Tunneling and Speedup in Quantum Optimization for Permutation-Symmetric Problems

Muthukrishnan, Siddharth; Albash, Tameem; Lidar, Daniel A.

doi:10.1103/PhysRevX.6.031010

Title: Tunneling and Speedup in Quantum Optimization for Permutation-Symmetric Problems

Journal Article · 21 July 2016 · Physical Review. X

DOI: https://doi.org/10.1103/PhysRevX.6.031010 · OSTI ID:1267545

Muthukrishnan, Siddharth; Albash, Tameem; Lidar, Daniel A.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); UT-Batelle, LLC, Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1267545

Journal Information:: Physical Review. X, Journal Name: Physical Review. X Journal Issue: 3 Vol. 6; ISSN PRXHAE; ISSN 2160-3308

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (40)

Quantum Ising Phases and Transitions in Transverse Ising Models Suzuki, Sei; Inoue, Jun-ichi; Chakrabarti, Bikas K. Lecture Notes in Physics https://doi.org/10.1007/978-3-642-33039-1	book	January 2013
Quantum annealing: A new method for minimizing multidimensional functions Finnila, A. B.; Gomez, M. A.; Sebenik, C. Chemical Physics Letters, Vol. 219, Issue 5-6 https://doi.org/10.1016/0009-2614(94)00117-0	journal	March 1994
A family of embedded Runge-Kutta formulae Dormand, J. R.; Prince, P. J. Journal of Computational and Applied Mathematics, Vol. 6, Issue 1 https://doi.org/10.1016/0771-050X(80)90013-3	journal	March 1980
Macroscopic quantum tunneling and quantum–classical phase transitions of the escape rate in large spin systems Owerre, S. A.; Paranjape, M. B. Physics Reports, Vol. 546 https://doi.org/10.1016/j.physrep.2014.09.001	journal	January 2015
Matrix Analysis Horn, Roger A.; Johnson, Charles R. https://doi.org/10.1017/CBO9781139020411	book	April 2013
Bounds for the adiabatic approximation with applications to quantum computation Jansen, Sabine; Ruskai, Mary-Beth; Seiler, Ruedi Journal of Mathematical Physics, Vol. 48, Issue 10 https://doi.org/10.1063/1.2798382	journal	October 2007
Adiabatic approximation with exponential accuracy for many-body systems and quantum computation Lidar, Daniel A.; Rezakhani, Ali T.; Hamma, Alioscia Journal of Mathematical Physics, Vol. 50, Issue 10 https://doi.org/10.1063/1.3236685	journal	October 2009
Strict detailed balance is unnecessary in Monte Carlo simulation Manousiouthakis, Vasilios I.; Deem, Michael W. The Journal of Chemical Physics, Vol. 110, Issue 6 https://doi.org/10.1063/1.477973	journal	February 1999
The fundamental gap for a class of Schrödinger operators on path and hypercube graphs Jarret, Michael; Jordan, Stephen P. Journal of Mathematical Physics, Vol. 55, Issue 5 https://doi.org/10.1063/1.4878120	journal	May 2014
Continuous-time quantum algorithms for unstructured problems Hen, Itay Journal of Physics A: Mathematical and Theoretical, Vol. 47, Issue 4 https://doi.org/10.1088/1751-8113/47/4/045305	journal	January 2014
Statistical Physics of Spin Glasses and Information Processing Nishimori, Hidetoshi https://doi.org/10.1093/acprof:oso/9780198509417.001.0001	book	July 2001
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
Landau-Zener model: Effects of finite coupling duration Vitanov, N. V.; Garraway, B. M. Physical Review A, Vol. 53, Issue 6 https://doi.org/10.1103/PhysRevA.53.4288	journal	June 1996
Erratum: Landau-Zener model: Effects of finite coupling duration Vitanov, N. V.; Garraway, B. M. Physical Review A, Vol. 54, Issue 6 https://doi.org/10.1103/PhysRevA.54.5458.2	journal	December 1996
Atomic Coherent States in Quantum Optics Arecchi, F. T.; Courtens, Eric; Gilmore, Robert Physical Review A, Vol. 6, Issue 6 https://doi.org/10.1103/PhysRevA.6.2211	journal	December 1972
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
Necessary condition for the quantum adiabatic approximation Boixo, S.; Somma, R. D. Physical Review A, Vol. 81, Issue 3 https://doi.org/10.1103/PhysRevA.81.032308	journal	March 2010
Accuracy versus run time in an adiabatic quantum search Rezakhani, A. T.; Pimachev, A. K.; Lidar, D. A. Physical Review A, Vol. 82, Issue 5 https://doi.org/10.1103/PhysRevA.82.052305	journal	November 2010
Probing for quantum speedup in spin-glass problems with planted solutions Hen, Itay; Job, Joshua; Albash, Tameem Physical Review A, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevA.92.042325	journal	October 2015
Quantum Monte Carlo simulations of tunneling in quantum adiabatic optimization Brady, Lucas T.; van Dam, Wim Physical Review A, Vol. 93, Issue 3 https://doi.org/10.1103/PhysRevA.93.032304	journal	March 2016
Sherrington-Kirkpatrick model in a transverse field: Absence of replica symmetry breaking due to quantum fluctuations Ray, P.; Chakrabarti, B. K.; Chakrabarti, Arunava Physical Review B, Vol. 39, Issue 16 https://doi.org/10.1103/PhysRevB.39.11828	journal	June 1989
Quantum annealing by the path-integral Monte Carlo method: The two-dimensional random Ising model Martoňák, Roman; Santoro, Giuseppe E.; Tosatti, Erio Physical Review B, Vol. 66, Issue 9 https://doi.org/10.1103/PhysRevB.66.094203	journal	September 2002
Path integrals and stationary-phase approximations Klauder, John R. Physical Review D, Vol. 19, Issue 8 https://doi.org/10.1103/PhysRevD.19.2349	journal	April 1979
Quantum annealing in the transverse Ising model Kadowaki, Tadashi; Nishimori, Hidetoshi Physical Review E, Vol. 58, Issue 5 https://doi.org/10.1103/PhysRevE.58.5355	journal	November 1998
Consistency of the Adiabatic Theorem Amin, M. H. S. Physical Review Letters, Vol. 102, Issue 22 https://doi.org/10.1103/PhysRevLett.102.220401	journal	June 2009
Quantum Speedup by Quantum Annealing Somma, Rolando D.; Nagaj, Daniel; Kieferová, Mária Physical Review Letters, Vol. 109, Issue 5 https://doi.org/10.1103/PhysRevLett.109.050501	journal	July 2012
Heavy Tails in the Distribution of Time to Solution for Classical and Quantum Annealing Steiger, Damian S.; Rønnow, Troels F.; Troyer, Matthias Physical Review Letters, Vol. 115, Issue 23 https://doi.org/10.1103/PhysRevLett.115.230501	journal	December 2015
Collective Monte Carlo Updating for Spin Systems Wolff, Ulli Physical Review Letters, Vol. 62, Issue 4 https://doi.org/10.1103/PhysRevLett.62.361	journal	January 1989
Colloquium : Quantum annealing and analog quantum computation Das, Arnab; Chakrabarti, Bikas K. Reviews of Modern Physics, Vol. 80, Issue 3 https://doi.org/10.1103/RevModPhys.80.1061	journal	September 2008
A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem Farhi, E.; Goldstone, J.; Gutmann, S. Science, Vol. 292, Issue 5516 https://doi.org/10.1126/science.1057726	journal	April 2001
Theory of Quantum Annealing of an Ising Spin Glass Santoro, G. E. Science, Vol. 295, Issue 5564 https://doi.org/10.1126/science.1068774	journal	March 2002
Defining and detecting quantum speedup Ronnow, T. F.; Wang, Z.; Job, J. Science, Vol. 345, Issue 6195 https://doi.org/10.1126/science.1252319	journal	June 2014
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
Quantum versus classical annealing of Ising spin glasses Heim, B.; Ronnow, T. F.; Isakov, S. V. Science, Vol. 348, Issue 6231 https://doi.org/10.1126/science.aaa4170	journal	March 2015
Quantum annealing: The fastest route to quantum computation? Suzuki, Sei; Das, Arnab The European Physical Journal Special Topics, Vol. 224, Issue 1 https://doi.org/10.1140/epjst/e2015-02336-2	journal	February 2015
Reexamining classical and quantum models for the D-Wave One processor: The role of excited states and ground state degeneracy Albash, T.; Rønnow, T. F.; Troyer, M. The European Physical Journal Special Topics, Vol. 224, Issue 1 https://doi.org/10.1140/epjst/e2015-02346-0	journal	February 2015
A variable order Runge-Kutta method for initial value problems with rapidly varying right-hand sides Cash, J. R.; Karp, Alan H. ACM Transactions on Mathematical Software, Vol. 16, Issue 3 https://doi.org/10.1145/79505.79507	journal	September 1990
Mean passage times for tridiagonal transition matrices and a two-parameter ehrenfest urn model Krafft, Olaf; Schaefer, Martin Journal of Applied Probability, Vol. 30, Issue 4 https://doi.org/10.2307/3214525	journal	December 1993
Mean passage times for tridiagonal transition matrices Stefanov, Valeri T. Journal of Applied Probability, Vol. 32, Issue 3 https://doi.org/10.2307/3215137	journal	September 1995
The role of symmetries in adiabatic quantum algorithms Schaller, G.; Schutzhold, R. Quantum Information and Computation, Vol. 10, Issue 1&2 https://doi.org/10.26421/QIC10.1-2-9	journal	January 2010

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Title: Tunneling and Speedup in Quantum Optimization for Permutation-Symmetric Problems

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