Quantum sampling algorithms, phase transitions, and computational complexity

Wild, Dominik S.; Sels, Dries; Pichler, Hannes; Zanoci, Cristian; Lukin, Mikhail D.

doi:10.1103/PhysRevA.104.032602

Title: Quantum sampling algorithms, phase transitions, and computational complexity

Journal Article · 02 September 2021 · Physical Review A

DOI: https://doi.org/10.1103/PhysRevA.104.032602 · OSTI ID:1818545

; Sels, Dries; Pichler, Hannes; Zanoci, Cristian; Lukin, Mikhail D.

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Sponsoring Organization:: USDOE

OSTI ID:: 1818545

Journal Information:: Physical Review A, Journal Name: Physical Review A Journal Issue: 3 Vol. 104; ISSN PLRAAN; ISSN 2469-9926

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (58)

Mixing in time and space for lattice spin systems: A combinatorial view Dyer, Martin; Sinclair, Alistair; Vigoda, Eric Random Structures and Algorithms, Vol. 24, Issue 4 https://doi.org/10.1002/rsa.20004	journal	January 2004
Critical Ising on the Square Lattice Mixes in Polynomial Time Lubetzky, Eyal; Sly, Allan Communications in Mathematical Physics, Vol. 313, Issue 3 https://doi.org/10.1007/s00220-012-1460-9	journal	April 2012
Quantum Gibbs Samplers: The Commuting Case Kastoryano, Michael J.; Brandão, Fernando G. S. L. Communications in Mathematical Physics, Vol. 344, Issue 3 https://doi.org/10.1007/s00220-016-2641-8	journal	May 2016
Finite Correlation Length Implies Efficient Preparation of Quantum Thermal States Brandão, Fernando G. S. L.; Kastoryano, Michael J. Communications in Mathematical Physics, Vol. 365, Issue 1 https://doi.org/10.1007/s00220-018-3150-8	journal	May 2018
Topological order in 1D Cluster state protected by symmetry Son, W.; Amico, L.; Vedral, V. Quantum Information Processing, Vol. 11, Issue 6 https://doi.org/10.1007/s11128-011-0346-7	journal	December 2011
Spin relaxation of the Ising chain Felderhof, B. U. Reports on Mathematical Physics, Vol. 1, Issue 3 https://doi.org/10.1016/S0034-4877(71)80006-X	journal	January 1971
From quantum mechanics to classical statistical physics: Generalized Rokhsar–Kivelson Hamiltonians and the “Stochastic Matrix Form” decomposition Castelnovo, Claudio; Chamon, Claudio; Mudry, Christopher Annals of Physics, Vol. 318, Issue 2 https://doi.org/10.1016/j.aop.2005.01.006	journal	August 2005
Schrieffer–Wolff transformation for quantum many-body systems Bravyi, Sergey; DiVincenzo, David P.; Loss, Daniel Annals of Physics, Vol. 326, Issue 10 https://doi.org/10.1016/j.aop.2011.06.004	journal	October 2011
Clique-detection models in computational biochemistry and genomics Butenko, S.; Wilhelm, W. E. European Journal of Operational Research, Vol. 173, Issue 1 https://doi.org/10.1016/j.ejor.2005.05.026	journal	August 2006
Community detection in graphs Fortunato, Santo Physics Reports, Vol. 486, Issue 3-5 https://doi.org/10.1016/j.physrep.2009.11.002	journal	February 2010
Quantum Computation and Quantum Information Nielsen, Michael A.; Chuang, Isaac L. Cambridge University Press https://doi.org/10.1017/CBO9780511976667	book	January 2011
Quantum Metropolis sampling Temme, K.; Osborne, T. J.; Vollbrecht, K. G. Nature, Vol. 471, Issue 7336 https://doi.org/10.1038/nature09770	journal	March 2011
Tunable two-dimensional arrays of single Rydberg atoms for realizing quantum Ising models Labuhn, Henning; Barredo, Daniel; Ravets, Sylvain Nature, Vol. 534, Issue 7609 https://doi.org/10.1038/nature18274	journal	June 2016
Probing many-body dynamics on a 51-atom quantum simulator Bernien, Hannes; Schwartz, Sylvain; Keesling, Alexander Nature, Vol. 551, Issue 7682 https://doi.org/10.1038/nature24622	journal	November 2017
Weak ergodicity breaking from quantum many-body scars Turner, C. J.; Michailidis, A. A.; Abanin, D. A. Nature Physics, Vol. 14, Issue 7 https://doi.org/10.1038/s41567-018-0137-5	journal	May 2018
On the complexity and verification of quantum random circuit sampling Bouland, Adam; Fefferman, Bill; Nirkhe, Chinmay Nature Physics, Vol. 15, Issue 2 https://doi.org/10.1038/s41567-018-0318-2	journal	October 2018
Quantum supremacy using a programmable superconducting processor Arute, Frank; Arya, Kunal; Babbush, Ryan Nature, Vol. 574, Issue 7779 https://doi.org/10.1038/s41586-019-1666-5	journal	October 2019
Quantum phases of matter on a 256-atom programmable quantum simulator Ebadi, Sepehr; Wang, Tout T.; Levine, Harry Nature, Vol. 595, Issue 7866 https://doi.org/10.1038/s41586-021-03582-4	journal	July 2021
Quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms Scholl, Pascal; Schuler, Michael; Williams, Hannah J. Nature, Vol. 595, Issue 7866 https://doi.org/10.1038/s41586-021-03585-1	journal	July 2021
Hard‐Sphere Lattice Gases. I. Plane‐Square Lattice Gaunt, David S.; Fisher, Michael E. The Journal of Chemical Physics, Vol. 43, Issue 8 https://doi.org/10.1063/1.1697217	journal	October 1965
Time‐Dependent Statistics of the Ising Model Glauber, Roy J. Journal of Mathematical Physics, Vol. 4, Issue 2 https://doi.org/10.1063/1.1703954	journal	February 1963
A quantum-quantum Metropolis algorithm Yung, M. -H.; Aspuru-Guzik, A. Proceedings of the National Academy of Sciences, Vol. 109, Issue 3 https://doi.org/10.1073/pnas.1111758109	journal	January 2012
From classical to quantum dynamics at Rokhsar–Kivelson points Henley, C. L. Journal of Physics: Condensed Matter, Vol. 16, Issue 11 https://doi.org/10.1088/0953-8984/16/11/045	journal	March 2004
Monte Carlo sampling methods using Markov chains and their applications Hastings, W. K. Biometrika, Vol. 57, Issue 1 https://doi.org/10.1093/biomet/57.1.97	journal	April 1970
Product spectrum ansatz and the simplicity of thermal states Martyn, John; Swingle, Brian Physical Review A, Vol. 100, Issue 3 https://doi.org/10.1103/PhysRevA.100.032107	journal	September 2019
Grover’s quantum searching algorithm is optimal Zalka, Christof Physical Review A, Vol. 60, Issue 4 https://doi.org/10.1103/PhysRevA.60.2746	journal	October 1999
Problem of equilibration and the computation of correlation functions on a quantum computer Terhal, Barbara M.; DiVincenzo, David P. Physical Review A, Vol. 61, Issue 2 https://doi.org/10.1103/PhysRevA.61.022301	journal	January 2000
Quantum search by local adiabatic evolution Roland, Jérémie; Cerf, Nicolas J. Physical Review A, Vol. 65, Issue 4 https://doi.org/10.1103/PhysRevA.65.042308	journal	March 2002
Speedup via quantum sampling Wocjan, Pawel; Abeyesinghe, Anura Physical Review A, Vol. 78, Issue 4 https://doi.org/10.1103/PhysRevA.78.042336	journal	October 2008
Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields Skrøvseth, Stein Olav; Bartlett, Stephen D. Physical Review A, Vol. 80, Issue 2 https://doi.org/10.1103/PhysRevA.80.022316	journal	August 2009
Simulation of classical thermal states on a quantum computer: A transfer-matrix approach Yung, Man-Hong; Nagaj, Daniel; Whitfield, James D. Physical Review A, Vol. 82, Issue 6 https://doi.org/10.1103/PhysRevA.82.060302	journal	December 2010
Pseudospin formulation of kinetic Ising models Siggia, Eric D. Physical Review B, Vol. 16, Issue 5 https://doi.org/10.1103/PhysRevB.16.2319	journal	September 1977
Competing density-wave orders in a one-dimensional hard-boson model Fendley, Paul; Sengupta, K.; Sachdev, Subir Physical Review B, Vol. 69, Issue 7 https://doi.org/10.1103/PhysRevB.69.075106	journal	February 2004
Majorana zero modes in a quantum Ising chain with longer-ranged interactions Niu, Yuezhen; Chung, Suk Bum; Hsu, Chen-Hsuan Physical Review B, Vol. 85, Issue 3 https://doi.org/10.1103/PhysRevB.85.035110	journal	January 2012
Renormalization group circuits for gapless states Swingle, Brian; McGreevy, John; Xu, Shenglong Physical Review B, Vol. 93, Issue 20 https://doi.org/10.1103/PhysRevB.93.205159	journal	May 2016
One-dimensional symmetry protected topological phases and their transitions Verresen, Ruben; Moessner, Roderich; Pollmann, Frank Physical Review B, Vol. 96, Issue 16 https://doi.org/10.1103/PhysRevB.96.165124	journal	October 2017
Simulating Ising spin glasses on a quantum computer Lidar, Daniel A.; Biham, Ofer Physical Review E, Vol. 56, Issue 3 https://doi.org/10.1103/PhysRevE.56.3661	journal	September 1997
Minimal vertex covers on finite-connectivity random graphs: A hard-sphere lattice-gas picture Weigt, Martin; Hartmann, Alexander K. Physical Review E, Vol. 63, Issue 5 https://doi.org/10.1103/PhysRevE.63.056127	journal	April 2001
Quantum Simulations of Classical Annealing Processes Somma, R. D.; Boixo, S.; Barnum, H. Physical Review Letters, Vol. 101, Issue 13 https://doi.org/10.1103/PhysRevLett.101.130504	journal	September 2008
Quantum Adiabatic Brachistochrone Rezakhani, A. T.; Kuo, W. -J.; Hamma, A. Physical Review Letters, Vol. 103, Issue 8 https://doi.org/10.1103/PhysRevLett.103.080502	journal	August 2009
Preparing Thermal States of Quantum Systems by Dimension Reduction Bilgin, Ersen; Boixo, Sergio Physical Review Letters, Vol. 105, Issue 17 https://doi.org/10.1103/PhysRevLett.105.170405	journal	October 2010
Thermalization in Nature and on a Quantum Computer Riera, Arnau; Gogolin, Christian; Eisert, Jens Physical Review Letters, Vol. 108, Issue 8 https://doi.org/10.1103/PhysRevLett.108.080402	journal	February 2012
Liquid Ground State, Gap, and Excited States of a Strongly Correlated Spin Chain Lesanovsky, Igor Physical Review Letters, Vol. 108, Issue 10 https://doi.org/10.1103/PhysRevLett.108.105301	journal	March 2012
Rapid Adiabatic Preparation of Injective Projected Entangled Pair States and Gibbs States Ge, Yimin; Molnár, András; Cirac, J. Ignacio Physical Review Letters, Vol. 116, Issue 8 https://doi.org/10.1103/PhysRevLett.116.080503	journal	February 2016
Variational Thermal Quantum Simulation via Thermofield Double States Wu, Jingxiang; Hsieh, Timothy H. Physical Review Letters, Vol. 123, Issue 22 https://doi.org/10.1103/PhysRevLett.123.220502	journal	November 2019
Quantum Sampling Algorithms for Near-Term Devices Wild, Dominik S.; Sels, Dries; Pichler, Hannes Physical Review Letters, Vol. 127, Issue 10 https://doi.org/10.1103/PhysRevLett.127.100504	journal	September 2021
Nonuniversal critical dynamics in Monte Carlo simulations Swendsen, Robert H.; Wang, Jian-Sheng Physical Review Letters, Vol. 58, Issue 2 https://doi.org/10.1103/PhysRevLett.58.86	journal	January 1987
Superconductivity and the Quantum Hard-Core Dimer Gas Rokhsar, Daniel S.; Kivelson, Steven A. Physical Review Letters, Vol. 61, Issue 20 https://doi.org/10.1103/PhysRevLett.61.2376	journal	November 1988
Criticality, the Area Law, and the Computational Power of Projected Entangled Pair States Verstraete, F.; Wolf, M. M.; Perez-Garcia, D. Physical Review Letters, Vol. 96, Issue 22 https://doi.org/10.1103/PhysRevLett.96.220601	journal	June 2006
Quantum Approach to Classical Statistical Mechanics Somma, R. D.; Batista, C. D.; Ortiz, G. Physical Review Letters, Vol. 99, Issue 3 https://doi.org/10.1103/PhysRevLett.99.030603	journal	July 2007
Quantum Spin-Ice and Dimer Models with Rydberg Atoms Glaetzle, A. W.; Dalmonte, M.; Nath, R. Physical Review X, Vol. 4, Issue 4 https://doi.org/10.1103/PhysRevX.4.041037	journal	November 2014
Some Inequalities for Reversible Markov Chains Aldous, David J. Journal of the London Mathematical Society, Vol. s2-25, Issue 3 https://doi.org/10.1112/jlms/s2-25.3.564	journal	June 1982
Optimization by Simulated Annealing Kirkpatrick, S.; Gelatt, C. D.; Vecchi, M. P. Science, Vol. 220, Issue 4598 https://doi.org/10.1126/science.220.4598.671	journal	May 1983
Universal Quantum Simulators Lloyd, S. Science, Vol. 273, Issue 5278 https://doi.org/10.1126/science.273.5278.1073	journal	August 1996
Quantum computational advantage using photons Zhong, Han-Sen; Wang, Hui; Deng, Yu-Hao Science, Vol. 370, Issue 6523 https://doi.org/10.1126/science.abe8770	journal	December 2020
Complexity of Stoquastic Frustration-Free Hamiltonians Bravyi, Sergey; Terhal, Barbara SIAM Journal on Computing, Vol. 39, Issue 4 https://doi.org/10.1137/08072689X	journal	January 2010
Fast quantum methods for optimization Boixo, S.; Ortiz, G.; Somma, R. The European Physical Journal Special Topics, Vol. 224, Issue 1 https://doi.org/10.1140/epjst/e2015-02341-5	journal	February 2015
PEPS as unique ground states of local Hamiltonians Perez-Garcia, D.; Verstraete, F.; Cirac, J. I. Quantum Information and Computation, Vol. 8, Issue 6&7 https://doi.org/10.26421/QIC8.6-7-6	journal	July 2008

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