Combined Feed
https://feeds.library.caltech.edu/people/Preskill-J/combined.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 07 Dec 2023 22:05:50 +0000Cosmological production of superheavy magnetic monopoles
https://resolver.caltech.edu/CaltechAUTHORS:PREprl79
Authors: Preskill, John P.
Year: 1979
DOI: 10.1103/PhysRevLett.43.1365
Grand unified models of elementary particle interactions contain stable superheavy magnetic monopoles. The density of such monopoles in the early universe is estimated to be unacceptably large. Cosmological monopole production may be suppressed if the phase transition at the grand unification mass scale is strongly first order.https://authors.library.caltech.edu/records/zsrdb-ajf25CP Nonconservation without Elementary Scalar Fields
https://resolver.caltech.edu/CaltechAUTHORS:EICprl80
Authors: Eichten, Estia; Lane, Kenneth; Preskill, J.
Year: 1980
DOI: 10.1103/PhysRevLett.45.225
Dynamically broken gauge theories of electroweak interactions provide a natural mechanism for generating CP nonconservation. Even if all vacuum angles are unobservable, strong CP nonconservation is not automatically avoided. In the absence of strong CP nonconservation, the neutron electric dipole moment is expected to be of order 10^-24e·cm.https://authors.library.caltech.edu/records/qnn2b-x5686Subgroup Alignment in Hypercolor Theories
https://resolver.caltech.edu/CaltechAUTHORS:20140724-133643360
Authors: Preskill, John
Year: 1981
DOI: 10.1016/0550-3213(81)90265-0
To analyze the physical consequences of a dynamically broken theory of the weak interactions, we must know how the weak gauge group is aligned in an approximate flavor-symmetry group. For a large class of models, spectral-function sum rules enables us to determine this alignment explicitly. We work out the pattern of the electroweak symmetry breakdown for several sample models. Critical values of weak mixing angles are found at which the breakdown pattern changes discontinously. We compute pseudo-Goldstone boson masses, and find that some models contain unusually light charged or colored pseudo-Goldstone bosons.https://authors.library.caltech.edu/records/4vph1-e5a91"Decoupling" constraints on massless composite particles
https://resolver.caltech.edu/CaltechAUTHORS:PREprd81
Authors: Preskill, John; Weinberg, Steven
Year: 1981
DOI: 10.1103/PhysRevD.24.1059
It is pointed out that the use of the "decoupling" constraints on the spectrum of composite massless particles is not justified without further assumptions. There is an alternative condition, whose use would not be subject to the same criticisms, which would lead to the same constraints as the decoupling condition, and which would lead to other results as well, for instance that the nonchiral global symmetries in quantum chromodynamics (QCD) with n massless flavors can not be spontaneously broken. However, this condition is found to be violated in a specific model. It is still an open possibility that the chiral symmetries of QCD are unbroken for n not a multiple of 3.https://authors.library.caltech.edu/records/2c92t-v1a69Magnetic Monopoles
https://resolver.caltech.edu/CaltechAUTHORS:20120706-134558232
Authors: Preskill, John
Year: 1984
DOI: 10.1146/annurev.nucl.34.1.461
How is it possible to justify a lengthy review of the physics of the magnetic
monopole when nobody has ever seen one? In spite of the unfortunate lack
of favorable experimental evidence, there are sound theoretical reasons for
believing that the magnetic monopole must exist. The case for its existence
is surely as strong as the case for any other undiscovered particle.
Moreover, as of this writing (early 1984), it is not certain that nobody has
ever seen one. What seems certain is that nobody has ever seen two.https://authors.library.caltech.edu/records/nmrdx-92w08Poisson clusters and Poisson voids
https://resolver.caltech.edu/CaltechAUTHORS:POLprl86
Authors: Politzer, H. David; Preskill, John P.
Year: 1986
DOI: 10.1103/PhysRevLett.56.99
Expressions are derived for the expected abundance of clusters and voids in a sample of randomly distributed objects.https://authors.library.caltech.edu/records/x7sp7-x4d29The significance of voids
https://resolver.caltech.edu/CaltechAUTHORS:20161005-151942807
Authors: Otto, S.; Politzer, H. David; Preskill, John; Wise, Mark B.
Year: 1986
DOI: 10.1086/164144
The statistical significance of voids in the spatial distribution of galaxies or clusters of galaxies is studied. The probability per unit volume of finding a large void is expressed in terms of correlation functions. Numerical simulations are used to estimate the likelihood of observing a large void in the distribution of rich clusters of galaxies, assuming that rich clusters arose wherever suitably averaged primordial density fluctuations were unusually large.https://authors.library.caltech.edu/records/k1gh0-z3441Wormholes in spacetime and θQCD
https://resolver.caltech.edu/CaltechAUTHORS:20170810-153648292
Authors: Preskill, John; Trivedi, Sandip P.; Wise, Mark B.
Year: 1989
DOI: 10.1016/0370-2693(89)90913-1
We calculate in chiral perturbation theory the dependence of Newton's gravitational constant G on the θ parameter of quantum chromodynamics, and we find that G, as a function of θ, is minimized at θ≌π. This calculation suggests that quantum fluctuations in the topology of spacetime would cause θ to assume a value very near π, contrary to the phenomenological evidence indicating that θ is actually near 0.https://authors.library.caltech.edu/records/3c568-y0p63Growing hair on black holes
https://resolver.caltech.edu/CaltechAUTHORS:COLprl91
Authors: Coleman, Sidney; Preskill, John; Wilczek, Frank
Year: 1991
DOI: 10.1103/PhysRevLett.67.1975
A black hole can carry quantum numbers that are not associated with massless gauge fields, contrary to the spirit of the "no-hair" theorems. In the Higgs phase of a gauge theory, electric charge on a black hole generates a nonzero electric field outside the event horizon. This field is nonperturbative in ħ and is exponentially screened far from the hole. It arises from the cloud of virtual cosmic strings that surround the black hole. In the confinement phase, a magnetic charge on a black hole generates a classical field that is screened at long range by nonperturbative effects. Despite the sharp difference in their formal descriptions, the electric and magnetic cases are closely similar physically.https://authors.library.caltech.edu/records/y6nsv-wvx39Internal frame dragging and a global analog of the Aharonov-Bohm effect
https://resolver.caltech.edu/CaltechAUTHORS:MARprl92
Authors: March-Russell, John; Preskill, John; Wilczek, Frank
Year: 1992
DOI: 10.1103/PhysRevLett.68.2567
It is shown that the breakdown of a global symmetry group to a discrete subgroup can lead to analogs of the Aharonov-Bohm effect. At sufficiently low momentum transfer, the cross section for scattering of a particle with nontrivial Z2 charge off a global vortex is almost equal to (but definitely different from) maximal Aharonov-Bohm scattering; the effect goes away at large momentum transfer. The scattering of a spin-1/2 particle off a magnetic vortex provides an amusing experimentally realizable example.https://authors.library.caltech.edu/records/f9br0-fen58Quantum Hair on Black Holes
https://resolver.caltech.edu/CaltechAUTHORS:20120314-134754496
Authors: Coleman, Sidney; Preskill, John; Wilczek, Frank
Year: 1992
DOI: 10.1016/0550-3213(92)90008-Y
A black hole may carry quantum numbers that are not associated with massless gauge fields, contrary to the spirit of the "no-hair" theorems. We describe in detail two different types of black-hole hair that decay exponentially at long range. The first type is associated with discrete gauge charge and the screening is due to the Higgs mechanism. The second type is associated with color magnetic charge, and the screening is due to color confinement. In both cases, we perform semiclassical calculations of the effect of the hair on local observables outside the horizon, and on black-hole thermodynamics. These effects are generated by virtual cosmic strings, or virtual electric flux tubes, that sweep around the event horizon. The effects of discrete gauge charge are nonperturbative in ħ, but the effects of color magnetic charge become ħ-independent in a suitable limit. We present an alternative treatment of discrete gauge charge using dual variables, and examine the possibility of black-hole hair associated with discrete global symmetry. We draw the distinction between primary hair, which endows a black hole with new quantum numbers, and secondary hair, which does not, and we point out some varieties of secondary hair that occur in the standard model of particle physics.https://authors.library.caltech.edu/records/x7gc8-5m951Do Black Holes Destroy Information?
https://resolver.caltech.edu/CaltechAUTHORS:20120925-151257143
Authors: Preskill, John
Year: 1992
DOI: 10.48550/arXiv.9209058
I review the information loss paradox that was first formulated by Hawking, and discuss possible ways of resolving it. All proposed solutions have serious drawbacks. I conclude that the information loss paradox may well presage a
revolution in fundamental physics.https://authors.library.caltech.edu/records/y45bm-sz592Quantum Field Theory of Nonabelian Strings and Vortices
https://resolver.caltech.edu/CaltechAUTHORS:20120314-135053542
Authors: Alford, Mark G.; Lee, Kai-Ming; March-Russell, John; Preskill, John
Year: 1992
DOI: 10.1016/0550-3213(92)90468-Q
We develop an operator formalism for investigating the properties of non-abelian cosmic strings (and vortices) in quantum field theory. Operators are constructed that introduce classical string sources and that create dynamical string loops. The operator construction in lattice gauge theory is explicitly described, and correlation functions are computed in the strong-coupling and weak-coupling limits. These correlation functions are used to study the long-range interactions of non-abelian strings, taking account of charge-screening effects due to virtual particles. Among the phenomena investigated are the Aharonov-Bohm interactions of strings with charged particles, holonomy interactions between string loops, string entanglement, the transfer of "Cheshire charge" to a string loop, and domain-wall decay via spontaneous string nucleation. We also anayze the Aharonov-Bohm interactions of magnetic monopoles with electric flux tubes in a confining gauge theory. We propose that the Aharonov-Bohm effect can be invoked to distinguish among various phases of a non-abelian gauge theory coupled to matter.https://authors.library.caltech.edu/records/e4pkc-ns232Topological Approach to Alice Electrodynamics
https://resolver.caltech.edu/CaltechAUTHORS:20120314-135309738
Authors: Bucher, Martin; Lo, Hoi-Kwong; Preskill, John
Year: 1992
DOI: 10.1016/0550-3213(92)90173-9
We analyze the unlocalized "Cheshire charge" carried by "Alice strings." The magnetic charge on a string loop is carefully defined, and the transfer of magnetic charge from a monopole to a string loop is analyzed using global topological methods. A semiclassical theory of electric charge transfer is also described.https://authors.library.caltech.edu/records/t9gh6-7ac86On Detecting Discrete Cheshire Charge
https://resolver.caltech.edu/CaltechAUTHORS:20120314-135655591
Authors: Bucher, Martin; Lee, Kai-Ming; Preskill, John
Year: 1992
DOI: 10.1016/0550-3213(92)90174-A
We analyze the charges carried by loops of string in models with non-abelian local discrete symmetry. The charge on a loop has no localized source, but can be detected by means of the Aharonov-Bohm interaction of the loop with another string. We describe the process of charge detection, and the transfer of charge between point particles and string loops, in terms of gauge-invariant correlation functions.https://authors.library.caltech.edu/records/b4ngw-0a940Semilocal defects
https://resolver.caltech.edu/CaltechAUTHORS:PREprd92
Authors: Preskill, John
Year: 1992
DOI: 10.1103/PhysRevD.46.4218
I analyze the interplay of gauge and global symmetries in the theory of topological defects. In a two-dimensional model in which both gauge symmetries and exact global symmetries are spontaneously broken, stable vortices may fail to exist even though magnetic flux is topologically conserved. Following Vachaspati and Achúcarro, I formulate the condition that must be satisfied by the pattern of symmetry breakdown for finite-energy configurations to exist in which the conserved magnetic flux is spread out instead of confined to a localized vortex. If this condition is met, vortices are always unstable at sufficiently weak gauge coupling. I also describe the properties of defects in models with an "accidental" symmetry that is partially broken by gauge-boson exchange. In some cases, the spontaneously broken accidental symmetry is not restored inside the core of the defect. Then the structure of the defect can be analyzed using an effective field theory; the details of the physics responsible for the spontaneous symmetry breakdown need not be considered. Examples include domain walls and vortices that are classically unstable, but are stabilized by loop corrections, and magnetic monopoles that have an unusual core structure. Finally, I examine the general theory of the "electroweak strings" that were recently discussed by Vachaspati. These arise only in models with gauge-boson "mixing," and can always end on magnetic monopoles. Cosmological implications are briefly discussed.https://authors.library.caltech.edu/records/r36mt-66125Decay of metastable topological defects
https://resolver.caltech.edu/CaltechAUTHORS:PREprd93
Authors: Preskill, John; Vilenkin, Alexander
Year: 1993
DOI: 10.1103/PhysRevD.47.2324
We systematically analyze the decay of metastable topological defects that arise from the spontaneous breakdown of gauge or global symmetries. Quantum-mechanical tunneling rates are estimated for a variety of decay processes. The decay rate for a global string, vortex, domain wall, or kink is typically suppressed compared to the decay rate for its gauged counterpart. We also discuss the decay of global texture, and of semilocal and electroweak strings.https://authors.library.caltech.edu/records/4rhwx-46704Non-Abelian vortices and non-Abelian statistics
https://resolver.caltech.edu/CaltechAUTHORS:LOHprd93
Authors: Lo, Hoi-Kwong; Preskill, John
Year: 1993
DOI: 10.1103/PhysRevD.48.4821
We study the interactions of non-Abelian vortices in two spatial dimensions. These interactions have novel features, because the Aharonov-Bohm effect enables a pair of vortices to exchange quantum numbers. The cross section for vortex-vortex scattering is typically a multivalued function of the scattering angle. There can be an exchange contribution to the vortex-vortex scattering amplitude that adds coherently with the direct amplitude, even if the two vortices have distinct quantum numbers. Thus two vortices can be "indistinguishable" even though they are not the same.https://authors.library.caltech.edu/records/m4fce-yeb90Complementarity in Wormhole Chromodynamics
https://resolver.caltech.edu/CaltechAUTHORS:20120229-152505223
Authors: Lo, Hoi-Kwong; Lee, Kai-Ming; Preskill, John
Year: 1993
DOI: 10.1016/0370-2693(93)90130-A
The electric charge of a wormhole mouth and the magnetic flux "linked" by the wormhole are non-commuting observables, and
so cannot be simultaneously diagonalized. We use this observation to resolve some puzzles in wormhole electrodynamics and
chromodynamics. Specifically, we analyze the color electric field that results when a colored object traverses a wormhole, and we
discuss the measurement of the wormhole charge and flux using Aharonov-Bohm interference effects.https://authors.library.caltech.edu/records/tw8yz-87h63Black hole thermodynamics and information loss in two dimensions
https://resolver.caltech.edu/CaltechAUTHORS:FIOprd94
Authors: Fiola, Thomas M.; Preskill, John; Strominger, Andrew; Trivedi, Sandip P.
Year: 1994
DOI: 10.1103/PhysRevD.50.3987
Black hole evaporation is investigated in a (1+1)-dimensional model of quantum gravity. Quantum corrections to the black hole entropy are computed, and the fine-grained entropy of the Hawking radiation is studied. A generalized second law of thermodynamics is formulated, and shown to be valid under suitable conditions. It is also shown that, in this model, a black hole can consume an arbitrarily large amount of information.https://authors.library.caltech.edu/records/ne3vv-se627Efficient networks for quantum factoring
https://resolver.caltech.edu/CaltechAUTHORS:BECpra96
Authors: Beckman, David; Chari, Amalavoyal N.; Devabhaktuni, Srikrishna; Preskill, John
Year: 1996
DOI: 10.1103/PhysRevA.54.1034
We consider how to optimize memory use and computation time in operating a quantum computer. In particular, we estimate the number of memory quantum bits (qubits) and the number of operations required to perform factorization, using the algorithm suggested by Shor [in Proceedings of the 35th Annual Symposium on Foundations of Computer Science, edited by S. Goldwasser (IEEE Computer Society, Los Alamitos, CA, 1994), p. 124]. A K-bit number can be factored in time of order K3 using a machine capable of storing 5K+1 qubits. Evaluation of the modular exponential function (the bottleneck of Shor's algorithm) could be achieved with about 72K3 elementary quantum gates; implementation using a linear ion trap would require about 396K3 laser pulses. A proof-of-principle demonstration of quantum factoring (factorization of 15) could be performed with only 6 trapped ions and 38 laser pulses. Though the ion trap may never be a useful computer, it will be a powerful device for exploring experimentally the properties of entangled quantum states.https://authors.library.caltech.edu/records/nhgz2-p7a17Fault-tolerant quantum computers
https://resolver.caltech.edu/CaltechAUTHORS:PREiqci98
Authors: Preskill, John
Year: 1998
The discovery of quantum error correction has greatly improved the long-term prospects for quantum computing technology. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment, or due to imperfect implementations of quantum logical operations. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. In principle, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per quantum gate is less than a certain critical value, the accuracy threshold. It may be possible to incorporate intrinsic fault tolerance into the design of quantum computing hardware, perhaps by invoking topological Aharonov-Bohm interactions to process quantum information.https://authors.library.caltech.edu/records/e298b-gkh85Reliable quantum computers
https://resolver.caltech.edu/CaltechAUTHORS:20200929-143507282
Authors: Preskill, John
Year: 1998
DOI: 10.1098/rspa.1998.0167
The new field of quantum error correction has developed spectacularly since its origin less than two years ago. Encoded quantum information can be protected from errors that arise due to uncontrolled interactions with the environment. Recovery from errors can work effectively even if occasional mistakes occur during the recovery procedure. Furthermore, encoded quantum information can be processed without serious propagation of errors. Hence, an arbitrarily long quantum computation can be performed reliably, provided that the average probability of error per quantum gate is less than a certain critical value, the accuracy threshold. A quantum computer storing about 10⁶ qubits, with a probability of error per quantum gate of order 10⁻⁶, would be a formidable factoring engine. Even a smaller less–accurate quantum computer would be able to perform many useful tasks.
This paper is based on a talk presented at the ITP Conference on Quantum Coherence and Decoherence, 15 to 18 December 1996.https://authors.library.caltech.edu/records/mc0ry-r1e30Quantum computing: pro and con
https://resolver.caltech.edu/CaltechAUTHORS:20200916-090616410
Authors: Preskill, John
Year: 1998
DOI: 10.1098/rspa.1998.0171
I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and consider the prospects for finding new ones. Quantum computers are notoriously susceptible to making errors; I discuss recently developed fault–tolerant procedures that enable a quantum computer with noisy gates to perform reliably. Quantum computing hardware is still in its infancy; I comment on the specifications that should be met by future hardware. Over the past few years, work on quantum computation has erected a new classification of computational complexity, has generated profound insights into the nature of decoherence, and has stimulated the formulation of new techniques in high–precision experimental physics. A broad interdisciplinary effort will be needed if quantum computers are to fulfil their destiny as the world's fastest computing devices.
This paper is an expanded version of remarks that were prepared for a panel discussion at the ITP Conference on Quantum Coherence and Decoherence, December 1996.https://authors.library.caltech.edu/records/7398j-9nm96Robust solutions to hard problems
https://resolver.caltech.edu/CaltechAUTHORS:20150605-102149860
Authors: Preskill, John
Year: 1998
DOI: 10.1038/35484
Twenty-first century computers could achieve astonishing speed by exploiting the principles of quantum mechanics. New techniques of quantum error correction will be essential to prevent those machines from crashing.https://authors.library.caltech.edu/records/a0a80-0mf28Topological Quantum Computation
https://resolver.caltech.edu/CaltechAUTHORS:20200715-072635515
Authors: Ogburn, R. Walter; Preskill, John
Year: 1999
DOI: 10.1007/3-540-49208-9_31
Following a suggestion of A. Kitaev, we explore the connection between fault-tolerant quantum computation and nonabelian quantum statistics in two spatial dimensions. A suitably designed spin system can support localized excitations (quasiparticles) that exhibit long-range nonabelian Aharonov-Bohm interactions. Quantum information encoded in the charges of the quasiparticles is highly resistant to decoherence, and can be reliably processed by carrying one quasiparticle around another. If information is encoded in pairs of quasiparticles, then the Aharonov-Bohm interactions can be adequate for universal fault-tolerant quantum computation.https://authors.library.caltech.edu/records/my6w1-9q013The Feynman processor: Quantum entanglement and the computing revolution [Book Review]
https://resolver.caltech.edu/CaltechAUTHORS:20150608-103533216
Authors: Preskill, John
Year: 1999
DOI: 10.1038/18151
During the second half of this century we
have witnessed staggering progress in the
development of information technology. At
present, the pace of progress shows no sign
of slowing. But in the early twenty-first
century, conventional integrated-circuit
technology will approach the fundamental
limitations imposed by the atomic size scale.
At that stage, continued improvement in
computing performance, and the continued
expansion of the world economy, may
hinge on the development of radically new
methods for processing information.https://authors.library.caltech.edu/records/kv4be-6p109Plug-in quantum software
https://resolver.caltech.edu/CaltechAUTHORS:20150608-104757494
Authors: Preskill, John
Year: 1999
DOI: 10.1038/46434
Some quantum states are hard to create and maintain, but are a valuable resource for computing. Twenty-first century entrepreneurs could make a fortune selling disposable quantum states.https://authors.library.caltech.edu/records/t6j23-nc795Quantum information and physics: Some future directions
https://resolver.caltech.edu/CaltechAUTHORS:20111129-141152912
Authors: Preskill, John
Year: 2000
DOI: 10.1080/09500340008244031
I consider some promising future directions for quantum information theory that could influence the development of 21st century physics. Advances in the theory of the distinguishability of superoperators may lead to new strategies for improving the precision of quantum-limited measurements. A better grasp of the properties of multi-partite quantum entanglement may lead to deeper understanding of strongly-coupled dynamics in quantum many-body systems, quantum field theory, and quantum gravity.https://authors.library.caltech.edu/records/4vvyt-7zz06Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
https://resolver.caltech.edu/CaltechAUTHORS:SHOprl00
Authors: Shor, Peter W.; Preskill, John
Year: 2000
DOI: 10.1103/PhysRevLett.85.441
We prove that the 1984 protocol of Bennett and Brassard (BB84) for quantum key distribution is secure. We first give a key distribution protocol based on entanglement purification, which can be proven secure using methods from Lo and Chau's proof of security for a similar protocol. We then show that the security of this protocol implies the security of BB84. The entanglement purification based protocol uses Calderbank-Shor-Steane codes, and properties of these codes are used to remove the use of quantum computation from the Lo-Chau protocol.https://authors.library.caltech.edu/records/2r7tp-05e65Secure quantum key distribution using squeezed states
https://resolver.caltech.edu/CaltechAUTHORS:GOTpra01a
Authors: Gottesman, Daniel; Preskill, John
Year: 2001
DOI: 10.1103/PhysRevA.63.022309
We prove the security of a quantum key distribution scheme based on transmission of squeezed quantum states of a harmonic oscillator. Our proof employs quantum error-correcting codes that encode a finite-dimensional quantum system in the infinite-dimensional Hilbert space of an oscillator, and protect against errors that shift the canonical variables p and q. If the noise in the quantum channel is weak, squeezing signal states by 2.51 dB (a squeeze factor er=1.34) is sufficient in principle to ensure the security of a protocol that is suitably enhanced by classical error correction and privacy amplification. Secure key distribution can be achieved over distances comparable to the attenuation length of the quantum channel.https://authors.library.caltech.edu/records/hxeeh-acm71Encoding a qubit in an oscillator
https://resolver.caltech.edu/CaltechAUTHORS:GOTpra01b
Authors: Gottesman, Daniel; Kitaev, Alexei; Preskill, John
Year: 2001
DOI: 10.1103/PhysRevA.64.012310
Quantum error-correcting codes are constructed that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. These codes exploit the noncommutative geometry of phase space to protect against errors that shift the values of the canonical variables q and p. In the setting of quantum optics, fault-tolerant universal quantum computation can be executed on the protected code subspace using linear optical operations, squeezing, homodyne detection, and photon counting; however, nonlinear mode coupling is required for the preparation of the encoded states. Finite-dimensional versions of these codes can be constructed that protect encoded quantum information against shifts in the amplitude or phase of a d-state system. Continuous-variable codes can be invoked to establish lower bounds on the quantum capacity of Gaussian quantum channels.https://authors.library.caltech.edu/records/9pn21-d2z44Causal and localizable quantum operations
https://resolver.caltech.edu/CaltechAUTHORS:BECpra01
Authors: Beckman, David; Gottesman, Daniel; Nielsen, M. A.; Preskill, John
Year: 2001
DOI: 10.1103/PhysRevA.64.052309
We examine constraints on quantum operations imposed by relativistic causality. A bipartite superoperator is said to be localizable if it can be implemented by two parties (Alice and Bob) who share entanglement but do not communicate; it is causal if the superoperator does not convey information from Alice to Bob or from Bob to Alice. We characterize the general structure of causal complete-measurement superoperators, and exhibit examples that are causal but not localizable. We construct another class of causal bipartite superoperators that are not localizable by invoking bounds on the strength of correlations among the parts of a quantum system. A bipartite superoperator is said to be semilocalizable if it can be implemented with one-way quantum communication from Alice to Bob, and it is semicausal if it conveys no information from Bob to Alice. We show that all semicausal complete-measurement superoperators are semilocalizable, and we establish a general criterion for semicausality. In the multipartite case, we observe that a measurement superoperator that projects onto the eigenspaces of a stabilizer code is localizable.https://authors.library.caltech.edu/records/v9xay-ydw79Achievable rates for the Gaussian quantum channel
https://resolver.caltech.edu/CaltechAUTHORS:HARpra01
Authors: Harrington, Jim; Preskill, John
Year: 2001
DOI: 10.1103/PhysRevA.64.062301
We study the properties of quantum stabilizer codes that embed a finite-dimensional protected code space in an infinite-dimensional Hilbert space. The stabilizer group of such a code is associated with a symplectically integral lattice in the phase space of 2N canonical variables. From the existence of symplectically integral lattices with suitable properties, we infer a lower bound on the quantum capacity of the Gaussian quantum channel that matches the one-shot coherent information optimized over Gaussian input states.https://authors.library.caltech.edu/records/dfsfp-pxf22Robustness of adiabatic quantum computation
https://resolver.caltech.edu/CaltechAUTHORS:CHIpra02
Authors: Childs, Andrew M.; Farhi, Edward; Preskill, John
Year: 2002
DOI: 10.1103/PhysRevA.65.012322
We study the fault tolerance of quantum computation by adiabatic evolution, a quantum algorithm for solving various combinatorial search problems. We describe an inherent robustness of adiabatic computation against two kinds of errors, unitary control errors and decoherence, and we study this robustness using numerical simulations of the algorithm.https://authors.library.caltech.edu/records/ewct1-r0251Measurability of Wilson loop operators
https://resolver.caltech.edu/CaltechAUTHORS:BECprd02
Authors: Beckman, David; Gottesman, Daniel; Kitaev, Alexei; Preskill, John
Year: 2002
DOI: 10.1103/PhysRevD.65.065022
We show that the nondemolition measurement of a spacelike Wilson loop operator W(C) is impossible in a relativistic non-Abelian gauge theory. In particular, if two spacelike-separated magnetic flux tubes both link with the loop C, then a nondemolition measurement of W(C) would cause electric charge to be transferred from one flux tube to the other, a violation of relativistic causality. A destructive measurement of W(C) is possible in a non-Abelian gauge theory with suitable matter content. In an Abelian gauge theory, many cooperating parties distributed along the loop C can perform a nondemolition measurement of the Wilson loop operator if they are equipped with a shared entangled ancilla that has been prepared in advance. We also note that Abelian electric charge (but not non-Abelian charge) can be transported superluminally, without any accompanying transmission of information.https://authors.library.caltech.edu/records/4rebx-j5r09Topological quantum memory
https://resolver.caltech.edu/CaltechAUTHORS:DENjmp02.842
Authors: Dennis, Eric; Kitaev, Alexei; Landahl, Andrew; Preskill, John
Year: 2002
DOI: 10.1063/1.1499754
We analyze surface codes, the topological quantum error-correcting codes introduced by Kitaev. In these codes, qubits are arranged in a two-dimensional array on a surface of nontrivial topology, and encoded quantum operations are associated with nontrivial homology cycles of the surface. We formulate protocols for error recovery, and study the efficacy of these protocols. An order-disorder phase transition occurs in this system at a nonzero critical value of the error rate; if the error rate is below the critical value (the accuracy threshold), encoded information can be protected arbitrarily well in the limit of a large code block. This phase transition can be accurately modeled by a three-dimensional Z(2) lattice gauge theory with quenched disorder. We estimate the accuracy threshold, assuming that all quantum gates are local, that qubits can be measured rapidly, and that polynomial-size classical computations can be executed instantaneously. We also devise a robust recovery procedure that does not require measurement or fast classical processing; however, for this procedure the quantum gates are local only if the qubits are arranged in four or more spatial dimensions. We discuss procedures for encoding, measurement, and performing fault-tolerant universal quantum computation with surface codes, and argue that these codes provide a promising framework for quantum computing architectures.https://authors.library.caltech.edu/records/kag81-nk917Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
https://resolver.caltech.edu/CaltechAUTHORS:20111017-135406894
Authors: Wang, Chenyang; Harrington, Jim; Preskill, John
Year: 2003
DOI: 10.1016/S0003-4916(02)00019-2
We study the ±J random-plaquette Z_2 gauge model (RPGM) in three spatial dimensions, a three-dimensional analog of the two-dimensional ±J random-bond Ising model (RBIM). The model is a pure Z_2 gauge theory in which randomly chosen plaquettes (occurring with concentration p) have couplings with the "wrong sign" so that magnetic flux is energetically favored on these plaquettes. Excitations of the model are one-dimensional "flux tubes" that terminate at "magnetic monopoles" located inside lattice cubes that contain an odd number of wrong-sign plaquettes. Electric confinement can be driven by thermal fluctuations of the flux tubes, by the quenched background of magnetic monopoles, or by a combination of the two. Like the RBIM, the RPGM has enhanced symmetry along a "Nishimori line" in the p–T plane (where T is the temperature). The critical concentration p_c of wrong-sign plaquettes at the confinement-Higgs phase transition along the Nishimori line can be identified with the accuracy threshold for robust storage of quantum information using topological error-correcting codes: if qubit phase errors, qubit bit-flip errors, and errors in the measurement of local check operators all occur at rates below p_c, then encoded quantum information can be protected perfectly from damage in the limit of a large code block. Through Monte-Carlo simulations, we measure p_(c0), the critical concentration along the T=0 axis (a lower bound on p_c), finding p_(c0)=.0293±.0002. We also measure the critical concentration of antiferromagnetic bonds in the two-dimensional RBIM on the T=0 axis, finding p_(c0)=.1031±.0001. Our value of p_(c0) is incompatible with the value of p_c=.1093±.0002 found in earlier numerical studies of the RBIM, in disagreement with the conjecture that the phase boundary of the RBIM is vertical (parallel to the T axis) below the Nishimori line. The model can be generalized to a rank-r antisymmetric tensor field in d dimensions, in the presence of quenched disorder.https://authors.library.caltech.edu/records/4042z-r4y52Secure Quantum Key Distribution with an Uncharacterized Source
https://resolver.caltech.edu/CaltechAUTHORS:KOAprl03
Authors: Koashi, Masato; Preskill, John
Year: 2003
DOI: 10.1103/PhysRevLett.90.057902
We prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol for an arbitrary source whose averaged states are basis independent, a condition that is automatically satisfied if the source is suitably designed. The proof is based on the observation that, to an adversary, the key extraction process is equivalent to a measurement in the sigma-hatx basis performed on a pure sigma-hatz-basis eigenstate. The dependence of the achievable key length on the bit error rate is the same as that established by Shor and Preskill [Phys. Rev. Lett. 85, 441 (2000)] for a perfect source, indicating that the defects in the source are efficiently detected by the protocol.https://authors.library.caltech.edu/records/meg81-qbx38Comment on "The black hole final state"
https://resolver.caltech.edu/CaltechAUTHORS:GOTjhep04
Authors: Gottesman, Daniel; Preskill, John
Year: 2004
DOI: 10.1088/1126-6708/2004/03/026
Horowitz and Maldacena have suggested that the unitarity of the black hole S-matrix can be reconciled with Hawking's semiclassical arguments if a final-state boundary condition is imposed at the spacelike singularity inside the black hole. We point out that, in this scenario, departures from unitarity can arise due to interactions between the collapsing body and the infalling Hawking radiation inside the event horizon. The amount of information lost when a black hole evaporates depends on the extent to which these interactions are entangling.https://authors.library.caltech.edu/records/0hw5g-z0t77Superselection rules and quantum protocols
https://resolver.caltech.edu/CaltechAUTHORS:KITpra04
Authors: Kitaev, Alexei; Mayers, Dominic; Preskill, John
Year: 2004
DOI: 10.1103/PhysRevA.69.052326
We show that superselection rules do not enhance the information-theoretic security of quantum cryptographic protocols. Our analysis employs two quite different methods. The first method uses the concept of a reference system—in a world subject to a superselection rule, unrestricted operations can be simulated by parties who share access to a reference system with suitable properties. By this method, we prove that if an n-party protocol is secure in a world subject to a superselection rule, then the security is maintained even if the superselection rule is relaxed. However, the proof applies only to a limited class of superselection rules, those in which the superselection sectors are labeled by unitary irreducible representations of a compact symmetry group. The second method uses the concept of the format of a message sent between parties—by verifying the format, the recipient of a message can check whether the message could have been sent by a party who performed charge-conserving operations. By this method, we prove that protocols subject to general superselection rules (including those pertaining to non-Abelian anyons in two dimensions) are no more secure than protocols in the unrestricted world. However, the proof applies only to two-party protocols. Our results show in particular that, if no assumptions are made about the computational power of the cheater, then secure quantum bit commitment and strong quantum coin flipping with arbitrarily small bias are impossible in a world subject to superselection rules.https://authors.library.caltech.edu/records/ym8rj-ydt09Fault-Tolerant Quantum Computation with Long-Range Correlated Noise
https://resolver.caltech.edu/CaltechAUTHORS:AHAprl06
Authors: Aharonov, Dorit; Kitaev, Alexei; Preskill, John
Year: 2006
DOI: 10.1103/PhysRevLett.96.050504
We prove a new version of the quantum accuracy threshold theorem that applies to non-Markovian noise with algebraically decaying spatial correlations. We consider noise in a quantum computer arising from a perturbation that acts collectively on pairs of qubits and on the environment, and we show that an arbitrarily long quantum computation can be executed with high reliability in D spatial dimensions, if the perturbation is sufficiently weak and decays with the distance r between the qubits faster than 1/r^D.https://authors.library.caltech.edu/records/3y99p-gqe61Topological Entanglement Entropy
https://resolver.caltech.edu/CaltechAUTHORS:KITprl06
Authors: Kitaev, Alexei; Preskill, John
Year: 2006
DOI: 10.1103/PhysRevLett.96.110404
We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of the disk, we obtain a marginal density operator rho for the degrees of freedom in the interior. The von Neumann entropy of rho, a measure of the entanglement of the interior and exterior variables, has the form S(rho)=alphaL-gamma+[centered ellipsis], where the ellipsis represents terms that vanish in the limit L-->[infinity]. We show that -gamma is a universal constant characterizing a global feature of the entanglement in the ground state. Using topological quantum field theory methods, we derive a formula for gamma in terms of properties of the superselection sectors of the medium.https://authors.library.caltech.edu/records/bs5y2-6qt49Black holes as mirrors: quantum information in random subsystems
https://resolver.caltech.edu/CaltechAUTHORS:HAYjhep07
Authors: Hayden, Patrick; Preskill, John
Year: 2007
DOI: 10.1088/1126-6708/2007/09/120
We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the ``half-way'' point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis.https://authors.library.caltech.edu/records/xz5az-sy825Fault-tolerant quantum computation against biased noise
https://resolver.caltech.edu/CaltechAUTHORS:ALIpra08
Authors: Aliferis, Panos; Preskill, John
Year: 2008
DOI: 10.1103/PhysRevA.78.052331
We formulate a scheme for fault-tolerant quantum computation that works effectively against highly biased noise, where dephasing is far stronger than all other types of noise. In our scheme, the fundamental operations performed by the quantum computer are single-qubit preparations, single-qubit measurements, and conditional-phase (CPHASE) gates, where the noise in the CPHASE gates is biased. We show that the accuracy threshold for quantum computation can be improved by exploiting this noise asymmetry; e.g., if dephasing dominates all other types of noise in the CPHASE gates by four orders of magnitude, we find a rigorous lower bound on the accuracy threshold higher by a factor of 5 than for the case of unbiased noise.https://authors.library.caltech.edu/records/mc8s7-y9s52Fibonacci scheme for fault-tolerant quantum computation
https://resolver.caltech.edu/CaltechAUTHORS:ALIpra09
Authors: Aliferis, Panos; Preskill, John
Year: 2009
DOI: 10.1103/PhysRevA.79.012332
We rigorously analyze Knill's Fibonacci scheme for fault-tolerant quantum computation, which is based on the recursive preparation of Bell states protected by a concatenated error-detecting code. We prove lower bounds on the threshold fault rate of 0.67×10^−3 for adversarial local stochastic noise, and 1.25×10^−3 for independent depolarizing noise. In contrast to other schemes with comparable proved accuracy thresholds, the Fibonacci scheme has a significantly reduced overhead cost because it uses postselection far more sparingly.https://authors.library.caltech.edu/records/9mb0w-ptf96Fault-tolerant computing with biased-noise superconducting qubits: a case study
https://resolver.caltech.edu/CaltechAUTHORS:ALInjp09
Authors: Aliferis, P.; Brito, F.; DiVincenzo, D. P.; Preskill, J.; Steffen, M.; Terhal, B. M.
Year: 2009
DOI: 10.1088/1367-2630/11/1/013061
We present a universal scheme of pulsed operations suitable for the IBM oscillator-stabilized flux qubit comprising the controlled-sigma(z) (CPHASE) gate, single-qubit preparations and measurements. Based on numerical simulations, we argue that the error rates for these operations can be as low as about 0.5% and that noise is highly biased, with phase errors being stronger than all other types of errors by a factor of nearly 10^3. In contrast, the design of a controlled σ(x) (CNOT) gate for this system with an error rate of less than about 1.2% seems extremely challenging. We propose a special encoding that exploits the noise bias allowing us to implement a logical CNOT gate where phase errors and all other types of errors have nearly balanced rates of about 0.4%. Our results illustrate how the design of an encoding scheme can be adjusted and optimized according to the available physical operations and the particular noise characteristics of experimental devices.https://authors.library.caltech.edu/records/bjjjz-zcp08Fault-tolerant quantum computation versus Gaussian noise
https://resolver.caltech.edu/CaltechAUTHORS:20090728-112832875
Authors: Ng, Hui Khoon; Preskill, John
Year: 2009
DOI: 10.1103/PhysRevA.79.032318
We study the robustness of a fault-tolerant quantum computer subject to Gaussian non-Markovian quantum noise, and we show that scalable quantum computation is possible if the noise power spectrum satisfies an appropriate "threshold condition." Our condition is less sensitive to very-high-frequency noise than previously derived threshold conditions for non-Markovian noise.https://authors.library.caltech.edu/records/byys8-9ky04Interface between Topological and Superconducting Qubits
https://resolver.caltech.edu/CaltechAUTHORS:20110419-095245511
Authors: Jiang, Liang; Kane, Charles L.; Preskill, John
Year: 2011
DOI: 10.1103/PhysRevLett.106.130504
We propose and analyze an interface between a topological qubit and a superconducting flux qubit. In our scheme, the interaction between Majorana fermions in a topological insulator is coherently controlled by a superconducting phase that depends on the quantum state of the flux qubit. A controlled-phase gate, achieved by pulsing this interaction on and off, can transfer quantum information between the topological qubit and the superconducting qubit.https://authors.library.caltech.edu/records/dvp5g-dfc28Combining dynamical decoupling with fault-tolerant quantum computation
https://resolver.caltech.edu/CaltechAUTHORS:20110715-131156639
Authors: Ng, Hui Khoon; Lidar, Daniel A.; Preskill, John
Year: 2011
DOI: 10.1103/PhysRevA.84.012305
We study how dynamical decoupling (DD) pulse sequences can improve the reliability of quantum computers. We prove upper bounds on the accuracy of DD-protected quantum gates and derive sufficient conditions for DD-protected gates to outperform unprotected gates. Under suitable conditions, fault-tolerant quantum circuits constructed from DD-protected gates can tolerate stronger noise and have a lower overhead cost than fault-tolerant circuits constructed from unprotected gates. Our accuracy estimates depend on the dynamics of the bath that couples to the quantum computer and can be expressed either in terms of the operator norm of the bath's Hamiltonian or in terms of the power spectrum of bath correlations; we explain in particular how the performance of recursively generated concatenated pulse sequences can be analyzed from either viewpoint. Our results apply to Hamiltonian noise models with limited spatial correlations.https://authors.library.caltech.edu/records/smghm-x7a39Quantum computing and the entanglement frontier - Rapporteur talk at the 25th Solvay Conference
https://resolver.caltech.edu/CaltechAUTHORS:20120516-084322874
Authors: Preskill, John
Year: 2012
DOI: 10.48550/arXiv.1203.5813
Quantum information science explores the frontier of highly complex quantum states,
the "entanglement frontier". This study is motivated by the observation (widely believed
but unproven) that classical systems cannot simulate highly entangled quantum systems
efficiently, and we hope to hasten the day when well controlled quantum systems can
perform tasks surpassing what can be done in the classical world. One way to achieve
such "quantum supremacy" would be to run an algorithm on a quantum computer which
solves a problem with a super-polynomial speedup relative to classical computers, but
there may be other ways that can be achieved sooner, such as simulating exotic quantum
states of strongly correlated matter. To operate a large scale quantum computer reliably
we will need to overcome the debilitating effects of decoherence, which might be done
using "standard" quantum hardware protected by quantum error-correcting codes, or by
exploiting the nonabelian quantum statistics of anyons realized in solid state systems,
or by combining both methods. Only by challenging the entanglement frontier will we
learn whether Nature provides extravagant resources far beyond what the classical world
would allow.https://authors.library.caltech.edu/records/zehqk-30k03Quantum Algorithms for Quantum Field Theories
https://resolver.caltech.edu/CaltechAUTHORS:20120522-122303309
Authors: Jordan, Stephen P.; Lee, Keith S. M.; Preskill, John
Year: 2012
DOI: 10.1126/science.1217069
Quantum field theory reconciles quantum mechanics and special relativity,
and plays a central role in many areas of physics. We develop a quantum
algorithm to compute relativistic scattering probabilities in a massive quantum
field theory with quartic self-interactions (φ^4 theory) in spacetime of four
and fewer dimensions. Its run time is polynomial in the number of particles,
their energy, and the desired precision, and applies at both weak and strong
coupling. In the strong-coupling and high-precision regimes, our quantum
algorithm achieves exponential speedup over the fastest known classical algorithm.https://authors.library.caltech.edu/records/y2zas-wkj03Logical-operator tradeoff for local quantum codes
https://resolver.caltech.edu/CaltechAUTHORS:20121012-142001671
Authors: Haah, Jeongwan; Preskill, John
Year: 2012
DOI: 10.1103/PhysRevA.86.032308
We study the structure of logical operators in local D-dimensional quantum codes, considering both subsystem
codes with geometrically local gauge generators and codes defined by geometrically local commuting projectors.
We show that if the code distance is d, then any logical operator can be supported on a set of specified geometry
containing ˜d qubits, where ˜dd^(1/(D−1)) = O(n) and n is the code length. Our results place limitations on partially
self-correcting quantum memories, in which at least some logical operators are protected by energy barriers that
grow with system size. We also show that for any two-dimensional local commuting projector code there is a
nontrivial logical "string" operator supported on a narrow strip, where the operator is only slightly entangling
across any cut through the strip.https://authors.library.caltech.edu/records/h4jha-99x39Sufficient condition on noise correlations for scalable quantum computing
https://resolver.caltech.edu/CaltechAUTHORS:20130321-160602027
Authors: Preskill, John
Year: 2013
DOI: 10.48550/arXiv.1207.6131
I study the effectiveness of fault-tolerant quantum computation against correlated Hamiltonian noise, and derive a sufficient condition for scalability. Arbitrarily long quantum
computations can be executed reliably provided that noise terms acting collectively on k
system qubits are sufficiently weak, and decay sufficiently rapidly with increasing k and
with increasing spatial separation of the qubits.https://authors.library.caltech.edu/records/y7cnh-sbx82Fault-tolerant quantum computation with asymmetric Bacon-Shor codes
https://resolver.caltech.edu/CaltechAUTHORS:20130404-091531009
Authors: Brooks, Peter; Preskill, John
Year: 2013
DOI: 10.1103/PhysRevA.87.032310
We develop a scheme for fault-tolerant quantum computation based on asymmetric Bacon-Shor codes, which works effectively against highly biased noise dominated by dephasing. We find the optimal Bacon-Shor block size as a function of the noise strength and the noise bias, and estimate the logical error rate and overhead cost achieved by this optimal code. Our fault-tolerant gadgets, based on gate teleportation, are well suited for hardware platforms with geometrically local gates in two dimensions.https://authors.library.caltech.edu/records/df89q-m2812Optimal Bacon-Shor codes
https://resolver.caltech.edu/CaltechAUTHORS:20130325-085516990
Authors: Napp, John; Preskill, John
Year: 2013
DOI: 10.48550/arXiv.1209.0794v1
We study the performance of Bacon-Shor codes, quantum subsystem codes which are well
suited for applications to fault-tolerant quantum memory because the error syndrome
can be extracted by performing two-qubit measurements. Assuming independent noise,
we find the optimal block size in terms of the bit-flip error probability pX and the
phase error probability pZ, and determine how the probability of a logical error depends
on pX and pZ. We show that a single Bacon-Shor code block, used by itself without
concatenation, can provide very effective protection against logical errors if the noise is
highly biased (pZ/pX ≫1) and the physical error rate pZ is a few percent or below. We
also derive an upper bound on the logical error rate for the case where the syndrome
data is noisy.https://authors.library.caltech.edu/records/rc7d1-d8473Protected gates for superconducting qubits
https://resolver.caltech.edu/CaltechAUTHORS:20130619-094717394
Authors: Brooks, Peter; Kitaev, Alexei; Preskill, John
Year: 2013
DOI: 10.1103/PhysRevA.87.052306
We analyze the accuracy of quantum phase gates acting on "0-π qubits" in superconducting circuits, where the gates are protected against thermal and Hamiltonian noise by continuous-variable quantum error-correcting codes. The gates are executed by turning on and off a tunable Josephson coupling between an LC oscillator and a qubit or pair of qubits; assuming perfect qubits, we show that the gate errors are exponentially small when the oscillator's impedance √L/C is large compared to ℏ/4e^2≈1 kΩ. The protected gates are not computationally universal by themselves, but a scheme for universal fault-tolerant quantum computation can be constructed by combining them with unprotected noisy operations. We validate our analytic arguments with numerical simulations.https://authors.library.caltech.edu/records/v84kc-nd242Can We Exploit the Weirdness of Quantum Mechanics?
https://resolver.caltech.edu/CaltechAUTHORS:20131202-091656426
Authors: Preskill, John
Year: 2013
Quantum theory is over a century old, yet physicists continue to be perplexed and delighted by the weirdness of the quantum world. Whereas the laws of classical physics successfully explain the phenomena we experience every day, atoms and other tiny objects obey quantum laws that sometimes seem to defy common sense, baffling our feeble human minds. In the 21st century, we hope to put this weirdness to work by building quantum computers capable of performing amazing tasks.https://authors.library.caltech.edu/records/bfj53-0nd11Quantum Algorithms for Fermionic Quantum Field Theories
https://resolver.caltech.edu/CaltechAUTHORS:20140529-115454760
Authors: Jordan, Stephen P.; Lee, Keith S. M.; Preskill, John
Year: 2014
DOI: 10.48550/arXiv.1404.7115
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.https://authors.library.caltech.edu/records/pt01q-wdy02Unitarity of black hole evaporation in final-state projection models
https://resolver.caltech.edu/CaltechAUTHORS:20140611-133437673
Authors: Lloyd, Seth; Preskill, John
Year: 2014
DOI: 10.1007/JHEP08(2014)126
Almheiri et al. have emphasized that otherwise reasonable beliefs about black hole evaporation are incompatible with the monogamy of quantum entanglement, a general property of quantum mechanics. We investigate the final-state projection model of black hole evaporation proposed by Horowitz and Maldacena, pointing out that this model admits cloning of quantum states and polygamous entanglement, allowing unitarity of the evaporation process to be reconciled with smoothness of the black hole event horizon. Though the model seems to require carefully tuned dynamics to ensure exact unitarity of the black hole S-matrix, for a generic final-state boundary condition the deviations from unitarity are exponentially small in the black hole entropy; furthermore observers inside black holes need not detect any deviations from standard quantum mechanics. Though measurements performed inside old black holes could potentially produce causality-violating phenomena, the computational complexity of decoding the Hawking radiation may render the causality violation unobservable. Final-state projection models illustrate how inviolable principles of standard quantum mechanics might be circumvented in a theory of quantum gravity.https://authors.library.caltech.edu/records/ggp7c-krz41Quantum Computation of Scattering in Scalar Quantum Field Theories
https://resolver.caltech.edu/CaltechAUTHORS:20120712-151413773
Authors: Jordan, Stephen P.; Lee, Keith S. M.; Preskill, John
Year: 2014
DOI: 10.48550/arXiv.1112.4833
Quantum field theory provides the framework for the most fundamental physical theories to be confirmed experimentally, and has enabled predictions of unprecedented precision. However, calculations of physical observables often require great computational complexity and can generally be performed only when the interaction strength is weak. A full understanding of the foundations and rich consequences of quantum field theory remains an outstanding challenge. We develop a quantum algorithm to compute relativistic scattering amplitudes in massive phi-fourth theory in spacetime of four and fewer dimensions. The algorithm runs in a time that is polynomial in the number of particles, their energy, and the desired precision, and applies at both weak and strong coupling. Thus, it offers exponential speedup over existing classical methods at high precision or strong coupling.https://authors.library.caltech.edu/records/37esa-c5164Perturbative instability of quantum memory based on effective long-range interactions
https://resolver.caltech.edu/CaltechAUTHORS:20150420-105848086
Authors: Landon-Cardinal, Olivier; Yoshida, Beni; Poulin, David; Preskill, John
Year: 2015
DOI: 10.1103/PhysRevA.91.032303
A two-dimensional topologically ordered quantum memory is well protected against error if the energy gap is large compared to the temperature, but this protection does not improve as the system size increases. We review and critique some recent proposals for improving the memory time by introducing long-range interactions among anyons, noting that instability with respect to small local perturbations of the Hamiltonian is a generic problem for such proposals. We also discuss some broader issues regarding the prospects for scalable quantum memory in two-dimensional systems.https://authors.library.caltech.edu/records/c3aqr-kaz15Holographic quantum error-correcting codes: toy models for the bulk/boundary correspondence
https://resolver.caltech.edu/CaltechAUTHORS:20150717-122900464
Authors: Pastawski, Fernando; Yoshida, Beni; Harlow, Daniel; Preskill, John
Year: 2015
DOI: 10.1007/JHEP06(2015)149
We propose a family of exactly solvable toy models for the AdS/CFT correspondence based on a novel construction of quantum error-correcting codes with a tensor network structure. Our building block is a special type of tensor with maximal entanglement along any bipartition, which gives rise to an isometry from the bulk Hilbert space to the boundary Hilbert space. The entire tensor network is an encoder for a quantum error-correcting code, where the bulk and boundary degrees of freedom may be identified as logical and physical degrees of freedom respectively. These models capture key features of entanglement in the AdS/CFT correspondence; in particular, the Ryu-Takayanagi formula and the negativity of tripartite information are obeyed exactly in many cases. That bulk logical operators can be represented on multiple boundary regions mimics the Rindlerwedge reconstruction of boundary operators from bulk operators, realizing explicitly the quantum error-correcting features of AdS/CFT recently proposed in [1].https://authors.library.caltech.edu/records/pr56h-jx184Universal form for quark and lepton mass matrices
https://resolver.caltech.edu/CaltechAUTHORS:20160104-165102169
Authors: Gu, Zheng-Cheng; Preskill, John
Year: 2015
DOI: 10.1103/PhysRevD.92.113005
We propose a universal form for quark and lepton mass matrices, which applies in a "leading order" approximation where CP-violating phases are ignored. Down-quark mass ratios are successfully predicted in our scheme using the measured Cabibbo-Kobayashi-Maskawa mixing angles as input. Assuming an additional discrete symmetry in the neutrino sector, we obtain the "golden ratio" pattern in the leading-order Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix; in addition we predict an inverted neutrino mass hierarchy with m_1-≃-m_2 ≃ 74 meV, m_3 ≃ 55 meV, and neutrinoless double beta decay mass parameter m_(0νββ) ≃ 33 meV. When CP-violating phases are included, our scheme suggests a residual ℤ_2 antiunitary symmetry of the neutrino mass matrix, in which the interchange of μ and τ neutrinos is accompanied by a time reversal transformation, thus predicting that the CP-violating angle in the neutrino sector is close to the maximal value δ = ± π/2, and that the diagonal phases in the PMNS matrix are α_ 1 ≃ 0, α_2 ≃ π.https://authors.library.caltech.edu/records/9eb85-7w423Protected gates for topological quantum field theories
https://resolver.caltech.edu/CaltechAUTHORS:20141209-131847639
Authors: Beverland, Michael E.; Oliver, Buerschaper; Koenig, Robert; Pastawski, Fernando; Preskill, John; Sijher, Sumit
Year: 2016
DOI: 10.1063/1.4939783
We study restrictions on locality-preserving unitary logical gates for topological quantum codes in two spatial dimensions. A locality-preserving operation is one which maps local operators to local operators — for example, a constant-depth quantum circuit of geometrically local gates, or evolution for a constant time governed by a geometrically local bounded-strength Hamiltonian. Locality-preserving logical gates of topological codes are intrinsically fault tolerant because spatially localized errors remain localized, and hence sufficiently dilute errors remain correctable. By invoking general properties of two-dimensional topological field theories, we find that the locality-preserving logical gates are severely limited for codes which admit non-abelian anyons, in particular, there are no locality-preserving logical gates on the torus or the sphere with M punctures if the braiding of anyons is computationally universal. Furthermore, for Ising anyons on the M-punctured sphere, locality-preserving gates must be elements of the logical Pauli group. We derive these results by relating logical gates of a topological code to automorphisms of the Verlinde algebra of the corresponding anyon model, and by requiring the logical gates to be compatible with basis changes in the logical Hilbert space arising from local F-moves and the mapping class group.https://authors.library.caltech.edu/records/jn1p7-am493Quantum Shannon Theory
https://resolver.caltech.edu/CaltechAUTHORS:20160426-213243084
Authors: Preskill, John
Year: 2016
DOI: 10.48550/arXiv.1604.07450
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.https://authors.library.caltech.edu/records/386jx-np407Error correction for encoded quantum annealing
https://resolver.caltech.edu/CaltechAUTHORS:20160315-111407944
Authors: Pastawski, Fernando; Preskill, John
Year: 2016
DOI: 10.1103/PhysRevA.93.052325
Recently, W. Lechner, P. Hauke, and P. Zoller [Sci. Adv. 1, e1500838 (2015)] have proposed a quantum annealing architecture, in which a classical spin glass with all-to-all pairwise connectivity is simulated by a spin glass with geometrically local interactions. We interpret this architecture as a classical error-correcting code, which is highly robust against weakly correlated bit-flip noise, and we analyze the code's performance using a belief-propagation decoding algorithm. Our observations may also apply to more general encoding schemes and noise models.https://authors.library.caltech.edu/records/p1gke-2sa33Code Properties from Holographic Geometries
https://resolver.caltech.edu/CaltechAUTHORS:20170517-114206968
Authors: Pastawski, Fernando; Preskill, John
Year: 2017
DOI: 10.1103/PhysRevX.7.021022
Almheiri, Dong, and Harlow [J. High Energy Phys. 04 (2015) 163.] proposed a highly illuminating connection between the AdS/CFT holographic correspondence and operator algebra quantum error correction (OAQEC). Here, we explore this connection further. We derive some general results about OAQEC, as well as results that apply specifically to quantum codes that admit a holographic interpretation. We introduce a new quantity called price, which characterizes the support of a protected logical system, and find constraints on the price and the distance for logical subalgebras of quantum codes. We show that holographic codes defined on bulk manifolds with asymptotically negative curvature exhibit uberholography, meaning that a bulk logical algebra can be supported on a boundary region with a fractal structure. We argue that, for holographic codes defined on bulk manifolds with asymptotically flat or positive curvature, the boundary physics must be highly nonlocal, an observation with potential implications for black holes and for quantum gravity in AdS space at distance scales that are small compared to the AdS curvature radius.https://authors.library.caltech.edu/records/jmnwe-2za28BQP-completeness of Scattering in Scalar Quantum Field Theory
https://resolver.caltech.edu/CaltechAUTHORS:20170720-172919513
Authors: Jordan, Stephen P.; Krovi, Hari; Lee, Keith S. M.; Preskill, John
Year: 2018
DOI: 10.22331/q-2018-01-08-44
Recent work has shown that quantum computers can compute scattering probabilities in massive quantum field theories, with a run time that is polynomial in the number of particles, their energy, and the desired precision. Here we study a closely related quantum field-theoretical problem: estimating the vacuum-to-vacuum transition amplitude, in the presence of spacetime-dependent classical sources, for a massive scalar field theory in (1+1) dimensions. We show that this problem is BQP-hard; in other words, its solution enables one to solve any problem that is solvable in polynomial time by a quantum computer. Hence, the vacuum-to-vacuum amplitude cannot be accurately estimated by any efficient classical algorithm, even if the field theory is very weakly coupled, unless BQP=BPP. Furthermore, the corresponding decision problem can be solved by a quantum computer in a time scaling polynomially with the number of bits needed to specify the classical source fields, and this problem is therefore BQP-complete. Our construction can be regarded as an idealized architecture for a universal quantum computer in a laboratory system described by massive phi^4 theory coupled to classical spacetime-dependent sources.https://authors.library.caltech.edu/records/2n7bh-ab342Achieving the Heisenberg limit in quantum metrology using quantum error correction
https://resolver.caltech.edu/CaltechAUTHORS:20170720-172112488
Authors: Zhou, Sisi; Zhang, Mengzhen; Preskill, John; Jiang, Liang
Year: 2018
DOI: 10.1038/s41467-017-02510-3
PMCID: PMC5758555
Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg limit, which can be achieved for noiseless quantum systems, but is not achievable in general for systems subject to noise. Here we study how measurement precision can be enhanced through quantum error correction, a general method for protecting a quantum system from the damaging effects of noise. We find a necessary and sufficient condition for achieving the Heisenberg limit using quantum probes subject to Markovian noise, assuming that noiseless ancilla systems are available, and that fast, accurate quantum processing can be performed. When the sufficient condition is satisfied, a quantum error-correcting code can be constructed that suppresses the noise without obscuring the signal; the optimal code, achieving the best possible precision, can be found by solving a semidefinite program.https://authors.library.caltech.edu/records/8h81k-m6g42Stephen Hawking (1942–2018)
https://resolver.caltech.edu/CaltechAUTHORS:20180412-141957828
Authors: Preskill, John
Year: 2018
DOI: 10.1126/science.aat6775
Stephen William Hawking died on 14 March (Albert Einstein's birthday) at the age of 76 after decades of battling the incurable disease amyotrophic lateral sclerosis (ALS). His early scientific work transformed our understanding of general relativity, Einstein's theory of gravitation. Later in life, Stephen became an immensely successful popularizer of science; his courage and high spirits in the face of his disability inspired millions. Stephen Hawking's achievements as a scientist, communicator, and public figure were commensurate with his great fame.https://authors.library.caltech.edu/records/4y39s-j1013Three-dimensional color code thresholds via statistical-mechanical mapping
https://resolver.caltech.edu/CaltechAUTHORS:20171004-145219476
Authors: Kubica, Aleksander; Beverland, Michael E.; Brandão, Fernando G. S. L.; Preskill, John; Svore, Krysta M.
Year: 2018
DOI: 10.1103/PhysRevLett.120.180501
Three-dimensional (3D) color codes have advantages for fault-tolerant quantum computing, such as protected quantum gates with relatively low overhead and robustness against imperfect measurement of error syndromes. Here we investigate the storage threshold error rates for bit-flip and phase-flip noise in the 3D color code (3DCC) on the body-centered cubic lattice, assuming perfect syndrome measurements. In particular, by exploiting a connection between error correction and statistical mechanics, we estimate the threshold for 1D stringlike and 2D sheetlike logical operators to be p^((1))_(3DCC) ≃ 1.9% and p^((2))_(3DCC) ≃ 27.6%. We obtain these results by using parallel tempering Monte Carlo simulations to study the disorder-temperature phase diagrams of two new 3D statistical-mechanical models: the four- and six-body random coupling Ising models.https://authors.library.caltech.edu/records/t1xc2-1sh56Quantum Computing in the NISQ era and beyond
https://resolver.caltech.edu/CaltechAUTHORS:20180521-094354257
Authors: Preskill, John
Year: 2018
DOI: 10.22331/q-2018-08-06-79
Noisy Intermediate-Scale Quantum (NISQ) technology will be available in the near future. Quantum computers with 50-100 qubits may be able to perform tasks which surpass the capabilities of today's classical digital computers, but noise in quantum gates will limit the size of quantum circuits that can be executed reliably. NISQ devices will be useful tools for exploring many-body quantum physics, and may have other useful applications, but the 100-qubit quantum computer will not change the world right away - we should regard it as a significant step toward the more powerful quantum technologies of the future. Quantum technologists should continue to strive for more accurate quantum gates and, eventually, fully fault-tolerant quantum computing.https://authors.library.caltech.edu/records/ywjn3-p4r08Simulating quantum field theory with a quantum computer
https://resolver.caltech.edu/CaltechAUTHORS:20190122-113145453
Authors: Preskill, John
Year: 2018
DOI: 10.48550/arXiv.1811.10085
Forthcoming exascale digital computers will further advance our knowledge of quantum chromodynamics, but formidable challenges will remain. In particular, Euclidean Monte Carlo methods are not well suited for studying real-time evolution in hadronic collisions, or the properties of hadronic matter at nonzero temperature and chemical potential. Digital computers may never be able to achieve accurate simulations of such phenomena in QCD and other strongly-coupled field theories; quantum computers will do so eventually, though I'm not sure when. Progress toward quantum simulation of quantum field theory will require the collaborative efforts of quantumists and field theorists, and though the physics payoff may still be far away, it's worthwhile to get started now. Today's research can hasten the arrival of a new era in which quantum simulation fuels rapid progress in fundamental physics.https://authors.library.caltech.edu/records/3qmfh-ft455Error-corrected quantum sensing
https://resolver.caltech.edu/CaltechAUTHORS:20190606-092443914
Authors: Zhou, Sisi; Layden, David; Zhang, Mengzhen; Preskill, John; Cappellaro, Paola; Jiang, Liang
Year: 2019
DOI: 10.1117/12.2511587
Quantum metrology has many important applications in science and technology, ranging from frequency spectroscopy to gravitational wave detection. Quantum mechanics imposes a fundamental limit on measurement precision, called the Heisenberg limit, which can be achieved for noiseless quantum systems, but is not achievable in general for systems subject to noise. Here we study how measurement precision can be enhanced through quantum error correction, a general method for protecting a quantum system from the damaging effects of noise. We find a necessary and sufficient condition for achieving the Heisenberg limit using quantum probes subject to Markovian noise, assuming that noiseless ancilla systems are available, and that fast, accurate quantum processing can be performed. When the sufficient condition is satisfied, the quantum error-correcting code achieving the best possible precision can be found by solving a semidefinite program. We also show that noiseless ancilla are not needed when the signal Hamiltonian and the error operators commute. Finally we provide two explicit, archetypal examples of quantum sensors: qubits undergoing dephasing and a lossy bosonic mode.https://authors.library.caltech.edu/records/rcywm-b6x50Cellular-automaton decoders with provable thresholds for topological codes
https://resolver.caltech.edu/CaltechAUTHORS:20190201-155942835
Authors: Kubica, Aleksander; Preskill, John
Year: 2019
DOI: 10.1103/PhysRevLett.123.020501
We propose a new cellular automaton (CA), the sweep rule, which generalizes Toom's rule to any locally Euclidean lattice. We use the sweep rule to design a local decoder for the toric code in d ≥ 3 dimensions, the sweep decoder, and rigorously establish a lower bound on its performance. We also numerically estimate the sweep decoder threshold for the three-dimensional toric code on the cubic and body-centered cubic lattices for phenomenological phase-flip noise. Our results lead to new CA decoders with provable error-correction thresholds for other topological quantum codes including the color code.https://authors.library.caltech.edu/records/20907-sm834Distributed quantum sensing enhanced by continuous-variable error correction
https://resolver.caltech.edu/CaltechAUTHORS:20200430-121016107
Authors: Zhuang, Quntao; Preskill, John; Jiang, Liang
Year: 2020
DOI: 10.1088/1367-2630/ab7257
A distributed sensing protocol uses a network of local sensing nodes to estimate a global feature of the network, such as a weighted average of locally detectable parameters. In the noiseless case, continuous-variable (CV) multipartite entanglement shared by the nodes can improve the precision of parameter estimation relative to the precision attainable by a network without shared entanglement; for an entangled protocol, the root mean square estimation error scales like 1/M with the number M of sensing nodes, the so-called Heisenberg scaling, while for protocols without entanglement, the error scales like 1√M. However, in the presence of loss and other noise sources, although multipartite entanglement still has some advantages for sensing displacements and phases, the scaling of the precision with M is less favorable. In this paper, we show that using CV error correction codes can enhance the robustness of sensing protocols against imperfections and reinstate Heisenberg scaling up to moderate values of M. Furthermore, while previous distributed sensing protocols could measure only a single quadrature, we construct a protocol in which both quadratures can be sensed simultaneously. Our work demonstrates the value of CV error correction codes in realistic sensing scenarios.https://authors.library.caltech.edu/records/at1n2-2qb69The ghost in the radiation: robust encodings of the black hole interior
https://resolver.caltech.edu/CaltechAUTHORS:20200608-102711610
Authors: Kim, Isaac; Tang, Eugene; Preskill, John
Year: 2020
DOI: 10.1007/jhep06(2020)031
We reconsider the black hole firewall puzzle, emphasizing that quantum error- correction, computational complexity, and pseudorandomness are crucial concepts for understanding the black hole interior. We assume that the Hawking radiation emitted by an old black hole is pseudorandom, meaning that it cannot be distinguished from a perfectly thermal state by any efficient quantum computation acting on the radiation alone. We then infer the existence of a subspace of the radiation system which we interpret as an encoding of the black hole interior. This encoded interior is entangled with the late outgoing Hawking quanta emitted by the old black hole, and is inaccessible to computationally bounded observers who are outside the black hole. Specifically, efficient operations acting on the radiation, those with quantum computational complexity polynomial in the entropy of the remaining black hole, commute with a complete set of logical operators acting on the encoded interior, up to corrections which are exponentially small in the entropy. Thus, under our pseudorandomness assumption, the black hole interior is well protected from exterior observers as long as the remaining black hole is macroscopic. On the other hand, if the radiation is not pseudorandom, an exterior observer may be able to create a firewall by applying a polynomial-time quantum computation to the radiation.https://authors.library.caltech.edu/records/qgzdq-w8z17Robust Encoding of a Qubit in a Molecule
https://resolver.caltech.edu/CaltechAUTHORS:20200413-094120710
Authors: Albert, Victor V.; Covey, Jacob P.; Preskill, John
Year: 2020
DOI: 10.1103/PhysRevX.10.031050
We construct quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of rotational states of a rigid body. These codes, which protect against both drift in the body's orientation and small changes in its angular momentum, may be well suited for robust storage and coherent processing of quantum information using rotational states of a polyatomic molecule. Extensions of such codes to rigid bodies with a symmetry axis are compatible with rotational states of diatomic molecules as well as nuclear states of molecules and atoms. We also describe codes associated with general non-Abelian groups and develop orthogonality relations for coset spaces, laying the groundwork for quantum information processing with exotic configuration spaces.https://authors.library.caltech.edu/records/2k0wk-5th07Coherence in logical quantum channels
https://resolver.caltech.edu/CaltechAUTHORS:20200827-141821017
Authors: Iverson, Joseph K.; Preskill, John
Year: 2020
DOI: 10.1088/1367-2630/ab8e5c
We study the effectiveness of quantum error correction against coherent noise. Coherent errors (for example, unitary noise) can interfere constructively, so that in some cases the average infidelity of a quantum circuit subjected to coherent errors may increase quadratically with the circuit size; in contrast, when errors are incoherent (for example, depolarizing noise), the average infidelity increases at worst linearly with circuit size. We consider the performance of quantum stabilizer codes against a noise model in which a unitary rotation is applied to each qubit, where the axes and angles of rotation are nearly the same for all qubits. In particular, we show that for the toric code subject to such independent coherent noise, and for minimal-weight decoding, the logical channel after error correction becomes increasingly incoherent as the length of the code increases, provided the noise strength decays inversely with the code distance. A similar conclusion holds for weakly correlated coherent noise. Our methods can also be used for analyzing the performance of other codes and fault-tolerant protocols against coherent noise. However, our result does not show that the coherence of the logical channel is suppressed in the more physically relevant case where the noise strength is held constant as the code block grows, and we recount the difficulties that prevented us from extending the result to that case. Nevertheless our work supports the idea that fault-tolerant quantum computing schemes will work effectively against coherent noise, providing encouraging news for quantum hardware builders who worry about the damaging effects of control errors and coherent interactions with the environment.https://authors.library.caltech.edu/records/414gf-y2669Predicting Many Properties of a Quantum System from Very Few Measurements
https://resolver.caltech.edu/CaltechAUTHORS:20200427-084340790
Authors: Huang, Hsin-Yuan (Robert); Kueng, Richard; Preskill, John
Year: 2020
DOI: 10.1038/s41567-020-0932-7
Predicting the properties of complex, large-scale quantum systems is essential for developing quantum technologies. We present an efficient method for constructing an approximate classical description of a quantum state using very few measurements of the state. This description, called a 'classical shadow', can be used to predict many different properties; order log(M) measurements suffice to accurately predict M different functions of the state with high success probability. The number of measurements is independent of the system size and saturates information-theoretic lower bounds. Moreover, target properties to predict can be selected after the measurements are completed. We support our theoretical findings with extensive numerical experiments. We apply classical shadows to predict quantum fidelities, entanglement entropies, two-point correlation functions, expectation values of local observables and the energy variance of many-body local Hamiltonians. The numerical results highlight the advantages of classical shadows relative to previously known methods.https://authors.library.caltech.edu/records/wn33r-r8106Continuous Symmetries and Approximate Quantum Error Correction
https://resolver.caltech.edu/CaltechAUTHORS:20201027-095348367
Authors: Faist, Philippe; Nezami, Sepehr; Albert, Victor V.; Salton, Grant; Pastawski, Fernando; Hayden, Patrick; Preskill, John
Year: 2020
DOI: 10.1103/physrevx.10.041018
Quantum error correction and symmetry arise in many areas of physics, including many-body systems, metrology in the presence of noise, fault-tolerant computation, and holographic quantum gravity. Here, we study the compatibility of these two important principles. If a logical quantum system is encoded into n physical subsystems, we say that the code is covariant with respect to a symmetry group G if a G transformation on the logical system can be realized by performing transformations on the individual subsystems. For a G-covariant code with G a continuous group, we derive a lower bound on the error-correction infidelity following erasure of a subsystem. This bound approaches zero when the number of subsystems n or the dimension d of each subsystem is large. We exhibit codes achieving approximately the same scaling of infidelity with n or d as the lower bound. Leveraging tools from representation theory, we prove an approximate version of the Eastin-Knill theorem for quantum computation: If a code admits a universal set of transversal gates and corrects erasure with fixed accuracy, then, for each logical qubit, we need a number of physical qubits per subsystem that is inversely proportional to the error parameter. We construct codes covariant with respect to the full logical unitary group, achieving good accuracy for large d (using random codes) or n (using codes based on W states). We systematically construct codes covariant with respect to general groups, obtaining natural generalizations of qubit codes to, for instance, oscillators and rotors. In the context of the AdS/CFT correspondence, our approach provides insight into how time evolution in the bulk corresponds to time evolution on the boundary without violating the Eastin-Knill theorem, and our five-rotor code can be stacked to form a covariant holographic code.https://authors.library.caltech.edu/records/0jpd4-pzg87Mixed-State Entanglement from Local Randomized Measurements
https://resolver.caltech.edu/CaltechAUTHORS:20201111-102025217
Authors: Elben, Andreas; Kueng, Richard; Huang, Hsin-Yuan (Robert); van Bijnen, Rick; Kokail, Christian; Dalmonte, Marcello; Calabrese, Pasquale; Kraus, Barbara; Preskill, John; Zoller, Peter; Vermersch, Benoît
Year: 2020
DOI: 10.1103/physrevlett.125.200501
We propose a method for detecting bipartite entanglement in a many-body mixed state based on estimating moments of the partially transposed density matrix. The estimates are obtained by performing local random measurements on the state, followed by postprocessing using the classical shadows framework. Our method can be applied to any quantum system with single-qubit control. We provide a detailed analysis of the required number of experimental runs, and demonstrate the protocol using existing experimental data [Brydges et al., Science 364, 260 (2019)].https://authors.library.caltech.edu/records/fk5fg-amw77Quantum Computer Systems for Scientific Discovery
https://resolver.caltech.edu/CaltechAUTHORS:20210514-140222766
Authors: Alexeev, Yuri; Bacon, Dave; Brown, Kenneth R.; Calderbank, Robert; Carr, Lincoln D.; Chong, Frederic T.; DeMarco, Brian; Englund, Dirk; Farhi, Edward; Fefferman, Bill; Gorshkov, Alexey V.; Houck, Andrew; Kim, Jungsang; Kimmel, Shelby; Lange, Michael; Lloyd, Seth; Lukin, Mikhail D.; Maslov, Dmitri; Maunz, Peter; Monroe, Christopher; Preskill, John; Roetteler, Martin; Savage, Martin J.; Thompson, Jeff
Year: 2021
DOI: 10.1103/prxquantum.2.017001
The great promise of quantum computers comes with the dual challenges of building them and finding their useful applications. We argue that these two challenges should be considered together, by codesigning full-stack quantum computer systems along with their applications in order to hasten their development and potential for scientific discovery. In this context, we identify scientific and community needs, opportunities, a sampling of a few use case studies, and significant challenges for the development of quantum computers for science over the next 2–10 years. This document is written by a community of university, national laboratory, and industrial researchers in the field of Quantum Information Science and Technology, and is based on a summary from a U.S. National Science Foundation workshop on Quantum Computing held on October 21–22, 2019 in Alexandria, VA.https://authors.library.caltech.edu/records/7581k-z2914Opportunities for DOE National Laboratory-led QuantISED Experiments
https://resolver.caltech.edu/CaltechAUTHORS:20210512-104044668
Authors: Barry, Peter; Berggren, Karl; Balantekin, A. Baha; Bollinger, John; Bunker, Ray; Charaev, Ilya; Chiles, Jeff; Chou, Aaron; Demarteau, Marcel; Formaggio, Joe; Graham, Peter; Habib, Salman; Hume, David; Irwin, Kent; Lukin, Mikhail; Lykken, Joseph; Maruyama, Reina; Mueller, Holger; Nam, SaeWoo; Nomerotski, Andrei; Orrell, John; Plunkett, Robert; Pooser, Raphael; Preskill, John; Rajendran, Surjeet; Sushkov, Alex; Walsworth, Ronald
Year: 2021
DOI: 10.48550/arXiv.2102.10996
A subset of QuantISED Sensor PIs met virtually on May 26, 2020 to discuss a response to a charge by the DOE Office of High Energy Physics. In this document, we summarize the QuantISED sensor community discussion, including a consideration of HEP science enabled by quantum sensors, describing the distinction between Quantum 1.0 and Quantum 2.0, and discussing synergies/complementarity with the new DOE NQI centers and with research supported by other SC offices.
Quantum 2.0 advances in sensor technology offer many opportunities and new approaches for HEP experiments. The DOE HEP QuantISED program could support a portfolio of small experiments based on these advances. QuantISED experiments could use sensor technologies that exemplify Quantum 2.0 breakthroughs. They would strive to achieve new HEP science results, while possibly spinning off other domain science applications or serving as pathfinders for future HEP science targets. QuantISED experiments should be led by a DOE laboratory, to take advantage of laboratory technical resources, infrastructure, and expertise in the safe and efficient construction, operation, and review of experiments.
The QuantISED PIs emphasized that the quest for HEP science results under the QuantISED program is distinct from the ongoing DOE HEP programs on the energy, intensity, and cosmic frontiers. There is robust evidence for the existence of particles and phenomena beyond the Standard Model, including dark matter, dark energy, quantum gravity, and new physics responsible for neutrino masses, cosmic inflation, and the cosmic preference for matter over antimatter. Where is this physics and how do we find it? The QuantISED program can exploit new capabilities provided by quantum technology to probe these kinds of science questions in new ways and over a broader range of science parameters than can be achieved with conventional techniques.https://authors.library.caltech.edu/records/439gs-vdh32Models of quantum complexity growth
https://resolver.caltech.edu/CaltechAUTHORS:20210512-095238258
Authors: Brandão, Fernando G. S. L.; Chemissany, Wissam; Hunter-Jones, Nicholas; Kueng, Richard; Preskill, John
Year: 2021
DOI: 10.48550/arXiv.1912.04297
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.https://authors.library.caltech.edu/records/gcbp1-s4w76Information-Theoretic Bounds on Quantum Advantage in Machine Learning
https://resolver.caltech.edu/CaltechAUTHORS:20210512-104048123
Authors: Huang, Hsin-Yuan; Kueng, Richard; Preskill, John
Year: 2021
DOI: 10.1103/PhysRevLett.126.190505
We study the performance of classical and quantum machine learning (ML) models in predicting outcomes of physical experiments. The experiments depend on an input parameter x and involve execution of a (possibly unknown) quantum process E. Our figure of merit is the number of runs of E required to achieve a desired prediction performance. We consider classical ML models that perform a measurement and record the classical outcome after each run of E, and quantum ML models that can access E coherently to acquire quantum data; the classical or quantum data are then used to predict the outcomes of future experiments. We prove that for any input distribution D(x), a classical ML model can provide accurate predictions on average by accessing E a number of times comparable to the optimal quantum ML model. In contrast, for achieving an accurate prediction on all inputs, we prove that the exponential quantum advantage is possible. For example, to predict the expectations of all Pauli observables in an n-qubit system ρ, classical ML models require 2^(Ω(n)) copies of ρ, but we present a quantum ML model using only O(n) copies. Our results clarify where the quantum advantage is possible and highlight the potential for classical ML models to address challenging quantum problems in physics and chemistry.https://authors.library.caltech.edu/records/z9aq9-n0937The ghost in the radiation: robust encodings of the black hole interior (invited paper)
https://resolver.caltech.edu/CaltechAUTHORS:20220802-839157000
Authors: Kim, Isaac H.; Tang, Eugene; Preskill, John
Year: 2021
DOI: 10.1145/3406325.3465357
We reconsider the black hole firewall puzzle, emphasizing that quantum error-correction, computational complexity, and pseudorandomness are crucial concepts for understanding the black hole interior. We assume that the Hawking radiation emitted by an old black hole is pseudorandom, meaning that it cannot be distinguished from a perfectly thermal state by any efficient quantum computation acting on the radiation alone. We then infer the existence of a subspace of the radiation system which we interpret as an encoding of the black hole interior. This encoded interior is entangled with the late outgoing Hawking quanta emitted by the old black hole, and is inaccessible to computationally bounded observers who are outside the black hole. Specifically, efficient operations acting on the radiation, those with quantum computational complexity polynomial in the entropy of the remaining black hole, commute with a complete set of logical operators acting on the encoded interior, up to corrections which are exponentially small in the entropy. Thus, under our pseudorandomness assumption, the black hole interior is well protected from exterior observers as long as the remaining black hole is macroscopic. On the other hand, if the radiation is not pseudorandom, an exterior observer may be able to create a firewall by applying a polynomial-time quantum computation to the radiation.https://authors.library.caltech.edu/records/tsbcw-8jh66Quantum computing 40 years later
https://resolver.caltech.edu/CaltechAUTHORS:20220104-233143218
Authors: Preskill, John
Year: 2021
DOI: 10.48550/arXiv.2106.10522
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.https://authors.library.caltech.edu/records/d3hjb-yrc95Efficient Estimation of Pauli Observables by Derandomization
https://resolver.caltech.edu/CaltechAUTHORS:20210512-104041014
Authors: Huang, Hsin-Yuan; Kueng, Richard; Preskill, John
Year: 2021
DOI: 10.1103/PhysRevLett.127.030503
We consider the problem of jointly estimating expectation values of many Pauli observables, a crucial subroutine in variational quantum algorithms. Starting with randomized measurements, we propose an efficient derandomization procedure that iteratively replaces random single-qubit measurements by fixed Pauli measurements; the resulting deterministic measurement procedure is guaranteed to perform at least as well as the randomized one. In particular, for estimating any L low-weight Pauli observables, a deterministic measurement on only of order log(L) copies of a quantum state suffices. In some cases, for example, when some of the Pauli observables have high weight, the derandomized procedure is substantially better than the randomized one. Specifically, numerical experiments highlight the advantages of our derandomized protocol over various previous methods for estimating the ground-state energies of small molecules.https://authors.library.caltech.edu/records/np5h4-gda18Steven Weinberg (1933–2021)
https://resolver.caltech.edu/CaltechAUTHORS:20210914-191005909
Authors: Preskill, John
Year: 2021
DOI: 10.1126/science.abl8187
Steven Weinberg, widely regarded as the preeminent theoretical particle physicist of his era, passed away on 23 July at age 88. Steve took a pivotal step toward establishing what came to be known as the standard model of the fundamental particles and their interactions, for which he shared the 1979 Nobel Prize in Physics with Sheldon Glashow and Abdus Salam. That contribution was just one highlight in a career studded with major accomplishments. In later years, Steve authored a series of highly influential physics textbooks, as well as eloquent books and essays for the general public expounding on societal and scientific issues. He remained scientifically active up to his final days.https://authors.library.caltech.edu/records/he8qz-9xy32Spin chains, defects, and quantum wires for the quantum-double edge
https://resolver.caltech.edu/CaltechAUTHORS:20220113-182244311
Authors: Albert, Victor V.; Aasen, David; Xu, Wenqing; Ji, Wenjie; Alicea, Jason; Preskill, John
Year: 2021
DOI: 10.48550/arXiv.2111.12096
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.https://authors.library.caltech.edu/records/gnrr3-rdt94Provably efficient machine learning for quantum many-body problems
https://resolver.caltech.edu/CaltechAUTHORS:20220104-233146603
Authors: Huang, Hsin-Yuan; Kueng, Richard; Torlai, Giacomo; Albert, Victor V.; Preskill, John
Year: 2022
DOI: 10.48550/arXiv.2106.12627
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.https://authors.library.caltech.edu/records/2vwsn-wzz50Provably accurate simulation of gauge theories and bosonic systems
https://resolver.caltech.edu/CaltechAUTHORS:20220113-182219174
Authors: Tong, Yu; Albert, Victor V.; McClean, Jarrod R.; Preskill, John; Su, Yuan
Year: 2022
DOI: 10.48550/arXiv.2110.06942
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).https://authors.library.caltech.edu/records/z351a-qyb72Building a fault-tolerant quantum computer using concatenated cat codes
https://resolver.caltech.edu/CaltechAUTHORS:20201209-172305164
Authors: Chamberland, Christopher; Noh, Kyungjoo; Arrangoiz-Arriola, Patricio; Campbell, Earl T.; Hann, Connor T.; Iverson, Joseph K.; Putterman, Harald; Bohdanowicz, Thomas C.; Flammia, Steven T.; Keller, Andrew J.; Refael, Gil; Preskill, John; Jiang, Liang; Safavi-Naeini, Amir H.; Painter, Oskar; Brandão, Fernando G. S. L.
Year: 2022
DOI: 10.1103/PRXQuantum.3.010329
We present a comprehensive architectural analysis for a proposed fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware, we propose a system of acoustic resonators coupled to superconducting circuits with a two-dimensional layout. Using estimated physical parameters for the hardware, we perform a detailed error analysis of measurements and gates, including cnot and Toffoli gates. Having built a realistic noise model, we numerically simulate quantum error correction when the outer code is either a repetition code or a thin rectangular surface code. Our next step toward universal fault-tolerant quantum computation is a protocol for fault-tolerant Toffoli magic state preparation that significantly improves upon the fidelity of physical Toffoli gates at very low qubit cost. To achieve even lower overheads, we devise a new magic state distillation protocol for Toffoli states. Combining these results together, we obtain realistic full-resource estimates of the physical error rates and overheads needed to run useful fault-tolerant quantum algorithms. We find that with around 1000 superconducting circuit components, one could construct a fault-tolerant quantum computer that can run circuits, which are currently intractable for classical computers. Hardware with 18 000 superconducting circuit components, in turn, could simulate the Hubbard model in a regime beyond the reach of classical computing.https://authors.library.caltech.edu/records/m0b5h-7gr74Collisions of False-Vacuum Bubble Walls in a Quantum Spin Chain
https://resolver.caltech.edu/CaltechAUTHORS:20210512-104051553
Authors: Milsted, Ashley; Liu, Junyu; Preskill, John; Vidal, Guifre
Year: 2022
DOI: 10.1103/PRXQuantum.3.020316
We simulate, using nonperturbative methods, the real-time dynamics of small bubbles of "false vacuum" in a quantum spin chain near criticality, where the low-energy physics is described by a relativistic (1+1)-dimensional quantum field theory. We consider bubbles whose walls are kink and antikink quasiparticle excitations, so that wall collisions are kink-antikink scattering events. To construct these bubbles in the presence of strong correlations, we extend a recently proposed matrix product state (MPS) ansatz for quasiparticle wavepackets. We simulate dynamics within a window of about
1000
spins embedded in an infinite chain at energies of up to about
5
times the mass gap. By choosing the wavepacket width and the bubble size appropriately, we avoid strong lattice effects and observe relativistic kink-antikink collisions. We use the MPS quasiparticle ansatz to detect scattering outcomes. (i) In the Ising model, with transverse and longitudinal fields, we do not observe particle production despite nonintegrability (supporting recent observations of nonthermalizing states in this model). (ii) Switching on an additional interaction, we see production of confined and unconfined particle pairs. We characterize the amount of entanglement generated as a function of energy and time and conclude that our classical simulation methods will ultimately fail as these increase. We anticipate that kink-antikink scattering in 1+1 dimensions will be an instructive benchmark problem for future quantum computers and analog quantum simulators.https://authors.library.caltech.edu/records/008px-xj904Quantum advantage in learning from experiments
https://resolver.caltech.edu/CaltechAUTHORS:20220113-234532429
Authors: Huang, Hsin-Yuan; Broughton, Michael; Cotler, Jordan; Chen, Sitan; Li, Jerry; Mohseni, Masoud; Neven, Hartmut; Babbush, Ryan; Kueng, Richard; Preskill, John; McClean, Jarrod R.
Year: 2022
DOI: 10.1126/science.abn7293
Quantum technology promises to revolutionize how we learn about the physical world. An experiment that processes quantum data with a quantum computer could have substantial advantages over conventional experiments in which quantum states are measured and outcomes are processed with a classical computer. We proved that quantum machines could learn from exponentially fewer experiments than the number required by conventional experiments. This exponential advantage is shown for predicting properties of physical systems, performing quantum principal component analysis, and learning about physical dynamics. Furthermore, the quantum resources needed for achieving an exponential advantage are quite modest in some cases. Conducting experiments with 40 superconducting qubits and 1300 quantum gates, we demonstrated that a substantial quantum advantage is possible with today's quantum processors.https://authors.library.caltech.edu/records/wp6wx-eyx42Provably accurate simulation of gauge theories and bosonic systems
https://resolver.caltech.edu/CaltechAUTHORS:20221024-125854800.25
Authors: Tong, Yu; Albert, Victor V.; McClean, Jarrod R.; Preskill, John; Su, Yuan
Year: 2022
DOI: 10.22331/q-2022-09-22-816
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).https://authors.library.caltech.edu/records/bhehc-dps52Provably efficient machine learning for quantum many-body problems
https://resolver.caltech.edu/CaltechAUTHORS:20221207-387978400.2
Authors: Huang, Hsin-Yuan; Kueng, Richard; Torlai, Giacomo; Albert, Victor V.; Preskill, John
Year: 2022
DOI: 10.1126/science.abk3333
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 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 after learning from other Hamiltonians in the same quantum phase of matter. By contrast, under a widely accepted conjecture, 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. Extensive numerical experiments corroborate our theoretical results in a variety of scenarios, including Rydberg atom systems, two-dimensional random Heisenberg models, symmetry-protected topological phases, and topologically ordered phases.https://authors.library.caltech.edu/records/9mn4q-p0t46The randomized measurement toolbox
https://resolver.caltech.edu/CaltechAUTHORS:20230227-88449200.49
Authors: Elben, Andreas; Flammia, Steven T.; Huang, Hsin-Yuan; Kueng, Richard; Preskill, John; Vermersch, Benoît; Zoller, Peter
Year: 2023
DOI: 10.1038/s42254-022-00535-2
Programmable quantum simulators and quantum computers are opening unprecedented opportunities for exploring and exploiting the properties of highly entangled complex quantum systems. The complexity of large quantum systems is the source of computational power but also makes them difficult to control precisely or characterize accurately using measured classical data. We review protocols for probing the properties of complex many-qubit systems using measurement schemes that are practical using today's quantum platforms. In these protocols, a quantum state is repeatedly prepared and measured in a randomly chosen basis; then a classical computer processes the measurement outcomes to estimate the desired property. The randomization of the measurement procedure has distinct advantages. For example, a single data set can be used multiple times to pursue a variety of applications, and imperfections in the measurements are mapped to a simplified noise model that can more easily be mitigated. We discuss a range of cases that have already been realized in quantum devices, including Hamiltonian simulation tasks, probes of quantum chaos, measurements of non-local order parameters, and comparison of quantum states produced in distantly separated laboratories. By providing a workable method for translating a complex quantum state into a succinct classical representation that preserves a rich variety of relevant physical properties, the randomized measurement toolbox strengthens our ability to grasp and control the quantum world.https://authors.library.caltech.edu/records/30w4k-j9r86Complementarity and the unitarity of the black hole S-matrix
https://resolver.caltech.edu/CaltechAUTHORS:20230321-821105700.17
Authors: Kim, Isaac H.; Preskill, John
Year: 2023
DOI: 10.1007/jhep02(2023)233
Recently, Akers et al. proposed a non-isometric holographic map from the interior of a black hole to its exterior. Within this model, we study properties of the black hole S-matrix, which are in principle accessible to observers who stay outside the black hole. Specifically, we investigate a scenario in which an infalling agent interacts with radiation both outside and inside the black hole. Because the holographic map involves postselection, the unitarity of the S-matrix is not guaranteed in this scenario, but we find that unitarity is satisfied to very high precision if suitable conditions are met. If the internal black hole dynamics is described by a pseudorandom unitary transformation, and if the operations performed by the infaller have computational complexity scaling polynomially with the black hole entropy, then the S-matrix is unitary up to corrections that are superpolynomially small in the black hole entropy. Furthermore, while in principle quantum computation assisted by postselection can be very powerful, we find under similar assumptions that the S-matrix of an evaporating black hole has polynomial computational complexity.https://authors.library.caltech.edu/records/fv0tt-s9x63Evaluating the evidence for exponential quantum advantage in ground-state quantum chemistry
https://resolver.caltech.edu/CaltechAUTHORS:20230630-524987000.10
Authors: Lee, Seunghoon; Lee, Joonho; Zhai, Huanchen; Tong, Yu; Dalzell, Alexander M.; Kumar, Ashutosh; Helms, Phillip; Gray, Johnnie; Cui, Zhi-Hao; Liu, Wenyuan; Kastoryano, Michael; Babbush, Ryan; Preskill, John; Reichman, David R.; Campbell, Earl T.; Valeev, Edward F.; Lin, Lin; Chan, Garnet Kin-Lic
Year: 2023
DOI: 10.1038/s41467-023-37587-6
PMCID: PMC10082187
Due to intense interest in the potential applications of quantum computing, it is critical to understand the basis for potential exponential quantum advantage in quantum chemistry. Here we gather the evidence for this case in the most common task in quantum chemistry, namely, ground-state energy estimation, for generic chemical problems where heuristic quantum state preparation might be assumed to be efficient. The availability of exponential quantum advantage then centers on whether features of the physical problem that enable efficient heuristic quantum state preparation also enable efficient solution by classical heuristics. Through numerical studies of quantum state preparation and empirical complexity analysis (including the error scaling) of classical heuristics, in both ab initio and model Hamiltonian settings, we conclude that evidence for such an exponential advantage across chemical space has yet to be found. While quantum computers may still prove useful for ground-state quantum chemistry through polynomial speedups, it may be prudent to assume exponential speedups are not generically available for this problem.https://authors.library.caltech.edu/records/vvrrt-yf504Quantum Simulation for High-Energy Physics
https://resolver.caltech.edu/CaltechAUTHORS:20230605-335313000.44
Authors: Bauer, Christian W.; Davoudi, Zohreh; Balantekin, A. Baha; Bhattacharya, Tanmoy; Carena, Marcela; de Jong, Wibe A.; Draper, Patrick; El-Khadra, Aida; Gemelke, Nate; Hanada, Masanori; Kharzeev, Dmitri; Lamm, Henry; Li, Ying-Ying; Liu, Junyu; Lukin, Mikhail D.; Meurice, Yannick; Monroe, Christopher; Nachman, Benjamin; Pagano, Guido; Preskill, John; Rinaldi, Enrico; Roggero, Alessandro; Santiago, David I.; Savage, Martin J.; Siddiqi, Irfan; Siopsis, George; Van Zanten, David; Wiebe, Nathan; Yamauchi, Yukari; Yeter-Aydeniz, Kübra; Zorzetti, Silvia
Year: 2023
DOI: 10.1103/prxquantum.4.027001
It is for the first time that quantum simulation for high-energy physics (HEP) is studied in the U.S. decadal particle-physics community planning, and in fact until recently, this was not considered a mainstream topic in the community. This fact speaks of a remarkable rate of growth of this subfield over the past few years, stimulated by the impressive advancements in quantum information sciences (QIS) and associated technologies over the past decade, and the significant investment in this area by the government and private sectors in the U.S. and other countries. High-energy physicists have quickly identified problems of importance to our understanding of nature at the most fundamental level, from tiniest distances to cosmological extents, that are intractable with classical computers but may benefit from quantum advantage. They have initiated, and continue to carry out, a vigorous program in theory, algorithm, and hardware co-design for simulations of relevance to the HEP mission. This Roadmap is an attempt to bring this exciting and yet challenging area of research to the spotlight, and to elaborate on what the promises, requirements, challenges, and potential solutions are over the next decade and beyond.https://authors.library.caltech.edu/records/7m9ph-kpm77Emergent quantum mechanics at the boundary of a local classical lattice model
https://authors.library.caltech.edu/records/eekt9-88e13
Authors: Slagle, Kevin; Preskill, John
Year: 2023
DOI: 10.1103/physreva.108.012217
<p>We formulate a model in which quantum mechanics emerges from classical mechanics. Given a local Hamiltonian <i>H</i> acting on <i>n</i> qubits, we define a local classical model with an additional spatial dimension whose boundary dynamics is approximately—but to arbitrary precision—described by Schrödinger's equation and <i>H</i>. The bulk consists of a lattice of classical bits that propagate towards the boundary through a circuit of stochastic matrices. The bits reaching the boundary are governed by a probability distribution whose deviation from the uniform distribution can be interpreted as the quantum-mechanical wave function. Bell nonlocality is achieved because information can move through the bulk much faster than the boundary speed of light. We analytically estimate how much the model deviates from quantum mechanics, and we validate these estimates using computer simulations.</p>https://authors.library.caltech.edu/records/eekt9-88e13