3-regular three-XORSAT planted solutions benchmark of classical and quantum heuristic optimizers

Kowalsky, Matthew; Albash, Tameem; Hen, Itay; Lidar, Daniel A.

doi:10.1088/2058-9565/ac4d1b

3-regular three-XORSAT planted solutions benchmark of classical and quantum heuristic optimizers

Journal Article · Mon Feb 14 00:00:00 EST 2022 · Quantum Science and Technology

DOI:https://doi.org/10.1088/2058-9565/ac4d1b· OSTI ID:1979466

Kowalsky, Matthew ^[1]; ^[2]; ^[3]; ^[4]

University of Southern California, Los Angeles, CA (United States); USRA Research Institute for Advanced Computer Science, Mountain View, CA (United States); NASA Ames Research Center, Moffett Field, CA (United States); OSTI
University of New Mexico, Albuquerque, NM (United States)
University of Southern California, Los Angeles, and Marina del Rey, CA (United States)
University of Southern California, Los Angeles, CA (United States)

With current semiconductor technology reaching its physical limits, special-purpose hardware has emerged as an option to tackle specific computing-intensive challenges. Optimization in the form of solving quadratic unconstrained binary optimization problems, or equivalently Ising spin glasses, has been the focus of several new dedicated hardware platforms. These platforms come in many different flavors, from highly-efficient hardware implementations on digital-logic of established algorithms to proposals of analog hardware implementing new algorithms. In this work, we use a mapping of a specific class of linear equations whose solutions can be found efficiently, to a hard constraint satisfaction problem (three-regular three-XORSAT, or an Ising spin glass) with a 'golf-course' shaped energy landscape, to benchmark several of these different approaches. We perform a scaling and prefactor analysis of the performance of Fujitsu's digital annealer unit (DAU), the D-Wave advantage quantum annealer, a virtual MemComputing machine, Toshiba's simulated bifurcation machine (SBM), the SATonGPU algorithm from Bernaschi et al, and our implementation of parallel tempering. We identify the SATonGPU and DAU as currently having the smallest scaling exponent for this benchmark, with SATonGPU having a small scaling advantage and in addition having by far the smallest prefactor thanks to its use of massive parallelism. Furthermore, our work provides an objective assessment and a snapshot of the promise and limitations of dedicated optimization hardware relative to a particular class of optimization problems.

View Accepted Manuscript (DOE)

Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: US Army Research Office; USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0019219

OSTI ID:: 1979466

Journal Information:: Quantum Science and Technology, Journal Name: Quantum Science and Technology Journal Issue: 2 Vol. 7; ISSN 2058-9565

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

References (69)

A cluster Monte Carlo algorithm for 2-dimensional spin glasses Houdayer, J. The European Physical Journal B, Vol. 22, Issue 4 https://doi.org/10.1007/pl00011151	journal	August 2001
Minor-embedding in adiabatic quantum computation: I. The parameter setting problem Choi, Vicky Quantum Information Processing, Vol. 7, Issue 5 https://doi.org/10.1007/s11128-008-0082-9	journal	September 2008
Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design Choi, Vicky Quantum Information Processing, Vol. 10, Issue 3 https://doi.org/10.1007/s11128-010-0200-3	journal	October 2010
Adiabatic quantum programming: minor embedding with hard faults Klymko, Christine; Sullivan, Blair D.; Humble, Travis S. Quantum Information Processing, Vol. 13, Issue 3 https://doi.org/10.1007/s11128-013-0683-9	journal	November 2013
Fast clique minor generation in Chimera qubit connectivity graphs Boothby, Tomas; King, Andrew D.; Roy, Aidan Quantum Information Processing, Vol. 15, Issue 1 https://doi.org/10.1007/s11128-015-1150-6	journal	October 2015
Garden optimization problems for benchmarking quantum annealers Gonzalez Calaza, Carlos D.; Willsch, Dennis; Michielsen, Kristel Quantum Information Processing, Vol. 20, Issue 9 https://doi.org/10.1007/s11128-021-03226-6	journal	September 2021
borealis—A generalized global update algorithm for Boolean optimization problems Zhu, Zheng; Fang, Chao; Katzgraber, Helmut G. Optimization Letters, Vol. 14, Issue 8 https://doi.org/10.1007/s11590-020-01570-7	journal	March 2020
Roulette-wheel selection via stochastic acceptance Lipowski, Adam; Lipowska, Dorota Physica A: Statistical Mechanics and its Applications, Vol. 391, Issue 6 https://doi.org/10.1016/j.physa.2011.12.004	journal	March 2012
Tunable quantum tunnelling of magnetic domain walls Brooke, J.; Rosenbaum, T. F.; Aeppli, G. Nature, Vol. 413, Issue 6856 https://doi.org/10.1038/35098037	journal	October 2001
Quantum annealing with manufactured spins Johnson, M. W.; Amin, M. H. S.; Gildert, S. Nature, Vol. 473, Issue 7346 https://doi.org/10.1038/nature10012	journal	May 2011
Computational multiqubit tunnelling in programmable quantum annealers Boixo, Sergio; Smelyanskiy, Vadim N.; Shabani, Alireza Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms10327	journal	January 2016
Quantum annealing with all-to-all connected nonlinear oscillators Puri, Shruti; Andersen, Christian Kraglund; Grimsmo, Arne L. Nature Communications, Vol. 8, Issue 1 https://doi.org/10.1038/ncomms15785	journal	June 2017
Thermally assisted quantum annealing of a 16-qubit problem Dickson, N. G.; Johnson, M. W.; Amin, M. H. Nature Communications, Vol. 4, Issue 1 https://doi.org/10.1038/ncomms2920	journal	May 2013
Coherent Ising machines—optical neural networks operating at the quantum limit Yamamoto, Yoshihisa; Aihara, Kazuyuki; Leleu, Timothee npj Quantum Information, Vol. 3, Issue 1 https://doi.org/10.1038/s41534-017-0048-9	journal	December 2017
Analog errors in quantum annealing: doom and hope Pearson, Adam; Mishra, Anurag; Hen, Itay npj Quantum Information, Vol. 5, Issue 1 https://doi.org/10.1038/s41534-019-0210-7	journal	November 2019
Bifurcation-based adiabatic quantum computation with a nonlinear oscillator network Goto, Hayato Scientific Reports, Vol. 6, Issue 1 https://doi.org/10.1038/srep21686	journal	February 2016
Equation of State Calculations by Fast Computing Machines Metropolis, Nicholas; Rosenbluth, Arianna W.; Rosenbluth, Marshall N. The Journal of Chemical Physics, Vol. 21, Issue 6 https://doi.org/10.1063/1.1699114	journal	June 1953
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
Recycling random numbers in the stochastic simulation algorithm Yates, Christian A.; Klingbeil, Guido The Journal of Chemical Physics, Vol. 138, Issue 9 https://doi.org/10.1063/1.4792207	journal	March 2013
Perspective: Memcomputing: Leveraging memory and physics to compute efficiently Di Ventra, Massimiliano; Traversa, Fabio L. Journal of Applied Physics, Vol. 123, Issue 18 https://doi.org/10.1063/1.5026506	journal	May 2018
A scalable readout system for a superconducting adiabatic quantum optimization system Berkley, A. J.; Johnson, M. W.; Bunyk, P. Superconductor Science and Technology, Vol. 23, Issue 10 https://doi.org/10.1088/0953-2048/23/10/105014	journal	September 2010
A scalable control system for a superconducting adiabatic quantum optimization processor Johnson, M. W.; Bunyk, P.; Maibaum, F. Superconductor Science and Technology, Vol. 23, Issue 6 https://doi.org/10.1088/0953-2048/23/6/065004	journal	April 2010
Feedback-optimized parallel tempering Monte Carlo Katzgraber, Helmut G.; Trebst, Simon; Huse, David A. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2006, Issue 03 https://doi.org/10.1088/1742-5468/2006/03/p03018	journal	March 2006
Test-driving 1000 qubits Job, Joshua; Lidar, Daniel Quantum Science and Technology, Vol. 3, Issue 3 https://doi.org/10.1088/2058-9565/aabd9b	journal	June 2018
Analog errors in Ising machines Albash, Tameem; Martin-Mayor, Victor; Hen, Itay Quantum Science and Technology, Vol. 4, Issue 2 https://doi.org/10.1088/2058-9565/ab13ea	journal	April 2019
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
Entropic barriers as a reason for hardness in both classical and quantum algorithms Bellitti, Matteo; Ricci-Tersenghi, Federico; Scardicchio, Antonello Physical Review Research, Vol. 3, Issue 4 https://doi.org/10.1103/PhysRevResearch.3.043015	journal	October 2021
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
Performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs Farhi, Edward; Gosset, David; Hen, Itay Physical Review A, Vol. 86, Issue 5 https://doi.org/10.1103/physreva.86.052334	journal	November 2012
Consistency tests of classical and quantum models for a quantum annealer Albash, Tameem; Vinci, Walter; Mishra, Anurag Physical Review A, Vol. 91, Issue 4 https://doi.org/10.1103/physreva.91.042314	journal	April 2015
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
Searching for quantum speedup in quasistatic quantum annealers Amin, Mohammad H. Physical Review A, Vol. 92, Issue 5 https://doi.org/10.1103/physreva.92.052323	journal	November 2015
Best-case performance of quantum annealers on native spin-glass benchmarks: How chaos can affect success probabilities Zhu, Zheng; Ochoa, Andrew J.; Schnabel, Stefan Physical Review A, Vol. 93, Issue 1 https://doi.org/10.1103/physreva.93.012317	journal	January 2016
Strengths and weaknesses of weak-strong cluster problems: A detailed overview of state-of-the-art classical heuristics versus quantum approaches Mandrà, Salvatore; Zhu, Zheng; Wang, Wenlong Physical Review A, Vol. 94, Issue 2 https://doi.org/10.1103/physreva.94.022337	journal	August 2016
Equation Planting: A Tool for Benchmarking Ising Machines Hen, Itay Physical Review Applied, Vol. 12, Issue 1 https://doi.org/10.1103/physrevapplied.12.011003	journal	July 2019
Readiness of Quantum Optimization Machines for Industrial Applications Perdomo-Ortiz, Alejandro; Feldman, Alexander; Ozaeta, Asier Physical Review Applied, Vol. 12, Issue 1 https://doi.org/10.1103/physrevapplied.12.014004	journal	July 2019
Optimally Stopped Optimization Vinci, Walter; Lidar, Daniel A. Physical Review Applied, Vol. 6, Issue 5 https://doi.org/10.1103/physrevapplied.6.054016	journal	November 2016
Coherent Coupled Qubits for Quantum Annealing Weber, Steven J.; Samach, Gabriel O.; Hover, David Physical Review Applied, Vol. 8, Issue 1 https://doi.org/10.1103/physrevapplied.8.014004	journal	July 2017
Experimental investigation of an eight-qubit unit cell in a superconducting optimization processor Harris, R.; Johnson, M. W.; Lanting, T. Physical Review B, Vol. 82, Issue 2 https://doi.org/10.1103/physrevb.82.024511	journal	July 2010
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
Domain-wall free energy of spin-glass models: Numerical method and boundary conditions Hukushima, Koji Physical Review E, Vol. 60, Issue 4 https://doi.org/10.1103/physreve.60.3606	journal	October 1999
Complexity of several constraint-satisfaction problems using the heuristic classical algorithm WalkSAT Guidetti, Marco; Young, A. P. Physical Review E, Vol. 84, Issue 1 https://doi.org/10.1103/physreve.84.011102	journal	July 2011
Rejection-free Monte Carlo sampling for general potentials Peters, E. A. J. F.; de With, G. Physical Review E, Vol. 85, Issue 2 https://doi.org/10.1103/physreve.85.026703	journal	February 2012
First-Order Transitions and the Performance of Quantum Algorithms in Random Optimization Problems Jörg, Thomas; Krzakala, Florent; Semerjian, Guilhem Physical Review Letters, Vol. 104, Issue 20 https://doi.org/10.1103/physrevlett.104.207206	journal	May 2010
Efficient Cluster Algorithm for Spin Glasses in Any Space Dimension Zhu, Zheng; Ochoa, Andrew J.; Katzgraber, Helmut G. Physical Review Letters, Vol. 115, Issue 7 https://doi.org/10.1103/physrevlett.115.077201	journal	August 2015
Temperature Scaling Law for Quantum Annealing Optimizers Albash, Tameem; Martin-Mayor, Victor; Hen, Itay Physical Review Letters, Vol. 119, Issue 11 https://doi.org/10.1103/physrevlett.119.110502	journal	September 2017
Replica Monte Carlo Simulation of Spin-Glasses Swendsen, Robert H.; Wang, Jian-Sheng Physical Review Letters, Vol. 57, Issue 21 https://doi.org/10.1103/physrevlett.57.2607	journal	November 1986
Hiding Solutions in Random Satisfiability Problems: A Statistical Mechanics Approach Barthel, W.; Hartmann, A. K.; Leone, M. Physical Review Letters, Vol. 88, Issue 18 https://doi.org/10.1103/physrevlett.88.188701	journal	April 2002
Perils of embedding for sampling problems Marshall, Jeffrey; Di Gioacchino, Andrea; Rieffel, Eleanor G. Physical Review Research, Vol. 2, Issue 2 https://doi.org/10.1103/physrevresearch.2.023020	journal	April 2020
Demonstration of a Scaling Advantage for a Quantum Annealer over Simulated Annealing Albash, Tameem; Lidar, Daniel A. Physical Review X, Vol. 8, Issue 3 https://doi.org/10.1103/physrevx.8.031016	journal	July 2018
Fast, Lifetime-Preserving Readout for High-Coherence Quantum Annealers Grover, Jeffrey A.; Basham, James I.; Marakov, Alexander PRX Quantum, Vol. 1, Issue 2 https://doi.org/10.1103/prxquantum.01.020314	journal	November 2020
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
STATICA: A 512-Spin 0.25M-Weight Annealing Processor With an All-Spin-Updates-at-Once Architecture for Combinatorial Optimization With Complete Spin–Spin Interactions Yamamoto, Kasho; Kawamura, Kazushi; Ando, Kota IEEE Journal of Solid-State Circuits, Vol. 56, Issue 1 https://doi.org/10.1109/jssc.2020.3027702	journal	January 2021
Architectural Considerations in the Design of a Superconducting Quantum Annealing Processor Bunyk, P. I.; Hoskinson, Emile M.; Johnson, Mark W. IEEE Transactions on Applied Superconductivity, Vol. 24, Issue 4 https://doi.org/10.1109/tasc.2014.2318294	journal	August 2014
Memcomputing NP -complete problems in polynomial time using polynomial resources and collective states Traversa, Fabio Lorenzo; Ramella, Chiara; Bonani, Fabrizio Science Advances, Vol. 1, Issue 6 https://doi.org/10.1126/sciadv.1500031	journal	July 2015
Experimental investigation of performance differences between coherent Ising machines and a quantum annealer Hamerly, Ryan; Inagaki, Takahiro; McMahon, Peter L. Science Advances, Vol. 5, Issue 5 https://doi.org/10.1126/sciadv.aau0823	journal	May 2019
Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems Goto, Hayato; Tatsumura, Kosuke; Dixon, Alexander R. Science Advances, Vol. 5, Issue 4 https://doi.org/10.1126/sciadv.aav2372	journal	April 2019
High-performance combinatorial optimization based on classical mechanics Goto, Hayato; Endo, Kotaro; Suzuki, Masaru Science Advances, Vol. 7, Issue 6 https://doi.org/10.1126/sciadv.abe7953	journal	February 2021
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
Being Glassy Without Being Hard to Solve Ricci-Tersenghi, F. Science, Vol. 330, Issue 6011 https://doi.org/10.1126/science.1189804	journal	December 2010
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
Quantum Annealing of a Disordered Magnet Brooke, J. Science, Vol. 284, Issue 5415 https://doi.org/10.1126/science.284.5415.779	journal	April 1999
A fully programmable 100-spin coherent Ising machine with all-to-all connections McMahon, Peter L.; Marandi, Alireza; Haribara, Yoshitaka Science, Vol. 354, Issue 6312 https://doi.org/10.1126/science.aah5178	journal	October 2016
Exchange Monte Carlo Method and Application to Spin Glass Simulations Hukushima, Koji; Nemoto, Koji Journal of the Physical Society of Japan, Vol. 65, Issue 6 https://doi.org/10.1143/jpsj.65.1604	journal	June 1996
How we are leading a 3-XORSAT challenge: From the energy landscape to the algorithm and its efficient implementation on GPUs ^(a) Bernaschi, M.; Bisson, M.; Fatica, M. Europhysics Letters, Vol. 133, Issue 6 https://doi.org/10.1209/0295-5075/133/60005	journal	March 2021
A ferromagnet with a glass transition Franz, S.; Mézard, M.; Ricci-Tersenghi, F. Europhysics Letters (EPL), Vol. 55, Issue 4 https://doi.org/10.1209/epl/i2001-00438-4	journal	August 2001
Physics-Inspired Optimization for Quadratic Unconstrained Problems Using a Digital Annealer Aramon, Maliheh; Rosenberg, Gili; Valiante, Elisabetta Frontiers in Physics, Vol. 7 https://doi.org/10.3389/fphy.2019.00048	journal	April 2019
Methods of conjugate gradients for solving linear systems Hestenes, M. R.; Stiefel, E. Journal of Research of the National Bureau of Standards, Vol. 49, Issue 6 https://doi.org/10.6028/jres.049.044	journal	December 1952
Quantum Computation Based on Quantum Adiabatic Bifurcations of Kerr-Nonlinear Parametric Oscillators Goto, Hayato Journal of the Physical Society of Japan, Vol. 88, Issue 6 https://doi.org/10.7566/jpsj.88.061015	journal	June 2019

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3-regular three-XORSAT planted solutions benchmark of classical and quantum heuristic optimizers

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