Lower Bounds on Quantum Annealing Times

García-Pintos, Luis Pedro; Brady, Lucas T.; Bringewatt, Jacob; Liu, Yi-Kai

doi:10.1103/physrevlett.130.140601

Lower Bounds on Quantum Annealing Times

Journal Article · Wed Apr 05 00:00:00 EDT 2023 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.130.140601· OSTI ID:2008288

^[1]; Brady, Lucas T. ^[2]; ^[3]; ^[4]

Univ. of Maryland, College Park, MD (United States). Joint Quantum Institute and Joint Center for Quantum Information and Computer Science; Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
NASA Ames Research Center, Moffett Field, CA (United States). Quantum Artificial Intelligence Laboratory; KBR, Houston, TX (United States)
Univ. of Maryland, College Park, MD (United States). Joint Quantum Institute and Joint Center for Quantum Information and Computer Science
Univ. of Maryland, College Park, MD (United States). Joint Center for Quantum Information and Computer Science; National Inst. of Standards and Technology (NIST), Gaithersburg, MD (United States)

The adiabatic theorem provides sufficient conditions for the time needed to prepare a target ground state. While it is possible to prepare a target state much faster with more general quantum annealing protocols, rigorous results beyond the adiabatic regime are rare. Here, we provide such a result, deriving lower bounds on the time needed to successfully perform quantum annealing. The bounds are asymptotically saturated by three toy models where fast annealing schedules are known: the Roland and Cerf unstructured search model, the Hamming spike problem, and the ferromagnetic p-spin model. Our bounds demonstrate that these schedules have optimal scaling. Herein, our results also show that rapid annealing requires coherent superpositions of energy eigenstates, singling out quantum coherence as a computational resource.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)

Grant/Contract Number:: 89233218CNA000001; AC52-06NA25396; PHY-1748958; SC0020312; OMA-2120757

OSTI ID:: 2008288

Report Number(s):: LA-UR-23-21139; TRN: US2406435

Journal Information:: Physical Review Letters, Vol. 130, Issue 14; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (39)

Relation between quantum fluctuations and the performance enhancement of quantum annealing in a nonstoquastic Hamiltonian Susa, Yuki; Jadebeck, Johann F.; Nishimori, Hidetoshi Physical Review A, Vol. 95, Issue 4 https://doi.org/10.1103/PhysRevA.95.042321	journal	April 2017
Prospects for quantum enhancement with diabatic quantum annealing Crosson, E. J.; Lidar, D. A. Nature Reviews Physics, Vol. 3, Issue 7 https://doi.org/10.1038/s42254-021-00313-6	journal	May 2021
Adiabatic quantum computation Albash, Tameem; Lidar, Daniel A. Reviews of Modern Physics, Vol. 90, Issue 1 https://doi.org/10.1103/RevModPhys.90.015002	journal	January 2018
Nonstoquastic Hamiltonians and quantum annealing of an Ising spin glass Hormozi, Layla; Brown, Ethan W.; Carleo, Giuseppe Physical Review B, Vol. 95, Issue 18 https://doi.org/10.1103/PhysRevB.95.184416	journal	May 2017
Anderson localization makes adiabatic quantum optimization fail Altshuler, Boris; Krovi, Hari; Roland, Jérémie Proceedings of the National Academy of Sciences, Vol. 107, Issue 28 https://doi.org/10.1073/pnas.1002116107	journal	June 2010
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
Bang-bang control as a design principle for classical and quantum optimization algorithms Bapat, Aniruddha; Jordan, Stephen Quantum Information and Computation, Vol. 19, Issue 5&6 https://doi.org/10.26421/QIC19.5-6-4	journal	May 2019
Tunneling and Speedup in Quantum Optimization for Permutation-Symmetric Problems Muthukrishnan, Siddharth; Albash, Tameem; Lidar, Daniel A. Physical Review X, Vol. 6, Issue 3 https://doi.org/10.1103/PhysRevX.6.031010	journal	July 2016
Necessary adiabatic run times in quantum optimization Brady, Lucas T.; van Dam, Wim Physical Review A, Vol. 95, Issue 3 https://doi.org/10.1103/PhysRevA.95.032335	journal	March 2017
Shortcuts to Adiabaticity by Counterdiabatic Driving del Campo, Adolfo Physical Review Letters, Vol. 111, Issue 10 https://doi.org/10.1103/PhysRevLett.111.100502	journal	September 2013
Non-stoquastic Hamiltonians in quantum annealing via geometric phases Vinci, Walter; Lidar, Daniel A. npj Quantum Information, Vol. 3, Issue 1 https://doi.org/10.1038/s41534-017-0037-z	journal	September 2017
Counterdiabatic driving in the quantum annealing of the p -spin model: A variational approach Passarelli, G.; Cataudella, V.; Fazio, R. Physical Review Research, Vol. 2, Issue 1 https://doi.org/10.1103/PhysRevResearch.2.013283	journal	March 2020
Analog nature of quantum adiabatic unstructured search Slutskii, Mikhail; Albash, Tameem; Barash, Lev New Journal of Physics, Vol. 21, Issue 11 https://doi.org/10.1088/1367-2630/ab51f9	journal	November 2019
Quantifying Coherence Baumgratz, T.; Cramer, M.; Plenio, M. B. Physical Review Letters, Vol. 113, Issue 14 https://doi.org/10.1103/PhysRevLett.113.140401	journal	September 2014
Polynomial scaling of the quantum approximate optimization algorithm for ground-state preparation of the fully connected p -spin ferromagnet in a transverse field Wauters, Matteo M.; Mbeng, Glen B.; Santoro, Giuseppe E. Physical Review A, Vol. 102, Issue 6 https://doi.org/10.1103/PhysRevA.102.062404	journal	December 2020
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
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
Many-body transverse interactions in the quantum annealing of thep-spin ferromagnet Seoane, Beatriz; Nishimori, Hidetoshi Journal of Physics A: Mathematical and Theoretical, Vol. 45, Issue 43 https://doi.org/10.1088/1751-8113/45/43/435301	journal	October 2012
Adiabatic Quantum Computation Is Equivalent to Standard Quantum Computation Aharonov, Dorit; van Dam, Wim; Kempe, Julia SIAM Review, Vol. 50, Issue 4 https://doi.org/10.1137/080734479	journal	January 2008
Coherence as a Resource for Shor’s Algorithm Ahnefeld, Felix; Theurer, Thomas; Egloff, Dario Physical Review Letters, Vol. 129, Issue 12 https://doi.org/10.1103/PhysRevLett.129.120501	journal	September 2022
Quantum annealing with antiferromagnetic fluctuations Seki, Yuya; Nishimori, Hidetoshi Physical Review E, Vol. 85, Issue 5 https://doi.org/10.1103/PhysRevE.85.051112	journal	May 2012
Spectral-gap analysis for efficient tunneling in quantum adiabatic optimization Brady, Lucas T.; van Dam, Wim Physical Review A, Vol. 94, Issue 3 https://doi.org/10.1103/PhysRevA.94.032309	journal	September 2016
Adiabatic Population Transfer with Control Fields Demirplak, Mustafa; Rice, Stuart A. The Journal of Physical Chemistry A, Vol. 107, Issue 46 https://doi.org/10.1021/jp030708a	journal	November 2003
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
Genetic optimization of quantum annealing Hegde, Pratibha Raghupati; Passarelli, Gianluca; Scocco, Annarita Physical Review A, Vol. 105, Issue 1 https://doi.org/10.1103/PhysRevA.105.012612	journal	January 2022
Focus on Shortcuts to Adiabaticity del Campo, Adolfo; Kim, Kihwan New Journal of Physics, Vol. 21, Issue 5 https://doi.org/10.1088/1367-2630/ab1437	journal	May 2019
Analog quantum approximate optimization algorithm Barraza, Nancy; Alvarado Barrios, Gabriel; Peng, Jie Quantum Science and Technology, Vol. 7, Issue 4 https://doi.org/10.1088/2058-9565/ac91f0	journal	September 2022
Coherence depletion in the Grover quantum search algorithm Shi, Hai-Long; Liu, Si-Yuan; Wang, Xiao-Hui Physical Review A, Vol. 95, Issue 3 https://doi.org/10.1103/PhysRevA.95.032307	journal	March 2017
How quantum is the speedup in adiabatic unstructured search? Hen, Itay Quantum Information Processing, Vol. 18, Issue 6 https://doi.org/10.1007/s11128-019-2281-y	journal	April 2019
Quantum adiabatic algorithms, small gaps, and different paths Farhi, Edward; Goldstone, Jeffrey; Gosset, David Quantum Information and Computation, Vol. 11, Issue 3&4 https://doi.org/10.26421/QIC11.3-4-1	journal	March 2011
Colloquium : Quantum coherence as a resource Streltsov, Alexander; Adesso, Gerardo; Plenio, Martin B. Reviews of Modern Physics, Vol. 89, Issue 4 https://doi.org/10.1103/RevModPhys.89.041003	journal	October 2017
Diffusion Monte Carlo approach versus adiabatic computation for local Hamiltonians Bringewatt, Jacob; Dorland, William; Jordan, Stephen P. Physical Review A, Vol. 97, Issue 2 https://doi.org/10.1103/PhysRevA.97.022323	journal	February 2018
Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variation Hillery, Mark Physical Review A, Vol. 93, Issue 1 https://doi.org/10.1103/PhysRevA.93.012111	journal	January 2016
Beweis des Adiabatensatzes Born, M.; Fock, V. Zeitschrift f�r Physik, Vol. 51, Issue 3-4 https://doi.org/10.1007/BF01343193	journal	March 1928
On quantum mean-field models and their quantum annealing Bapst, Victor; Semerjian, Guilhem Journal of Statistical Mechanics: Theory and Experiment, Vol. 2012, Issue 06 https://doi.org/10.1088/1742-5468/2012/06/P06007	journal	June 2012
De-Signing Hamiltonians for Quantum Adiabatic Optimization Crosson, Elizabeth; Albash, Tameem; Hen, Itay Quantum, Vol. 4 https://doi.org/10.22331/q-2020-09-24-334	journal	September 2020
Trace-distance measure of coherence Rana, Swapan; Parashar, Preeti; Lewenstein, Maciej Physical Review A, Vol. 93, Issue 1 https://doi.org/10.1103/PhysRevA.93.012110	journal	January 2016
Transitionless quantum driving Berry, M. V. Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 36 https://doi.org/10.1088/1751-8113/42/36/365303	journal	August 2009
Perspectives of quantum annealing: methods and implementations Hauke, Philipp; Katzgraber, Helmut G.; Lechner, Wolfgang Reports on Progress in Physics, Vol. 83, Issue 5 https://doi.org/10.1088/1361-6633/ab85b8	journal	May 2020

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