1)×U(1) global symmetry] realizing a direct transition between an integer quantum Hall effect of bosons and a trivial phase, where any intermediate phase is avoided by an additional symmetry interchanging the two species. If the latter symmetry is absent, we find intermediate superfluid phases where one or the other boson species condenses. We know the precise location of the transition since at this point our model has an exact nonlocal antiunitary particle-hole-like symmetry that resembles particle-hole symmetry in the lowest Landau level of electrons. We exactly map the direct transition to our earlier study of the self-dual line of the easy-plane NCCP1 model, in the mathematically equivalent reformulation in terms of two (new) particles with π statistics and identical energetics. While the transition in our model is first order, we hope that our mappings and recent renewed interest in such self-dual models will stimulate more searches for models with a continuous transition.

Publication: Physical Review B Vol.: 96 No.: 11 ISSN: 2469-9950

ID: CaltechAUTHORS:20170920-104241961

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Abstract: Time periodic modulations of the transverse field in the closed XY spin-1/2 chain generate a very rich dynamical phase diagram, with a hierarchy of Z_n topological phases characterized by differing numbers of Floquet-Majorana modes. This rich phase diagram survives when the system is coupled to dissipative end reservoirs. Circumventing the obstacle of preparing and measuring quasienergy configurations endemic to Floquet-Majorana detection schemes, we show that stroboscopic heat transport and spin density are robust observables to detect both the dynamical phase transitions and Majorana modes in dissipative settings. We find that the heat current provides very clear signatures of these Floquet topological phase transitions. In particular, we observe that the derivative of the heat current, with respect to a control parameter, changes sign at the boundaries separating topological phases with differing nonzero numbers of Floquet-Majorana modes. We present a simple scheme to directly count the number of Floquet-Majorana modes in a phase from the Fourier transform of the local spin density profile. Our results are valid provided the anisotropies are not strong and can be easily implemented in quantum engineered systems.

Publication: Physical Review B Vol.: 96 No.: 12 ISSN: 2469-9950

ID: CaltechAUTHORS:20171012-133910331

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Abstract: The technique of continuous unitary transformations has recently been used to provide physical insight into a diverse array of quantum mechanical systems. However, the question of how to best numerically implement the flow equations has received little attention. The most immediately apparent approach, using standard Runge-Kutta numerical integration algorithms, suffers from both severe inefficiency due to stiffness and the loss of unitarity. After reviewing the formalism of continuous unitary transformations and Wegner's original choice for the infinitesimal generator of the flow, we present a number of approaches to resolving these issues including a choice of generator which induces what we call the “uniform tangent decay flow” and three numerical integrators specifically designed to perform continuous unitary transformations efficiently while preserving the unitarity of flow. We conclude by applying one of the flow algorithms to a simple calculation that visually demonstrates the many-body localization transition.

Publication: Physical Review B Vol.: 96 No.: 11 ISSN: 2469-9950

ID: CaltechAUTHORS:20171004-144154017

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Abstract: Many-body localization was proven under realistic assumptions by constructing a quasi-local unitary rotation that diagonalizes the Hamiltonian (Imbrie, 2016). A natural generalization is to consider all unitaries that have a similar structure. We bound entanglement for states generated by such unitaries, thus providing an independent proof of area law in eigenstates of many-body localized systems. An error of approximating the unitary by a finite-depth local circuit is obtained. We connect the defined family of unitaries to other results about many-body localization (Kim et al, 2014), in particular Lieb-Robinson bound. Finally we argue that any Hamiltonian can be diagonalized by such a unitary, given it has a slow enough logarithmic lightcone in its Lieb-Robinson bound.

Publication: arXiv
ID: CaltechAUTHORS:20171103-150936253

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Abstract: Many-body localization (MBL) is a phase of matter that is characterized by the absence of thermalization. Dynamical generation of a large number of local quantum numbers has been identified as one key characteristic of this phase, quite possibly the microscopic mechanism of breakdown of thermalization and the phase transition itself. We formulate a robust algorithm, based on Wegner-Wilson flow (WWF) renormalization, for computing these conserved quantities and their interactions. We present evidence for the existence of distinct fixed point distributions of the latter: a Gaussian white-noise-like distribution in the ergodic phase, a 1/f law inside the MBL phase, and scale-free distributions in the transition regime.

Publication: Physical Review Letters Vol.: 119 No.: 7 ISSN: 0031-9007

ID: CaltechAUTHORS:20170817-073043882

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Abstract: The collective magnetic excitations in the spin-orbit Mott insulator (Sr_(1−x)La_x)_2IrO_4 (x=0, 0.01, 0.04, 0.1) were investigated by means of resonant inelastic x-ray scattering. We report significant magnon energy gaps at both the crystallographic and antiferromagnetic zone centers at all doping levels, along with a remarkably pronounced momentum-dependent lifetime broadening. The spin-wave gap is accounted for by a significant anisotropy in the interactions between J_(eff)=1/2 isospins, thus marking the departure of Sr_2IrO_4 from the essentially isotropic Heisenberg model appropriate for the superconducting cuprates.

Publication: Physical Review B Vol.: 96 No.: 7 ISSN: 2469-9950

ID: CaltechAUTHORS:20170901-091754761

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Abstract: We propose an optomechanics experiment that can search for signatures of a fundamentally classical theory of gravity and in particular of the many-body Schrödinger-Newton (SN) equation, which governs the evolution of a crystal under a self-gravitational field. The SN equation predicts that the dynamics of a macroscopic mechanical oscillator’s center-of-mass wave function differ from the predictions of standard quantum mechanics [H. Yang, H. Miao, D.-S. Lee, B. Helou, and Y. Chen, Phys. Rev. Lett. 110, 170401 (2013)]. This difference is largest for low-frequency oscillators, and for materials, such as tungsten or osmium, with small quantum fluctuations of the constituent atoms around their lattice equilibrium sites. Light probes the motion of these oscillators and is eventually measured in order to extract valuable information on the pendulum’s dynamics. Due to the nonlinearity contained in the SN equation, we analyze the fluctuations of measurement results differently than standard quantum mechanics. We revisit how to model a thermal bath, and the wave-function collapse postulate, resulting in two prescriptions for analyzing the quantum measurement of the light. We demonstrate that both predict features, in the outgoing light’s phase fluctuations’ spectrum, which are separate from classical thermal fluctuations and quantum shot noise, and which can be clearly resolved with state of the art technology.

Publication: Physical Review D Vol.: 96 No.: 4 ISSN: 2470-0010

ID: CaltechAUTHORS:20170605-082841289

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Abstract: We prove that the entanglement entropy of any state evolved under an arbitrary 1/r^α long-range-interacting D-dimensional lattice spin Hamiltonian cannot change faster than a rate proportional to the boundary area for any α>D+1. We also prove that for any α>2D+2, the ground state of such a Hamiltonian satisfies the entanglement area law if it can be transformed along a gapped adiabatic path into a ground state known to satisfy the area law. These results significantly generalize their existing counterparts for short-range interacting systems, and are useful for identifying dynamical phase transitions and quantum phase transitions in the presence of long-range interactions.

Publication: Physical Review Letters Vol.: 119 No.: 5 ISSN: 0031-9007

ID: CaltechAUTHORS:20170726-092004962

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Abstract: The quantum Cramér-Rao bound (QCRB) sets a fundamental limit for the measurement of classical signals with detectors operating in the quantum regime. Using linear-response theory and the Heisenberg uncertainty relation, we derive a general condition for achieving such a fundamental limit. When applied to classical displacement measurements with a test mass, this condition leads to an explicit connection between the QCRB and the standard quantum limit that arises from a tradeoff between the measurement imprecision and quantum backaction; the QCRB can be viewed as an outcome of a quantum nondemolition measurement with the backaction evaded. Additionally, we show that the test mass is more a resource for improving measurement sensitivity than a victim of the quantum backaction, which suggests a new approach to enhancing the sensitivity of a broad class of sensors. We illustrate these points with laser interferometric gravitational-wave detectors.

Publication: Physical Review Letters Vol.: 119 No.: 5 ISSN: 0031-9007

ID: CaltechAUTHORS:20170803-081632579

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Abstract: We investigate the effects of disorder in Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are induced by resonantly driving a transition between the valence and conduction bands. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a mobility gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator. Interestingly, the effects of disorder are not necessarily adverse: we show that in the same quantum well, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet topological Anderson insulator (FTAI). We identify the conditions on the driving field necessary for observing such a transition.

Publication: Physical Review B Vol.: 96 No.: 5 ISSN: 2469-9950

ID: CaltechAUTHORS:20170619-091103005

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Abstract: In continuously monitored systems the standard quantum limit is given by the trade-off between shot noise and back-action noise. In gravitational-wave detectors, such as Advanced LIGO, both contributions can be simultaneously squeezed in a broad frequency band by injecting a spectrum of squeezed vacuum states with a frequency-dependent squeeze angle. This approach requires setting up an additional long baseline, low-loss filter cavity in a vacuum system at the detector’s site. Here, we show that the need for such a filter cavity can be eliminated, by exploiting Einstein–Podolsky–Rosen (EPR)-entangled signals and idler beams. By harnessing their mutual quantum correlations and the difference in the way each beam propagates in the interferometer, we can engineer the input signal beam to have the appropriate frequency-dependent conditional squeezing once the out-going idler beam is detected. Our proposal is appropriate for all future gravitational-wave detectors for achieving sensitivities beyond the standard quantum limit.

Publication: Nature Physics Vol.: 13 No.: 8 ISSN: 1745-2473

ID: CaltechAUTHORS:20170321-110739258

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Abstract: We address the question of whether symmetry-protected topological (SPT) order can persist at nonzero temperature, with a focus on understanding the thermal stability of several models studied in the theory of quantum computation. We present three results in this direction. First, we prove that nontrivial SPT order protected by a global onsite symmetry cannot persist at nonzero temperature, demonstrating that several quantum computational structures protected by such onsite symmetries are not thermally stable. Second, we prove that the three-dimensional (3D) cluster-state model used in the formulation of topological measurement-based quantum computation possesses a nontrivial SPT-ordered thermal phase when protected by a generalized (1-form) symmetry. The SPT order in this model is detected by long-range localizable entanglement in the thermal state, which compares with related results characterizing SPT order at zero temperature in spin chains using localizable entanglement as an order parameter. Our third result is to demonstrate that the high-error tolerance of this 3D cluster-state model for quantum computation, even without a protecting symmetry, can be understood as an application of quantum error correction to effectively enforce a 1-form symmetry.

Publication: Physical Review A Vol.: 96 No.: 2 ISSN: 2469-9926

ID: CaltechAUTHORS:20170807-140223705

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Abstract: In this work we consider the ground space connectivity problem for commuting local Hamiltonians. The ground space connectivity problem asks whether it is possible to go from one (efficiently preparable) state to another by applying a polynomial length sequence of 2-qubit unitaries while remaining at all times in a state with low energy for a given Hamiltonian H. It was shown in [Gharibian and Sikora, ICALP15] that this problem is QCMA-complete for general local Hamiltonians, where QCMA is defined as QMA with a classical witness and BQP verifier. Here we show that the commuting version of the problem is also QCMA-complete. This provides one of the first examples where commuting local Hamiltonians exhibit complexity theoretic hardness equivalent to general local Hamiltonians.

Publication: Quantum Vol.: 1ISSN: 2521-327X

ID: CaltechAUTHORS:20171011-112512941

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Abstract: A path integral on a link complement of a three-sphere fixes a vector (the "link state") in Chern-Simons theory. The link state can be written in a certain basis with the colored link invariants as its coefficients. We use symmetric webs to systematically compute the colored link invariants, by which we can write down the multi-partite entangled state of any given link. It is still unknown if a product state necessarily implies that the corresponding components are unlinked, and we leave it as a conjecture.

Publication: arXiv
ID: CaltechAUTHORS:20170713-145329116

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Abstract: Subjecting a many-body localized system to a time-periodic drive generically leads to delocalization and a transition to ergodic behavior if the drive is sufficiently strong or of sufficiently low frequency. Here we show that a specific drive can have an opposite effect, taking a static delocalized system into the many-body localized phase. We demonstrate this effect using a one-dimensional system of interacting hard-core bosons subject to an oscillating linear potential. The system is weakly disordered, and is ergodic absent the driving. The time-periodic linear potential leads to a suppression of the effective static hopping amplitude, increasing the relative strengths of disorder and interactions. Using numerical simulations, we find a transition into the many-body localized phase above a critical driving frequency and in a range of driving amplitudes. Our findings highlight the potential of driving schemes exploiting the coherent destruction of tunneling for engineering long-lived Floquet phases.

Publication: Physical Review B Vol.: 96 No.: 2 ISSN: 2469-9950

ID: CaltechAUTHORS:20170719-094811145

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Abstract: Ultrafast optical manipulation of ordered phases in strongly correlated materials is a topic of significant theoretical, experimental, and technological interest. Inspired by a recent experiment on light-induced superconductivity in fullerenes [M. Mitrano et al., Nature (London) 530, 461 (2016)], we develop a comprehensive theory of light-induced superconductivity in driven electron-phonon systems with lattice nonlinearities. In analogy with the operation of parametric amplifiers, we show how the interplay between the external drive and lattice nonlinearities lead to significantly enhanced effective electron-phonon couplings. We provide a detailed and unbiased study of the nonequilibrium dynamics of the driven system using the real-time Green's function technique. To this end, we develop a Floquet generalization of the Migdal-Eliashberg theory and derive a numerically tractable set of quantum Floquet-Boltzmann kinetic equations for the coupled electron-phonon system. We study the role of parametric phonon generation and electronic heating in destroying the transient superconducting state. Finally, we predict the transient formation of electronic Floquet bands in time- and angle-resolved photoemission spectroscopy experiments as a consequence of the proposed mechanism.

Publication: Physical Review B Vol.: 96 No.: 1 ISSN: 2469-9950

ID: CaltechAUTHORS:20170619-085401037

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Abstract: We present the fabrication and characterization of an aluminum transmon qubit on a silicon-on-insulator substrate. Key to the qubit fabrication is the use of an anhydrous hydrofluoric vapor process which selectively removes the lossy silicon oxide buried underneath the silicon device layer. For a 5.6 GHz qubit measured dispersively by a 7.1 GHz resonator, we find T_1 = 3.5 μs and T_2* = 2.2 μs. This process in principle permits the co-fabrication of silicon photonic and mechanical elements, providing a route towards chip-scale integration of electro-opto-mechanical transducers for quantum networking of superconducting microwave quantum circuits. The additional processing steps are compatible with established fabrication techniques for aluminum transmon qubits on silicon.

Publication: Applied Physics Letters Vol.: 111 No.: 4 ISSN: 0003-6951

ID: CaltechAUTHORS:20170427-153536925

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Abstract: Direct detection of gravitational waves is opening a new window onto our universe. Here, we study the sensitivity to continuous-wave strain fields of a kg-scale optomechanical system formed by the acoustic motion of superfluid helium-4 parametrically coupled to a superconducting microwave cavity. This narrowband detection scheme can operate at very high Q-factors, while the resonant frequency is tunable through pressurization of the helium in the 0.1–1.5 kHz range. The detector can therefore be tuned to a variety of astrophysical sources and can remain sensitive to a particular source over a long period of time. For thermal noise limited sensitivity, we find that strain fields on the order of h ~ 10^(-23)/√Hz are detectable. Measuring such strains is possible by implementing state of the art microwave transducer technology. We show that the proposed system can compete with interferometric detectors and potentially surpass the gravitational strain limits set by them for certain pulsar sources within a few months of integration time.

Publication: New Journal of Physics Vol.: 19ISSN: 1367-2630

ID: CaltechAUTHORS:20170313-065536926

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Abstract: A central goal within quantum optics is to realize efficient, controlled interactions between photons and atomic media. A fundamental limit in nearly all applications based on such systems arises from spontaneous emission, in which photons are absorbed by atoms and then rescattered into undesired channels. In typical theoretical treatments of atomic ensembles, it is assumed that this rescattering occurs independently, and at a rate given by a single isolated atom, which in turn gives rise to standard limits of fidelity in applications such as quantum memories for light or photonic quantum gates. However, this assumption can in fact be dramatically violated. In particular, it has long been known that spontaneous emission of a collective atomic excitation can be significantly suppressed through strong interference in emission between atoms. While this concept of “subradiance” is not new, thus far the techniques to exploit the effect have not been well understood. In this work, we provide a comprehensive treatment of this problem. First, we show that in ordered atomic arrays in free space, subradiant states acquire an elegant interpretation in terms of optical modes that are guided by the array, which only emit due to scattering from the ends of the finite system. We also go beyond the typically studied regime of a single atomic excitation and elucidate the properties of subradiant states in the many-excitation limit. Finally, we introduce the new concept of “selective radiance.” Whereas subradiant states experience a reduced coupling to all optical modes, selectively radiant states are tailored to simultaneously radiate efficiently into a desired channel while scattering into undesired channels is suppressed, thus enabling an enhanced atom-light interface. We show that these states naturally appear in chains of atoms coupled to nanophotonic structures, and we analyze the performance of photon storage exploiting such states. We find numerically that selectively radiant states allow for a photon storage error that scales exponentially better with the number of atoms than previously known bounds.

Publication: Physical Review X Vol.: 7 No.: 3 ISSN: 2160-3308

ID: CaltechAUTHORS:20170511-120626043

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Abstract: In many-body localized systems, propagation of information forms a light cone that grows logarithmically with time. However, local changes in energy or other conserved quantities typically spread only within a finite distance. Is it possible to detect the logarithmic light cone generated by a local perturbation from the response of a local operator at a later time? We numerically calculate various correlators in the random-field Heisenberg chain. While the equilibrium retarded correlator A(t = 0)B(t > 0) is not sensitive to the unbounded information propagation, the out-of-time-ordered correlator A(t = 0)B(t > 0)A(t = 0)B(t > 0) can detect the logarithmic light cone. We relate out-of-time-ordered correlators to the Lieb-Robinson bound in many-body localized systems, and show how to detect the logarithmic light cone with retarded correlators in specially designed states. Furthermore, we study the temperature dependence of the logarithmic light cone using out-of-time-ordered correlators.

Publication: Annalen der Physik Vol.: 529 No.: 7 ISSN: 0003-3804

ID: CaltechAUTHORS:20161114-153129646

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Abstract: In this work, we develop a coupled layer construction of fracton topological orders in d=3 spatial dimensions. These topological phases have subextensive topological ground-state degeneracy and possess excitations whose movement is restricted in interesting ways. Our coupled layer approach is used to construct several different fracton topological phases, both from stacked layers of simple d=2 topological phases and from stacks of d=3 fracton topological phases. This perspective allows us to shed light on the physics of the X-cube model recently introduced by Vijay, Haah, and Fu, which we demonstrate can be obtained as the strong-coupling limit of a coupled three-dimensional stack of toric codes. We also construct two new models of fracton topological order: a semionic generalization of the X-cube model, and a model obtained by coupling together four interpenetrating X-cube models, which we dub the ‘four color cube model”. The couplings considered lead to fracton topological orders via mechanisms we dub “p-string condensation” and “p-membrane condensation”, in which strings or membranes built from particle excitations are driven to condense. This allows the fusion properties, braiding statistics, and ground-state degeneracy of the phases we construct to be easily studied in terms of more familiar degrees of freedom. Our work raises the possibility of studying fracton topological phases from within the framework of topological quantum field theory, which may be useful for obtaining a more complete understanding of such phases.

Publication: Physical Review B Vol.: 95 No.: 24 ISSN: 2469-9950

ID: CaltechAUTHORS:20170622-102731134

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Abstract: The effective Mott gap measured by scanning tunneling microscopy (STM) in the lightly doped Mott insulator (Sr_(1−x)La_x)_2IrO_4 differs greatly from values reported by photoemission and optical experiments. Here we show that this is a consequence of the poor electronic screening of the tip-induced electric field in this material. Such effects are well known from STM experiments on semiconductors and go under the name of tip-induced band bending (TIBB). We show that this phenomenon also exists in the lightly doped Mott insulator (Sr_(1−x)La_x)_2IrO_4 and that, at doping concentrations of x≤4%, it causes the measured energy gap in the sample density of states to be bigger than the one measured with other techniques. We develop a model able to retrieve the intrinsic energy gap leading to a value which is in rough agreement with other experiments, bridging the apparent contradiction. At doping x≈5% we further observe circular features in the conductance layers that point to the emergence of a significant density of free carriers in this doping range and to the presence of a small concentration of donor atoms. We illustrate the importance of considering the presence of TIBB when doing STM experiments on correlated-electron systems and discuss the similarities and differences between STM measurements on semiconductors and lightly doped Mott insulators.

Publication: Physical Review B Vol.: 95 No.: 23 ISSN: 2469-9950

ID: CaltechAUTHORS:20170627-091217306

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Abstract: We present designs for scalable quantum computers composed of qubits encoded in aggregates of four or more Majorana zero modes, realized at the ends of topological superconducting wire segments that are assembled into superconducting islands with significant charging energy. Quantum information can be manipulated according to a measurement-only protocol, which is facilitated by tunable couplings between Majorana zero modes and nearby semiconductor quantum dots. Our proposed architecture designs have the following principal virtues: (1) the magnetic field can be aligned in the direction of all of the topological superconducting wires since they are all parallel; (2) topological T junctions are not used, obviating possible difficulties in their fabrication and utilization; (3) quasiparticle poisoning is abated by the charging energy; (4) Clifford operations are executed by a relatively standard measurement: detection of corrections to quantum dot energy, charge, or differential capacitance induced by quantum fluctuations; (5) it is compatible with strategies for producing good approximate magic states.

Publication: Physical Review B Vol.: 95 No.: 23 ISSN: 2469-9950

ID: CaltechAUTHORS:20170621-103050950

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Abstract: We establish a converse bounds on the private transmission capabilities of a quantum channel. The main conceptual development builds firmly on the notion of a private state, which is a powerful, uniquely quantum method for simplifying the tripartite picture of privacy involving local operations and public classical communication to a bipartite picture of quantum privacy involving local operations and classical communication. This approach has previously led to some of the strongest upper bounds on secret key rates, including the squashed entanglement and the relative entropy of entanglement. Here we use this approach along with a “privacy test” to establish a general meta-converse bound for private communication.

ID: CaltechAUTHORS:20170816-155206778

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Abstract: We introduce a simple two-player test which certifies that the players apply tensor products of Pauli σ_X and σ_Z observables on the tensor product of n EPR pairs. The test has constant robustness: any strategy achieving success probability within an additive of the optimal must be poly(ε)-close, in the appropriate distance measure, to the honest n-qubit strategy. The test involves 2n-bit questions and 2-bit answers. The key technical ingredient is a quantum version of the classical linearity test of Blum, Luby, and Rubinfeld. As applications of our result we give (i) the first robust self-test for n EPR pairs; (ii) a quantum multiprover interactive proof system for the local Hamiltonian problem with a constant number of provers and classical questions and answers, and a constant completeness-soundness gap independent of system size; (iii) a robust protocol for verifiable delegated quantum computation with a constant number of quantum polynomial-time provers sharing entanglement.

ID: CaltechAUTHORS:20170710-154654821

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Abstract: We study the parallel repetition of one-round games involving players that can use quantum entanglement. A major open question in this area is whether parallel repetition reduces the entangled value of a game at an exponential rate - in other words, does an analogue of Raz's parallel repetition theorem hold for games with players sharing quantum entanglement? Previous results only apply to special classes of games. We introduce a class of games we call anchored. We then introduce a simple transformation on games called anchoring, inspired in part by the Feige-Kilian transformation, that turns any (multiplayer) game into an anchored game. Unlike the Feige-Kilian transformation, our anchoring transformation is completeness preserving. We prove an exponential-decay parallel repetition theorem for anchored games that involve any number of entangled players. We also prove a threshold version of our parallel repetition theorem for anchored games. Together, our parallel repetition theorems and anchoring transformation provide the first hardness amplification techniques for general entangled games. We give an application to the games version of the Quantum PCP Conjecture.

ID: CaltechAUTHORS:20170710-152910604

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Abstract: A Markov chain is a tripartite quantum state ρABC where there exists a recovery map RB→BC such that ρABC = RB→BC(ρAB). More generally, an approximate Markov chain ρABC is a state whose distance to the closest recovered state RB→BC(ρAB) is small. Recently it has been shown that this distance can be bounded from above by the conditional mutual information I(A : C|B)ρ of the state. We improve on this connection by deriving the first bound that is tight in the commutative case and features an explicit recovery map that only depends on the reduced state pBC. The key tool in our proof is a multivariate extension of the Golden-Thompson inequality, which allows us to extend logarithmic trace inequalities from two to arbitrarily many matrices.

ID: CaltechAUTHORS:20170816-174117187

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Abstract: We propose a quantum voting system in the spirit of quantum games such as the quantum prisoner's dilemma. Our scheme enables a constitution to violate a quantum analog of Arrow's impossibility theorem. Arrow's theorem is a claim proved deductively in economics: Every (classical) constitution endowed with three innocuous-seeming properties is a dictatorship. We construct quantum analogs of constitutions, of the properties, and of Arrow's theorem. A quantum version of majority rule, we show, violates this quantum Arrow conjecture. Our voting system allows for tactical-voting strategies reliant on entanglement, interference, and superpositions. This contribution to quantum game theory helps elucidate how quantum phenomena can be harnessed for strategic advantage.

Publication: Physical Review A Vol.: 95 No.: 6 ISSN: 2469-9926

ID: CaltechAUTHORS:20160613-093059687

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Abstract: Cooling of nanomechanical resonators to their motional ground state [1, 2] triggered recent achievements like non-classical mechanical state preparation [3] or coherent optical to microwave photon conversion [4]. Implementations of such system with optomechanical crystal (OMC) resonators use the co-localization of optical and acoustic modes in a periodically patterned device layer of a silicon-on-insulator (SOI) chip. An initialization of mechanical resonator to low thermal occupations is required by most quantum optomechanical operations. Reaching small thermal mechanical mode occupations and mechanical Q-factors ≳ 10^6 requires pre-cooling to millikelvin temperatures, where even weak optical absorption induces unfavorable local heating [5]. Commonly used one-dimensional nanobeam OMC resonators have significantly smaller thermal connectivity to the cool environment and reduced robustness against undesired heating than their two-dimensional counterparts. On the other hand drawbacks of 2D OMCs were their complex fabrication and weaker interaction strengths of acoustic and optical modes [6]. Here, we present a modified 2D OMC cavity that both exhibits simulated coupling strengths comparable to the previous optomechanical nanobeams and reduces the complexity for nanofabrication compared to previous 2D OMCs.

ID: CaltechAUTHORS:20180622-124453312

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Abstract: Engineering quantum states of light is at the basis of many quantum technologies such as quantum cryptography, teleportation, or metrology among others. Though, single photons can be generated in many scenarios, the efficient and reliable generation of complex single-mode multiphoton states is still a long-standing goal in the field, as current methods either suffer from low fidelities or small probabilities. Here we discuss several protocols which harness the strong and long-range atomic interactions induced by waveguide QED to efficiently load excitations in a collection of atoms, which can then be triggered to produce the desired multiphoton state. In order to boost the success probability and fidelity of each excitation process, atoms are used to both generate the excitations in the rest, as well as to herald the successful generation. Furthermore, to overcome the exponential scaling of the probability of success with the number of excitations, we design a protocol to merge excitations that are present in different internal atomic levels with a polynomial scaling.

Publication: Physical Review Letters Vol.: 118 No.: 21 ISSN: 0031-9007

ID: CaltechAUTHORS:20170511-121816378

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Abstract: Almheiri, Dong, and Harlow [J. High Energy Phys. 04 (2015) 163.] proposed a highly illuminating connection between the AdS/CFT holographic correspondence and operator algebra quantum error correction (OAQEC). Here, we explore this connection further. We derive some general results about OAQEC, as well as results that apply specifically to quantum codes that admit a holographic interpretation. We introduce a new quantity called price, which characterizes the support of a protected logical system, and find constraints on the price and the distance for logical subalgebras of quantum codes. We show that holographic codes defined on bulk manifolds with asymptotically negative curvature exhibit uberholography, meaning that a bulk logical algebra can be supported on a boundary region with a fractal structure. We argue that, for holographic codes defined on bulk manifolds with asymptotically flat or positive curvature, the boundary physics must be highly nonlocal, an observation with potential implications for black holes and for quantum gravity in AdS space at distance scales that are small compared to the AdS curvature radius.

Publication: Physical Review X Vol.: 7 No.: 2 ISSN: 2160-3308

ID: CaltechAUTHORS:20170517-114206968

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Abstract: In a bilayer system consisting of a composite-fermion Fermi sea in each layer, the tunnel current is exponentially suppressed at zero bias, followed by a strong peak at a finite bias voltage V_(max). This behavior, which is qualitatively different from that observed for the electron Fermi sea, provides fundamental insight into the strongly correlated non-Fermi liquid nature of the CF Fermi sea and, in particular, offers a window into the short-distance high-energy physics of this state. We identify the exciton responsible for the peak current and provide a quantitative account of the value of V_(max). The excitonic attraction is shown to be quantitatively significant, and its variation accounts for the increase of V_(max) with the application of an in-plane magnetic field. We also estimate the critical Zeeman energy where transition occurs from a fully spin polarized composite fermion Fermi sea to a partially spin polarized one, carefully incorporating corrections due to finite width and Landau level mixing, and find it to be in satisfactory agreement with the Zeeman energy where a qualitative change has been observed for the onset bias voltage [Eisenstein et al., Phys. Rev. B 94, 125409 (2016)]. For fractional quantum Hall states, we predict a substantial discontinuous jump in V_(max) when the system undergoes a transition from a fully spin polarized state to a spin singlet or a partially spin polarized state.

Publication: Physical Review B Vol.: 95 No.: 19 ISSN: 2469-9950

ID: CaltechAUTHORS:20170503-105416560

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Abstract: Double layer two-dimensional electron systems at high perpendicular magnetic field are used to realize magnetic tunnel junctions in which the electrons at the Fermi level in the two layers have either parallel or antiparallel spin magnetizations. In the antiparallel case the tunnel junction, at low temperatures, behaves as a nearly ideal spin diode. At elevated temperatures the diode character degrades as long-wavelength spin waves are thermally excited. These tunnel junctions provide a demonstration that the spin polarization of the electrons in the N=1 Landau level at filling factors ν=5/2 and 7/2 is essentially complete, and, with the aid of an in-plane magnetic field component, that Landau level mixing at these filling factors is weak in the samples studied.

Publication: Physical Review Letters Vol.: 118 No.: 18 ISSN: 0031-9007

ID: CaltechAUTHORS:20170505-110632677

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Abstract: Neutron single-crystal diffraction and rotational anisotropy optical second harmonic generation data are presented resolving the nature of the structural distortion realized in electron-doped (Sr_(1−x)La_x)_3Ir_2O_7 with x = 0.035 and x = 0.071. Once electrons are introduced into the bilayer spin-orbit assisted Mott insulator Sr_2Ir_2O_7, previous studies have identified the appearance of a low-temperature structural distortion and have suggested the presence of a competing electronic instability in the phase diagram of this material. Our measurements resolve a lowering of the structural symmetry from monoclinic C2/c to monoclinic P2_1/c and the creation of two unique Ir sites within the chemical unit cell as the lattice distorts below a critical temperature T_S. Details regarding the modifications to oxygen octahedral rotations and tilting through the transition are discussed as well as the evolution of the low-temperature distorted lattice as a function of carrier substitution.

Publication: Physical Review B Vol.: 95 No.: 17 ISSN: 2469-9950

ID: CaltechAUTHORS:20170530-122910588

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Abstract: We describe schemes of quantum computation with magic states on qubits for which contextuality and negativity of the Wigner function are necessary resources possessed by the magic states. These schemes satisfy a constraint. Namely, the non-negativity of Wigner functions must be preserved under all available measurement operations. Furthermore, we identify stringent consistency conditions on such computational schemes, revealing the general structure by which negativity of Wigner functions, hardness of classical simulation of the computation, and contextuality are connected.

Publication: Physical Review A Vol.: 95 No.: 5 ISSN: 0556-2791

ID: CaltechAUTHORS:20160622-152421080

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Abstract: We simulate the entanglement dynamics in a critical random quantum Ising chain with generic perturbations using the time-evolving block decimation algorithm. Starting from a product state, we observe super-logarithmic growth of entanglement entropy with time. The numerical result is consistent with the analytical prediction of Vosk and Altman using a real-space renormalization group technique.

Publication: Annals of Physics Vol.: 380ISSN: 0003-4916

ID: CaltechAUTHORS:20170313-083737697

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Abstract: We study universal quantum codes for entanglementassisted quantum communication over compound quantum channels. In this setting, sender and receiver do not know the specific channel that will be used for communication, but only know the set that the channel is selected from. We investigate different variations of the problem: uninformed users, informed receiver, informed sender, and feedback assistance. We derive single-letter formulas for all corresponding channel capacities. Our proofs are based on one-shot decoupling bounds and properties of smooth entropies.

Publication: IEEE Transactions on Information Theory Vol.: 63 No.: 5 ISSN: 0018-9448

ID: CaltechAUTHORS:20161024-120228304

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Abstract: Synthetic magnetism has been used to control charge neutral excitations for applications ranging from classical beam steering to quantum simulation. In optomechanics, radiation-pressure-induced parametric coupling between optical (photon) and mechanical (phonon) excitations may be used to break time-reversal symmetry, providing the prerequisite for synthetic magnetism. Here we design and fabricate a silicon optomechanical circuit with both optical and mechanical connectivity between two optomechanical cavities. Driving the two cavities with phase-correlated laser light results in a synthetic magnetic flux, which, in combination with dissipative coupling to the mechanical bath, leads to non-reciprocal transport of photons with 35 dB of isolation. Additionally, optical pumping with blue-detuned light manifests as a particle non-conserving interaction between photons and phonons, resulting in directional optical amplification of 12 dB in the isolator through-direction. These results suggest the possibility of using optomechanical circuits to create a more general class of non-reciprocal optical devices, and further, to enable new topological phases for both light and sound on a microchip.

Publication: Nature Physics Vol.: 13 No.: 5 ISSN: 1745-2473

ID: CaltechAUTHORS:20160824-093734211

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Abstract: We prove several trace inequalities that extend the Golden–Thompson and the Araki–Lieb–Thirring inequality to arbitrarily many matrices. In particular, we strengthen Lieb’s triple matrix inequality. As an example application of our four matrix extension of the Golden–Thompson inequality, we prove remainder terms for the monotonicity of the quantum relative entropy and strong sub-additivity of the von Neumann entropy in terms of recoverability. We find the first explicit remainder terms that are tight in the commutative case. Our proofs rely on complex interpolation theory as well as asymptotic spectral pinching, providing a transparent approach to treat generic multivariate trace inequalities.

Publication: Communications in Mathematical Physics Vol.: 352 No.: 1 ISSN: 0010-3616

ID: CaltechAUTHORS:20160622-115009117

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Abstract: There is a growing effort in creating chiral transport of sound waves. However, most approaches so far have been confined to the macroscopic scale. Here, we propose an approach suitable to the nanoscale that is based on pseudomagnetic fields. These pseudomagnetic fields for sound waves are the analogue of what electrons experience in strained graphene. In our proposal, they are created by simple geometrical modifications of an existing and experimentally proven phononic crystal design, the snowflake crystal. This platform is robust, scalable, and well-suited for a variety of excitation and readout mechanisms, among them optomechanical approaches.

Publication: Proceedings of the National Academy of Sciences of the United States of America Vol.: 114 No.: 17 ISSN: 0027-8424

ID: CaltechAUTHORS:20160824-094540945

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Abstract: Strong electron interactions can drive metallic systems toward a variety of well-known symmetry-broken phases, but the instabilities of correlated metals with strong spin-orbit coupling have only recently begun to be explored. We uncovered a multipolar nematic phase of matter in the metallic pyrochlore Cd_2Re_2O_7 using spatially resolved second-harmonic optical anisotropy measurements. Like previously discovered electronic nematic phases, this multipolar phase spontaneously breaks rotational symmetry while preserving translational invariance. However, it has the distinguishing property of being odd under spatial inversion, which is allowed only in the presence of spin-orbit coupling. By examining the critical behavior of the multipolar nematic order parameter, we show that it drives the thermal phase transition near 200 kelvin in Cd_2Re_2O_7 and induces a parity-breaking lattice distortion as a secondary order.

Publication: Science Vol.: 356 No.: 6335 ISSN: 0036-8075

ID: CaltechAUTHORS:20170420-145037343

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Abstract: We give a quantum algorithm for solving semidefinite programs (SDPs). It has worst case running time n^(1/2)m^(1/2)S^2 poly(log(n), log(m), R, r, 1/δ), with n and s the dimension and sparsity of the input matrices, respectively, m the number of constraints, δ the accuracy of the solution, and R, r upper bounds on the size of the optimal primal and dual solutions. This gives a square-root unconditional speed-up over any classical method for solving SDPs both in n and m. We prove the algorithm cannot be substantially improved giving a Ω(n^(1/2) + m^(1/2)) quantum lower bound for solving semidefinite programs with constant s, R, r and δ. We then argue that in some instances the algorithm offer even exponential speed-ups. This is the case whenever the quantum Gibbs states of Hamiltonians given by linear combinations of the input matrices of the SDP can be prepared efficiently on a quantum computer. An example are SDPs in which the input matrices have low-rank: For SDPs with the maximum rank of any input matrix bounded by rank, we show the quantum algorithm runs in time poly(log(n), log(m), rank, r, R, δ)m^(1/2). The quantum algorithm is constructed by a combination of quantum Gibbs sampling and the multiplicative weight method. In particular it is based on an classical algorithm of Arora and Kale for approximately solving SDPs. We present a modification of their algorithm to eliminate the need of solving an inner linear program which may be of independent interest.

ID: CaltechAUTHORS:20170726-063707920

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Abstract: Spontaneous collapse models are phenomological theories formulated to address major difficulties in macroscopic quantum mechanics. We place significant bounds on the parameters of the leading collapse models, the continuous spontaneous localization (CSL) model, and the Diosi-Penrose (DP) model, by using LISA Pathfinder’s measurement, at a record accuracy, of the relative acceleration noise between two free-falling macroscopic test masses. In particular, we bound the CSL collapse rate to be at most (2.96±0.12)×10^(−8) s^(−1). This competitive bound explores a new frequency regime, 0.7 to 20 mHz, and overlaps with the lower bound 10^(−8±2) s^(−1) proposed by Adler in order for the CSL collapse noise to be substantial enough to explain the phenomenology of quantum measurement. Moreover, we bound the regularization cutoff scale used in the DP model to prevent divergences to be at least 40.1±0.5 fm, which is larger than the size of any nucleus. Thus, we rule out the DP model if the cutoff is the size of a fundamental particle.

Publication: Physical Review D Vol.: 95 No.: 8 ISSN: 2470-0010

ID: CaltechAUTHORS:20161205-144444031

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Abstract: The gapless Bogoliubov-de Gennes (BdG) quasiparticles of a clean three dimensional spinless p_x + ip_y superconductor provide an intriguing example of a thermal Hall semimetal (ThSM) phase of Majorana-Weyl fermions; such a phase can support a large anomalous thermal Hall conductivity and protected surface Majorana-Fermi arcs at zero energy. We study the effects of quenched disorder on such a gapless topological phase by carrying out extensive numerical and analytical calculations on a lattice model for a disordered, spinless p_x + ip_y superconductor. Using the kernel polynomial method, we compute both average and typical density of states for the BdG quasiparticles, from which we construct the phase diagram of three dimensional dirty p_x + ip_y superconductors as a function of disorder strength and chemical potential of the underlying normal state. We establish that the power law quasi-localized states induced by rare statistical fluctuations of the disorder potential give rise to an exponentially small density of states at zero energy, and even infnitesimally weak disorder converts the ThSM into a thermal diffusive Hall metal (ThDM). Consequently, the phase diagram of the disordered model only consists of ThDM and thermal insulating phases. We show the existence of two types of thermal insulators: (i) a trivial thermal band insulator (ThBI) [or BEC phase] with a smeared gap that can occur for suitable band parameters and all strengths of disorder, supporting only exponentially localized Lifshitz states (at low energy), and (ii) a thermal Anderson insulator that only exists for large disorder strengths compared to all band parameters. We determine the nature of the two distinct localization-delocalization transitions between these two types of insulators and ThDM. Additionally, we establish the scaling properties of an avoided (or hidden) quantum critical point for moderate disorder strengths, which govern the crossover between ThSM and ThDM phases over a wide range of energy scales. We also discuss the experimental relevance of our findings for three dimensional, time reversal symmetry breaking, triplet superconducting states.

Publication: Physical Review B Vol.: 95 No.: 15 ISSN: 2469-9950

ID: CaltechAUTHORS:20170320-084528822

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Abstract: We derive an equality for non-equilibrium statistical mechanics in finite-dimensional quantum systems. The equality concerns the worst-case work output of a time-dependent Hamiltonian protocol in the presence of a Markovian heat bath. It has the form 'worst-case wo