TY - JOUR T1 - Provably accurate simulation of gauge theories and bosonic systems JF - Quantum Y1 - 2022 A1 - Yu Tong A1 - Victor V. Albert A1 - Jarrod R. McClean A1 - John Preskill A1 - Yuan Su AB -
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).
VL - 6 U4 - 816 UR - https://arxiv.org/abs/2110.06942 U5 - https://doi.org/10.22331%2Fq-2022-09-22-816 ER - TY - JOUR T1 - Provably efficient machine learning for quantum many-body problems JF - Science Y1 - 2022 A1 - Hsin-Yuan Huang A1 - Richard Kueng A1 - Giacomo Torlai A1 - Victor V. Albert A1 - John Preskill AB -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.
VL - 377 UR - https://arxiv.org/abs/2106.12627 U5 - 10.1126/science.abk3333 ER - TY - JOUR T1 - Spin chains, defects, and quantum wires for the quantum-double edge Y1 - 2021 A1 - Victor V. Albert A1 - David Aasen A1 - Wenqing Xu A1 - Wenjie Ji A1 - Jason Alicea A1 - John Preskill AB -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.
UR - https://arxiv.org/abs/2111.12096 ER - TY - JOUR T1 - Continuous symmetries and approximate quantum error correction JF - Phys. Rev. X Y1 - 2020 A1 - Philippe Faist A1 - Sepehr Nezami A1 - Victor V. Albert A1 - Grant Salton A1 - Fernando Pastawski A1 - Patrick Hayden A1 - John Preskill AB -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: 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.
VL - 10 UR - https://arxiv.org/abs/1902.07714 CP - 041018 U5 - https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.041018 ER - TY - JOUR T1 - Robust Encoding of a Qubit in a Molecule JF - Phys. Rev. X Y1 - 2020 A1 - Victor V. Albert A1 - Jacob P. Covey A1 - John Preskill AB -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.
VL - 10 UR - https://arxiv.org/abs/1911.00099 CP - 031050 U5 - https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.031050 ER - TY - JOUR T1 - Quantum Computer Systems for Scientific Discovery Y1 - 2019 A1 - Yuri Alexeev A1 - Dave Bacon A1 - Kenneth R. Brown A1 - Robert Calderbank A1 - Lincoln D. Carr A1 - Frederic T. Chong A1 - Brian DeMarco A1 - Dirk Englund A1 - Edward Farhi A1 - Bill Fefferman A1 - Alexey V. Gorshkov A1 - Andrew Houck A1 - Jungsang Kim A1 - Shelby Kimmel A1 - Michael Lange A1 - Seth Lloyd A1 - Mikhail D. Lukin A1 - Dmitri Maslov A1 - Peter Maunz A1 - Christopher Monroe A1 - John Preskill A1 - Martin Roetteler A1 - Martin Savage A1 - Jeff Thompson A1 - Umesh Vazirani AB -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 co-designing 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, 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.
UR - https://arxiv.org/abs/1912.07577 ER - TY - JOUR T1 - BQP-completeness of Scattering in Scalar Quantum Field Theory JF - Quantum Y1 - 2018 A1 - Stephen P. Jordan A1 - Hari Krovi A1 - Keith S. M. Lee A1 - John Preskill AB -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.
VL - 2 U4 - 44 UR - https://quantum-journal.org/papers/q-2018-01-08-44/ U5 - 10.22331/q-2018-01-08-44 ER - TY - JOUR T1 - Quantum Algorithms for Fermionic Quantum Field Theories Y1 - 2014 A1 - Stephen P. Jordan A1 - Keith S. M. Lee A1 - John Preskill AB - 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. UR - http://arxiv.org/abs/1404.7115v1 ER - TY - JOUR T1 - Quantum Computation of Scattering in Scalar Quantum Field Theories JF - Quantum Information and Computation Y1 - 2014 A1 - Stephen P. Jordan A1 - Keith S. M. Lee A1 - John Preskill AB - 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. VL - 14 U4 - 1014-1080 UR - http://arxiv.org/abs/1112.4833v1 CP - 11-12 J1 - Quantum Information and Computation 14 ER - TY - JOUR T1 - Quantum Algorithms for Quantum Field Theories JF - Science Y1 - 2012 A1 - Stephen P. Jordan A1 - Keith S. M. Lee A1 - John Preskill AB - 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 (phi-fourth 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. VL - 336 U4 - 1130 - 1133 UR - http://arxiv.org/abs/1111.3633v2 CP - 6085 J1 - Science U5 - 10.1126/science.1217069 ER - TY - JOUR T1 - Robustness of adiabatic quantum computation JF - Physical Review A Y1 - 2001 A1 - Andrew M. Childs A1 - Edward Farhi A1 - John Preskill AB - 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. VL - 65 UR - http://arxiv.org/abs/quant-ph/0108048v1 CP - 1 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.65.012322 ER - TY - JOUR T1 - Quantum information and precision measurement JF - Journal of Modern Optics Y1 - 2000 A1 - Andrew M. Childs A1 - John Preskill A1 - Joseph Renes AB - We describe some applications of quantum information theory to the analysis of quantum limits on measurement sensitivity. A measurement of a weak force acting on a quantum system is a determination of a classical parameter appearing in the master equation that governs the evolution of the system; limitations on measurement accuracy arise because it is not possible to distinguish perfectly among the different possible values of this parameter. Tools developed in the study of quantum information and computation can be exploited to improve the precision of physics experiments; examples include superdense coding, fast database search, and the quantum Fourier transform. VL - 47 U4 - 155 - 176 UR - http://arxiv.org/abs/quant-ph/9904021v2 CP - 2-3 J1 - Journal of Modern Optics U5 - 10.1080/09500340008244034 ER -