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: 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 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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 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: 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: 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: 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: 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: 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: 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: 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: We investigate the relationship between the energy spectrum of a local Hamiltonian and the geometric properties of its ground state. By generalizing a standard framework from the analysis of Markov chains to arbitrary (non-stoquastic) Hamiltonians we are naturally led to see that the spectral gap can always be upper bounded by an isoperimetric ratio that depends only on the ground state probability distribution and the range of the terms in the Hamiltonian, but not on any other details of the interaction couplings. This means that for a given probability distribution the inequality constrains the spectral gap of any local Hamiltonian with this distribution as its ground state probability distribution in some basis (Eldar and Harrow derived a similar result [1] in order to characterize the output of low-depth quantum circuits). Going further, we relate the Hilbert space localization properties of the ground state to higher energy eigenvalues by showing that the presence of k strongly localized ground state modes (i.e. clusters of probability, or subsets with small expansion) in Hilbert space implies the presence of k energy eigenvalues that are close to the ground state energy. Our results suggest that quantum adiabatic optimization using local Hamiltonians will inevitably encounter small spectral gaps when attempting to prepare ground states corresponding to multi-modal probability distributions with strongly localized modes, and this problem cannot necessarily be alleviated with the inclusion of non-stoquastic couplings.

Publication: arXiv
ID: CaltechAUTHORS:20171102-115811858

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Abstract: We give an arguably simpler and more direct proof of a recent result by Miller, Jain and Shi, who proved device-independent security of a protocol for quantum key distribution in which the devices can be used in parallel. Our proof combines existing results on immunization (Kempe et al., SICOMP 2011) and parallel repetition (Bavarian et al., STOC 2017) of entangled games.

ID: CaltechAUTHORS:20190320-102806367

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Abstract: No, in a rigorous sense specified below.

ID: CaltechAUTHORS:20170606-064632154

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Abstract: Quantum information processors need to be protected against errors and faults. One of the most widely considered fault-tolerant architecture is based on surface codes. While the general principles of these codes are well understood and basic code properties such as minimum distance and rate are easy to characterize, a code's average performance depends on the detailed geometric layout of the qubits. To date, optimizing a surface code architecture and comparing different geometric layouts relies on costly numerical simulations. Here, we propose a benchmarking algorithm for simulating the performance of surface codes, and generalizations thereof, that runs in linear time. We implemented this algorithm in a software that generates performance reports and allows to quickly compare different architectures.

Publication: arXiv
ID: CaltechAUTHORS:20171108-153922644

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Abstract: We present a local Master equation for open system dynamics in two forms:Markovian and non-Markovian. Both have a wider range of validity than the Lindblad equation investigated by Davies. For low temperatures, they do not require coupling to be exponentially weak in the system size. If the state remains a low bond dimension Matrix Product State throughout the evolution, the local equation can be simulated in time polynomial in system size.

Publication: arXiv
ID: CaltechAUTHORS:20171103-153609085

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Abstract: We give a simple proof of the exponential de Finetti theorem due to Renner. Like Renner's proof, ours combines the post-selection de Finetti theorem, the Gentle Measurement lemma, and the Chernoff bound, but avoids virtually all calculations, including any use of the theory of types.

ID: CaltechAUTHORS:20190320-103022957

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Abstract: We consider a notion of relative homology (and cohomology) for surfaces with two types of boundaries. Using this tool, we study a generalization of Kitaev's code based on surfaces with mixed boundaries. This construction includes both Bravyi and Kitaev's and Freedman and Meyer's extension of Kitaev's toric code. We argue that our generalization offers a denser storage of quantum information. In a planar architecture, we obtain a three-fold overhead reduction over the standard architecture consisting of a punctured square lattice.

Publication: arXiv
ID: CaltechAUTHORS:20171109-142607199

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Abstract: We give the first construction of a family of quantum-proof extractors that has optimal seed length dependence O(log(n/ǫ)) on the input length n and error ǫ. Our extractors support any min-entropy k = Ω(log n + log1+α (1/ǫ)) and extract m = (1 − α)k bits that are ǫ-close to uniform, for any desired constant α > 0. Previous constructions had a quadratically worse seed length or were restricted to very large input min-entropy or very few output bits. Our result is based on a generic reduction showing that any strong classical condenser is automatically quantum-proof, with comparable parameters. The existence of such a reduction for extractors is a long-standing open question; here we give an affirmative answer for condensers. Once this reduction is established, to obtain our quantum-proof extractors one only needs to consider high entropy sources. We construct quantum-proof extractors with the desired parameters for such sources by extending a classical approach to extractor construction, based on the use of block-sources and sampling, to the quantum setting. Our extractors can be used to obtain improved protocols for device-independent randomness expansion and for privacy amplification.

Publication: arXiv
ID: CaltechAUTHORS:20160517-182619760

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Abstract: This is the 10th and final chapter of my book on Quantum Information, based on the course I have been teaching at Caltech since 1997. An early version of this chapter (originally Chapter 5) has been available on the course website since 1998, but this version is substantially revised and expanded. The level of detail is uneven, as I've aimed to provide a gentle introduction, but I've also tried to avoid statements that are incorrect or obscure. Generally speaking, I chose to include topics that are both useful to know and relatively easy to explain; I had to leave out a lot of good stuff, but on the other hand the chapter is already quite long. This is a working draft of Chapter 10, which I will continue to update. See the URL on the title page for further updates and drafts of other chapters, and please send me an email if you notice errors. Eventually, the complete book will be published by Cambridge University Press.

Publication: arXiv
ID: CaltechAUTHORS:20160426-213243084

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Abstract: Dimensional regularization is a common method used to regulate the UV divergence of field theoretic quantities. When it is used in the context of Renyi entropy, however, it is important to consider whether such a procedure eliminates the statistical interpretation thereof as a measure of entanglement of states living on a Hilbert space. We therefore examine the dimensionally regularized Renyi entropy of a 4d unitary CFT and show that it admits no underlying Hilbert space in the state-counting sense. This gives a concrete proof that dimensionally regularized Renyi entropy cannot always be obtained as a limit of the Renyi entropy of some finite-dimensional quantum system.

Publication: N/A
ID: CaltechAUTHORS:20160622-112748138

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Abstract: The recent proposal of Almheiri et al.[http://arxiv.org/abs/1411.7041], together with the Ryu-Takayanagi formula, implies the entanglement wedge hypothesis for certain choices of boundary subregions. This fact is derived in the pure AdS space. A similar conclusion holds in the presence of quantum corrections, but in a more restricted domain of applicability. We also comment on this [http://arxiv.org/abs/1601.05416] and some similarities and differences with this work.

Publication: Journal of High Energy PhysicsISSN: 1126-6708

ID: CaltechAUTHORS:20160622-113158636

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Abstract: We give a quantum multiprover interactive proof system for the local Hamiltonian problem in which there is a constant number of provers, questions are classical of length polynomial in the number of qubits, and answers are of constant length. The main novelty of our protocol is that the gap between completeness and soundness is directly proportional to the promise gap on the (normalized) ground state energy of the Hamiltonian. This result can be interpreted as a concrete step towards a quantum PCP theorem giving entangled-prover interactive proof systems for QMA-complete problems. The key ingredient is a quantum version of the classical linearity test of Blum, Luby, and Rubinfeld, where the function f : {0,1}^n → {0,1} is replaced by a pair of functions X,Z : {0,1}^n → Obs_d(C), the set of d-dimensional Hermitian matrices that square to identity. The test enforces that (i) each function is exactly linear, X(a)X(b) = X(a+b) and Z(a)Z(b) = Z(a+b), and (ii) the two functions are approximately complementary, X(a)Z(b) ≈ (−1)^(a⋅b)Z(b)X(a).

ID: CaltechAUTHORS:20160318-160143988

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Abstract: We show that the quantum query complexity of evaluating nand-tree instances with average choice complexity at most W is O(W), where average choice complexity is a measure of the difficulty of winning the associated two-player game. This generalizes a superpolynomial speedup over classical query complexity due to Zhan et al. We further show that the player with a winning strategy for the two-player game associated with the nand-tree can win the game with an expected Õ(N^(1/4) √C(x)) quantum queries against a random opponent, where C(x) is the average choice complexity of the instance. This gives an improvement over the query complexity of the naive strategy, which costs Õ(√N) queries. The results rely on a connection between nand-tree evaluation and st-connectivity problems on certain graphs, and span programs for st-connectivity problems. Our results follow from relating average choice complexity to the effective resistance of these graphs, which itself corresponds to the span program witness size.

ID: CaltechAUTHORS:20160602-065519464

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Abstract: We propose an efficient algorithm for the ground state of frustration-free one-dimensional gapped Hamiltonians. This algorithm is much simpler than the original one by Landau et al., and thus may be easily accessible to a general audience in the community. We present all the details in two pages.

ID: CaltechAUTHORS:20160201-153526027

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Abstract: Significant work has gone into determining the minimal set of entropy inequalities that determine the holographic entropy cone. Holographic systems with three or more parties have been shown to obey additional inequalities that generic quantum systems do not. We consider a two dimensional conformal field theory that is a single boundary of a holographic system and find four additional non-linear inequalities which are derived from strong subadditivity and the formula for the entanglement entropy of a region on the conformal field theory. We also present an equality obtained by application of a hyperbolic extension of Ptolemy's theorem to a two dimensional conformal field theory.

Publication: N/A
ID: CaltechAUTHORS:20160622-113714676

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Abstract: The mechanical properties of light have found widespread use in the manipulation of gas-phase atoms and ions, helping create new states of matter and realize complex quantum interactions. The field of cavity-optomechanics strives to scale this interaction to much larger, even human-sized mechanical objects. Going beyond the canonical Fabry-Perot cavity with a movable mirror, here we explore a new paradigm in which multiple cavity-optomechanical elements are wired together to form optomechanical circuits. Using a pair of optomechanical cavities coupled together via a phonon waveguide we demonstrate a tunable delay and filter for microwave-over-optical signal processing. In addition, we realize a tight-binding form of mechanical coupling between distant optomechanical cavities, leading to direct phonon exchange without dissipation in the waveguide. These measurements indicate the feasibility of phonon-routing based information processing in optomechanical crystal circuitry, and further, to the possibility of realizing topological phases of photons and phonons in optomechanical cavity lattices.

Publication: arXiv
ID: CaltechAUTHORS:20150824-080921056

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Abstract: Because they coherently link radio/microwave-rate electrical signals with optical-rate signals derived from lasers and atomic transitions, frequency combs are having a remarkably broad impact on science and technology. Integrating these systems on a photonic chip would revolutionize instrumentation, time keeping, spectroscopy, navigation and potentially create new mass-market applications. A key element of such a system-on-a-chip will be a mode-locked comb that can be self-referenced. The recent demonstration of soliton pulses from a microresonator has placed this goal within reach. However, to provide the requisite link between microwave and optical rate signals soliton generation must occur within the bandwidth of electronic devices. So far this is possible in crystalline devices, but not chip-based devices. Here, a monolithic comb that generates electronic-rate soliton pulses is demonstrated.

ID: CaltechAUTHORS:20160404-091735690

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Abstract: Optical measurement of the motion of a 940 kHz mechanical resonance of a silicon nitride nanostring resonator is demonstrated with a read out noise imprecision reaching 37 dB below that of the resonator's zero-point fluctuations. Via intensity modulation of the optical probe laser, radiation pressure feedback is used to cool and damp the mechanical mode from an initial room temperature occupancy of n_b=6.5×10^6 (T_b=295K) down to a phonon occupation of (n)=66±10, representing a mode temperature of T_m≈3mK. The five decades of cooling is enabled by the system's large single-photon cooperativity (C_1=4) and high quantum efficiency of optical motion detection (η_t=0.27).

Publication: arXiv
ID: CaltechAUTHORS:20150824-081716175

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Abstract: We present rigorous bounds on the thermalization time of the family of quantum mechanical spin systems known as stabilizer Hamiltonians. The thermalizing dynamics are modeled by a Davies master equation that arises from a weak local coupling of the system to a large thermal bath. Two temperature regimes are considered. First we clarify how in the low temperature regime, the thermalization time is governed by a generalization of the energy barrier between orthogonal ground states. When no energy barrier is present the Hamiltonian thermalizes in a time that is at most quadratic in the system size. Secondly, we show that above a universal critical temperature, every stabilizer Hamiltonian relaxes to its unique thermal state in a time which scales at most linearly in the size of the system. We provide an explicit lower bound on the critical temperature. Finally, we discuss the implications of these result for the problem of self-correcting quantum memories with stabilizer Hamiltonians.

ID: CaltechAUTHORS:20161004-093445721

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Abstract: It has been speculated that gravity could be an emergent phenomenon, with classical general relativity as an effective, macroscopic theory, valid only for classical systems at large temporal and spatial scales. As in classical continuum dynamics, the existence of underlying microscopic degrees of freedom may lead to macroscopic dissipative behaviors. With the hope that such dissipative behaviors of gravity could be revealed by carefully designed experiments in the laboratory, we consider a phenomenological model that adds dissipations to the gravitational field, much similar to frictions in solids and fluids. Constraints to such dissipative behavior can already be imposed by astrophysical observations and existing experiments, but mostly in lower frequencies. We propose a series of experiments working in higher frequency regimes, which may potentially put more stringent bounds on these models.

Publication: Towards the Laboratory Search for Space-Time Dissipation
ID: CaltechAUTHORS:20160108-094643919

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Abstract: We fabricate and characterize a microscale silicon electro-opto-mechanical system whose mechanical motion is coupled capacitively to an electrical circuit and optically via radiation pressure to a photonic crystal cavity. To achieve large electromechanical interaction strength, we implement an inverse shadow mask fabrication scheme which obtains capacitor gaps as small as 30 nm while maintaining a silicon surface quality necessary for minimizing optical loss. Using the sensitive optical read-out of the photonic crystal cavity, we characterize the linear and nonlinear capacitive coupling to the fundamental 63 MHz in-plane flexural motion of the structure, showing that the large electromechanical coupling in such devices may be suitable for realizing efficient microwave-to-optical signal conversion.

ID: CaltechAUTHORS:20140728-081038978

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Abstract: Extending previous work on scalar field theories, we develop a quantum algorithm to compute relativistic scattering amplitudes in fermionic field theories, exemplified by the massive Gross-Neveu model, a theory in two spacetime dimensions with quartic interactions. The algorithm introduces new techniques to meet the additional challenges posed by the characteristics of fermionic fields, and its run time is polynomial in the desired precision and the energy. Thus, it constitutes further progress towards an efficient quantum algorithm for simulating the Standard Model of particle physics.

Publication: arXiv
ID: CaltechAUTHORS:20140529-115454760

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Abstract: Optical measurements of a nanoscale silicon optomechanical crystal cavity with a mechanical resonance frequency of 3.6 GHz are performed at sub-kelvin temperatures. We infer optical-absorption-induced heating and damping of the mechanical resonator from measurements of phonon occupancy and motional sideband asymmetry. At the lowest probe power and lowest fridge temperature(T_f = 10 mK), the localized mechanical resonance is found to couple at a rate of γ_i/2π = 400 Hz (Q_m = 9 x 10^6) to a thermal bath of temperature T_b ≈ 270 mK. These measurements indicate that silicon optomechanical crystals cooled to millikelvin temperatures should be suitable for a variety of experiments involving coherent coupling between photons and phonons at the single quanta level.

ID: CaltechAUTHORS:20140402-105840104

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Abstract: The gapless surface states of topological insulators (TI) can potentially be used to detect and harvest low-frequency infrared light. Nonetheless, it was shown that significant surface photocurrents due to light with frequency below the bulk gap are rather hard to produce. Here we demonstrate that a periodic magnetic pattern added to the surface dramatically enhances surface photocurrents in TI's . The ability to produce substantial photocurrents on TI surfaces from mid-range and far-infrared light could be used in photovoltaic applications, as well as for detection of micrometer wavelength radiation.

Publication: arXiv
ID: CaltechAUTHORS:20140715-162801579

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Abstract: The existence of three generations of neutrinos and their mass mixing are the deep mysteries of our universe. The history of neutrino physics can be traced back to Majorana's elegant work on a real solution of the Dirac equation known as the Majorana fermion. A cutting-edge step towards understanding the nature of neutrino has been taken by the experimental discovery of neutrino mass mixing during the past decade, which indicates neutrino has a small but non-vanishing mass. A natural way to explain the origin of this small mass is the so-called seesaw mechanism, which requires the neutrino to be a Majorana fermion. Recently, Majorana's spirit returns in modern condensed matter physics-in the context of Majorana zero modes in certain classes of topological superconductors(TSCs). In this paper, we attempt to investigate the topological nature of the neutrino by establishing a connection between the Majorana fermion and Majorana zero modes assuming a relativistic Majorana fermion is made up of four Majorana zero modes. We begin with an exactly solvable 1D condensed matter model which realizes a T^2 = -1 time reversal symmetry protected TSC. We show that the pair of Majorana zero modes on each end will realize a T^4 = -1 representation of the time reversal symmetry and carry 1/4 spin. We find that a pair of Majorana zero modes can realize a P^4 = -1 parity symmetry as well and even a nontrivial C^4 = -1 charge conjugation symmetry. The CPT symmetries for a Majorana fermion made up of four Majorana modes form a super algebra. We then generalize the CPT super algebra into quantum field theory and point out that the nontrivial charge conjugation symmetry can be promoted to a Z_2 gauge symmetry, whose spontaneously breaking leads to the origin of the (right-handed) neutrino mass. The Z_2 gauge symmetry indicates the existence of the fifth force in our universe, which is possible to be detected in future LHC experiment. Finally, we show that the origin of three generations of neutrinos can be naturally explained as three distinguishable ways to form a pair of complex fermions(a particle and an anti-particle) out of four Majorana zero modes, characterized by the T^4 = -1, (TP)^4 = -1 and (TC)^4 = -1 fractionalized symmetries that particles/anti-particles carry. Together with the Z_2 gauge (minimal coupling) principle, we are able to determine the mass mixing matrix with no fitting parameter at leading order(in the absence of the CP violation and charged lepton contribution). We obtain θ_(12) = 31.7º; θ_(23) = θ45º and θ_(13) = 0º(known as the golden ratio pattern), which are intrinsically close to the current experimental results. We further predict an exact mass ratio for the three mass eigenstates with m_1/m_3 = m_2/m_3 = 3/√5.

ID: CaltechAUTHORS:20130925-103447828

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Abstract: We respond to a recent manuscript by Tsang [arXiv:1306.2699 ], on whether the measurement presented in Safavi-Naeini et al. [Phys. Rev. Lett. 108, 033 602 (2012)] can be explained “withoutreference to quantum mechanics”. We show that the fully classical analysis provided by Tsang, and previously by Safavi-Naeini et al. [New J. Phys. 15, 035007 (2013)], has been ruled out by our published data. In addition, we discuss the role of the mathematical formulation used on the interpretation of the asymmetry effect, as has previously been considered by Khalili et al. [Phys. Rev. A 86, 033840 (2012)

ID: CaltechAUTHORS:20140102-104155905

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Abstract: We describe a new trap-door (and PKC) proposal. The proposal is ``multivariate quadratic'' (relies on the hardness of solving systems of quadratic equations); it is also code-based, and uses the code-scrambling technique of McEliece (1978). However, in the new proposal, the error-correcting code is not revealed in the public key, which protects against the leading attacks on McEliece's method.

No.: 2013/135
ID: CaltechAUTHORS:20140130-133600557

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Abstract: We give a new proof for the area law for general 1D gapped systems, which exponentially improves Hastings' famous result [1]. Specifically, we show that for a chain of d-dimensional spins, governed by a 1D local Hamiltonian with a spectral gap ε > 0, the entanglement entropy of the ground state with respect to any cut in the chain is upper bounded by O(log^3 d/ε ). Our approach uses the framework of Refs. [2, 3] to construct a Chebyshev-based AGSP (Approximate Ground Space Projection) with favorable factors. However, our construction uses the Hamiltonian directly, instead of using the Detectability lemma, which allows us to work with general (frustrated) Hamiltonians, as well as slightly improving the 1/ε dependence of the bound in Ref. [3]. To achieve that, we establish a new, “random-walk like”, bound on the entanglement rank of an arbitrary power of a 1D Hamiltonian, which might be of independent interest: ER(H^ℓ) ≤ (ℓd)O(√ℓ). Finally, treating d as a constant, our AGSP shows that the ground state is well approximated by a matrix product state with a sublinear bond dimension B = ε ^O(log^(3/4) n/ε^(1/4)). Using this in conjunction with known dynamical programing algorithms, yields an algorithm for a 1=poly(n) approximation of the ground energy with a subexponential running time T ≤ exp (εO(log^(3/4) n/ε^(1/4))).

ID: CaltechAUTHORS:20140130-142058060

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Abstract: We show that optomechanical systems in the quantum regime can be used to demonstrate EPR-type quantum entanglement between the optical field and the mechanical oscillator, via quantum-state steering. Namely, the conditional quantum state of the mechanical oscillator can be steered into different quantum states depending the choice made on which quadrature of the out-going field is to be measured via homodyne detection. More specifically, if quantum radiation pressure force dominates over thermal force, the oscillator's quantum state is steerable with a photodetection efficiency as low as 50%, approaching the ideal limit shown by Wiseman and Gambetta [Phys. Rev. Lett. 108, 220402 (2012)]. We also show that requirement for steerability is the same as those for achieving sub-Heisenberg state tomography using the same experimental setup.

Publication: arXiv
ID: CaltechAUTHORS:20130131-140930189

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Abstract: Recent results on the stability of the spectral gap under general perturbations for frustration-free Hamiltonians, have motivated the following question: Does the entanglement entropy of quantum states that are connected to states satisfying an area law along gapped Hamiltonian paths, also satisfy an area law? We answer this question in the affirmative, combining recent advances in quasi-adiabatic evolution and Lieb-Robinson bounds with ideas from the proof of the 1D area law.

ID: CaltechAUTHORS:20121102-135530255

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Abstract: We describe a new proposal for a trap-door one-way function. The new proposal belongs to the "multivariate quadratic" family but the trap-door is different from existing methods, and is simpler.

ID: CaltechAUTHORS:20120713-075312396

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Abstract: Inspired by quantum information theory, we look for representations of the braid groups B_n on V^(⊗(n+m−2)) for some fixed vector space V such that each braid generator σ_i, i = 1, ..., n−1, acts on m consecutive tensor factors from i through i +m−1. The braid relation for m = 2 is essentially the Yang-Baxter equation, and the cases for m > 2 are called generalized Yang-Baxter equations. We observe that certain objects in ribbon fusion categories naturally give rise to such representations for the case m = 3. Examples are given from the Ising theory (or the closely related SU(2)_2), SO(N)_2 for N odd, and SU(3)_3. The solution from the Jones-Kauffman theory at a 6th root of unity, which is closely related to SO(3)_2 or SU(2)_4, is explicitly described in the end.

ID: CaltechAUTHORS:20120713-102318475

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Abstract: Recently Haah introduced a new quantum error correcting code embedded on a cubic lattice. One of the defining properties of this code is the absence of string logical operator. We present new codes with similar properties by relaxing the condition on the local particle dimension. The resulting code is well-defined when the local Hilbert space dimension is prime. These codes can be divided into two different classes: the local stabilizer generators are either symmetric or antisymmetric with respect to the inversion operation. These is a nontrivial correspondence between these two classes. For any symmetric code without string logical operator, there exists a complementary antisymmetric code with the same property and vice versa. We derive a sufficient condition for the absence of string logical operator in terms of the algebraic constraints on the defining parameters of the code. Minimal number of local particle dimension which satisfies the condition is 5. These codes have logarithmic energy barrier for any logical error.

ID: CaltechAUTHORS:20120713-091419180

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Abstract: High coherence lasers are essential in a wide range of applications, however, such performance is normally associated with large laser cavities, because increasing energy storage reduces quantum phase noise and also renders the laser frequency less sensitive to cavity vibration. This basic scaling rule is at odds with an emerging set of optical systems that place focus on compact (optimally integrable) sources of high coherence light. These include phase-coherent optical communication using quadrature-amplitude-modulation, and also record-low phase noise microwave sources based upon optical comb techniques. In this work, the first, chip-based Brillouin laser is demonstrated. It features high-efficiency and single-line operation with the smallest recorded Schawlow-Townes frequency noise for any chip-based laser. Because the frequency offset between the laser's emission and the input pump is relatively small, the device provides a new function: spectral purification of compact, low coherence sources such as semiconductor lasers.

ID: CaltechAUTHORS:20120206-105450544

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Abstract: Non-Markovianity, as an important feature of general open quantum systems, is usually difficult to quantify with limited knowledge of how the plant that we are interested in interacts with its environment-the bath. It often happens that the reduced dynamics of the plant attached to a non-Markovian bath becomes indistinguishable from the one with a Markovian bath, if we left the entire system freely evolve. Here we show that non-Markovianity can be revealed via applying local unitary operations on the plant-they will influence the plant evolution at later times due to memory of the bath. This not only provides a new criterion for non-Markovianity, but also sheds light on protecting and recovering quantum coherence in non-Markovian systems, which will be useful for quantum-information processing.

ID: CaltechAUTHORS:20121102-100208411

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Abstract: Topological entanglement entropy is a topological invariant which can detect topological order of quantum many-body ground state. We assume an existence of such order parameter at finite temperature which is invariant under smooth deformation of the subsystems, and study its stability under hamiltonian perturbation. We apply this assumption to a Gibbs state of hamiltonian which satisfies so called `strong commuting' condition, which we shall define in the paper. Interesting models in this category include local hamiltonian models based on quantum error correcting code. We prove a stability of such topologically invariant order parameter against arbitrary perturbation which can be expressed as a sum of geometrically local bounded-norm terms. The first order correction against such perturbation vanishes in the thermodynamic limit.

ID: CaltechAUTHORS:20120713-140540112

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Abstract: The Turaev-Viro invariants are scalar topological invariants of three-dimensional manifolds. Here we show that the problem of estimating the Fibonacci version of the Turaev-Viro invariant of a mapping torus is a complete problem for the one clean qubit complexity class (DQC1). This complements a previous result showing that estimating the Turaev-Viro invariant for arbitrary manifolds presented as Heegaard splittings is a complete problem for the standard quantum computation model (BQP). We also discuss a beautiful analogy between these results and previously known results on the computational complexity of approximating the Jones polynomial.

ID: CaltechAUTHORS:20120713-083236942

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