Demonstration of a Scaling Advantage for a Quantum Annealer over Simulated Annealing
Abstract
The observation of an unequivocal quantum speedup remains an elusive objective for quantum computing. A more modest goal is to demonstrate a scaling advantage over a class of classical algorithms for a computational problem running on quantum hardware. The D-Wave quantum annealing processors have been at the forefront of experimental attempts to address this goal, given their relatively large numbers of qubits and programmability. A complete determination of the optimal time-to-solution using these processors has not been possible to date, preventing definitive conclusions about the presence of a scaling advantage. The main technical obstacle has been the inability to verify an optimal annealing time within the available range. Here, we overcome this obstacle using a class of problem instances constructed by systematically combining many-spin frustrated loops with few-qubit gadgets exhibiting a tunneling event—a combination that we find to promote the presence of tunneling energy barriers in the relevant semiclassical energy landscape of the full problem—and we observe an optimal annealing time using a D-Wave 2000Q processor over a range spanning up to more than 2000 qubits. We identify the gadgets as being responsible for the optimal annealing time, whose existence allows us to perform an optimal time-to-solution benchmarking analysis. Wemore »
- Authors:
- Publication Date:
- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1460927
- Alternate Identifier(s):
- OSTI ID: 1565694
- Grant/Contract Number:
- AC05-00OR22725
- Resource Type:
- Published Article
- Journal Name:
- Physical Review. X
- Additional Journal Information:
- Journal Name: Physical Review. X Journal Volume: 8 Journal Issue: 3; Journal ID: ISSN 2160-3308
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Albash, Tameem, and Lidar, Daniel A. Demonstration of a Scaling Advantage for a Quantum Annealer over Simulated Annealing. United States: N. p., 2018.
Web. doi:10.1103/PhysRevX.8.031016.
Albash, Tameem, & Lidar, Daniel A. Demonstration of a Scaling Advantage for a Quantum Annealer over Simulated Annealing. United States. https://doi.org/10.1103/PhysRevX.8.031016
Albash, Tameem, and Lidar, Daniel A. Sun .
"Demonstration of a Scaling Advantage for a Quantum Annealer over Simulated Annealing". United States. https://doi.org/10.1103/PhysRevX.8.031016.
@article{osti_1460927,
title = {Demonstration of a Scaling Advantage for a Quantum Annealer over Simulated Annealing},
author = {Albash, Tameem and Lidar, Daniel A.},
abstractNote = {The observation of an unequivocal quantum speedup remains an elusive objective for quantum computing. A more modest goal is to demonstrate a scaling advantage over a class of classical algorithms for a computational problem running on quantum hardware. The D-Wave quantum annealing processors have been at the forefront of experimental attempts to address this goal, given their relatively large numbers of qubits and programmability. A complete determination of the optimal time-to-solution using these processors has not been possible to date, preventing definitive conclusions about the presence of a scaling advantage. The main technical obstacle has been the inability to verify an optimal annealing time within the available range. Here, we overcome this obstacle using a class of problem instances constructed by systematically combining many-spin frustrated loops with few-qubit gadgets exhibiting a tunneling event—a combination that we find to promote the presence of tunneling energy barriers in the relevant semiclassical energy landscape of the full problem—and we observe an optimal annealing time using a D-Wave 2000Q processor over a range spanning up to more than 2000 qubits. We identify the gadgets as being responsible for the optimal annealing time, whose existence allows us to perform an optimal time-to-solution benchmarking analysis. We perform a comparison to several classical algorithms, including simulated annealing, spin-vector Monte Carlo, and discrete-time simulated quantum annealing (SQA), and establish the first example of a scaling advantage for an experimental quantum annealer over classical simulated annealing. Namely, we find that the D-Wave device exhibits certifiably better scaling than simulated annealing, with 95% confidence, over the range of problem sizes that we can test. However, we do not find evidence for a quantum speedup: SQA exhibits the best scaling for annealing algorithms by a significant margin. This is a finding of independent interest, since we associate SQA’s advantage with its ability to transverse energy barriers in the semiclassical energy landscape by mimicking tunneling. Our construction of instance classes with verifiably optimal annealing times opens up the possibility of generating many new such classes based on a similar principle of promoting the presence of energy barriers that can be overcome more efficiently using quantum rather than thermal fluctuations, paving the way for further definitive assessments of scaling advantages using current and future quantum annealing devices.},
doi = {10.1103/PhysRevX.8.031016},
journal = {Physical Review. X},
number = 3,
volume = 8,
place = {United States},
year = {2018},
month = {7}
}
Free Publicly Available Full Text
Publisher's Version of Record
https://doi.org/10.1103/PhysRevX.8.031016
https://doi.org/10.1103/PhysRevX.8.031016
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 11 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Seeking Quantum Speedup Through Spin Glasses: The Good, the Bad, and the Ugly
journal, September 2015
- Katzgraber, Helmut G.; Hamze, Firas; Zhu, Zheng
- Physical Review X, Vol. 5, Issue 3
Error-correcting codes for adiabatic quantum computation
journal, November 2006
- Jordan, Stephen P.; Farhi, Edward; Shor, Peter W.
- Physical Review A, Vol. 74, Issue 5
Probing for quantum speedup in spin-glass problems with planted solutions
journal, October 2015
- Hen, Itay; Job, Joshua; Albash, Tameem
- Physical Review A, Vol. 92, Issue 4
A cluster Monte Carlo algorithm for 2-dimensional spin glasses
journal, August 2001
- Houdayer, J.
- The European Physical Journal B, Vol. 22, Issue 4
The pitfalls of planar spin-glass benchmarks: raising the bar for quantum annealers (again)
journal, July 2017
- Mandrà, Salvatore; Katzgraber, Helmut G.; Thomas, Creighton
- Quantum Science and Technology, Vol. 2, Issue 3
Architectural Considerations in the Design of a Superconducting Quantum Annealing Processor
journal, August 2014
- Bunyk, P. I.; Hoskinson, Emile M.; Johnson, Mark W.
- IEEE Transactions on Applied Superconductivity, Vol. 24, Issue 4
Off-diagonal expansion quantum Monte Carlo
journal, December 2017
- Albash, Tameem; Wagenbreth, Gene; Hen, Itay
- Physical Review E, Vol. 96, Issue 6
Quantum annealing with manufactured spins
journal, May 2011
- Johnson, M. W.; Amin, M. H. S.; Gildert, S.
- Nature, Vol. 473, Issue 7346
Quantum annealing for problems with ground-state degeneracy
journal, January 2009
- Matsuda, Yoshiki; Nishimori, Hidetoshi; Katzgraber, Helmut G.
- Journal of Physics: Conference Series, Vol. 143
Evidence for quantum annealing with more than one hundred qubits
journal, February 2014
- Boixo, Sergio; Rønnow, Troels F.; Isakov, Sergei V.
- Nature Physics, Vol. 10, Issue 3
Complexity of Stoquastic Frustration-Free Hamiltonians
journal, January 2010
- Bravyi, Sergey; Terhal, Barbara
- SIAM Journal on Computing, Vol. 39, Issue 4
Searching for quantum speedup in quasistatic quantum annealers
journal, November 2015
- Amin, Mohammad H.
- Physical Review A, Vol. 92, Issue 5
Quantum trajectories for time-dependent adiabatic master equations
journal, February 2018
- Yip, Ka Wa; Albash, Tameem; Lidar, Daniel A.
- Physical Review A, Vol. 97, Issue 2
Error suppression in Hamiltonian-based quantum computation using energy penalties
journal, August 2015
- Bookatz, Adam D.; Farhi, Edward; Zhou, Leo
- Physical Review A, Vol. 92, Issue 2
Paths, Trees, and Flowers
journal, January 1965
- Edmonds, Jack
- Canadian Journal of Mathematics, Vol. 17
Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator
journal, November 2017
- Zhang, J.; Pagano, G.; Hess, P. W.
- Nature, Vol. 551, Issue 7682
Understanding Quantum Tunneling through Quantum Monte Carlo Simulations
journal, October 2016
- Isakov, Sergei V.; Mazzola, Guglielmo; Smelyanskiy, Vadim N.
- Physical Review Letters, Vol. 117, Issue 18
Quantum adiabatic Markovian master equations
journal, December 2012
- Albash, Tameem; Boixo, Sergio; Lidar, Daniel A.
- New Journal of Physics, Vol. 14, Issue 12
Application of a continuous time cluster algorithm to the two-dimensional random quantum Ising ferromagnet
journal, May 1999
- Rieger, H.; Kawashima, N.
- The European Physical Journal B, Vol. 9, Issue 2
Quantum annealing in the transverse Ising model
journal, November 1998
- Kadowaki, Tadashi; Nishimori, Hidetoshi
- Physical Review E, Vol. 58, Issue 5
Defining and detecting quantum speedup
journal, June 2014
- Ronnow, T. F.; Wang, Z.; Job, J.
- Science, Vol. 345, Issue 6195
Scaling analysis and instantons for thermally assisted tunneling and quantum Monte Carlo simulations
journal, January 2017
- Jiang, Zhang; Smelyanskiy, Vadim N.; Isakov, Sergei V.
- Physical Review A, Vol. 95, Issue 1
Stochastic series expansion method for quantum Ising models with arbitrary interactions
journal, November 2003
- Sandvik, Anders W.
- Physical Review E, Vol. 68, Issue 5
Macroscopic quantum tunneling and quantum–classical phase transitions of the escape rate in large spin systems
journal, January 2015
- Owerre, S. A.; Paranjape, M. B.
- Physics Reports, Vol. 546
Computational multiqubit tunnelling in programmable quantum annealers
journal, January 2016
- Boixo, Sergio; Smelyanskiy, Vadim N.; Shabani, Alireza
- Nature Communications, Vol. 7, Issue 1
Simple Glass Models and Their Quantum Annealing
journal, October 2008
- Jörg, Thomas; Krzakala, Florent; Kurchan, Jorge
- Physical Review Letters, Vol. 101, Issue 14
Equation of State Calculations by Fast Computing Machines
journal, June 1953
- Metropolis, Nicholas; Rosenbluth, Arianna W.; Rosenbluth, Marshall N.
- The Journal of Chemical Physics, Vol. 21, Issue 6
Adiabatic Quantum Computation in Open Systems
journal, December 2005
- Sarandy, M. S.; Lidar, D. A.
- Physical Review Letters, Vol. 95, Issue 25
Consistency tests of classical and quantum models for a quantum annealer
journal, April 2015
- Albash, Tameem; Vinci, Walter; Mishra, Anurag
- Physical Review A, Vol. 91, Issue 4
Probing many-body dynamics on a 51-atom quantum simulator
journal, November 2017
- Bernien, Hannes; Schwartz, Sylvain; Keesling, Alexander
- Nature, Vol. 551, Issue 7682
Quantum computational supremacy
journal, September 2017
- Harrow, Aram W.; Montanaro, Ashley
- Nature, Vol. 549, Issue 7671
Experimental signature of programmable quantum annealing
journal, June 2013
- Boixo, Sergio; Albash, Tameem; Spedalieri, Federico M.
- Nature Communications, Vol. 4, Issue 1
Monte Carlo sampling methods using Markov chains and their applications
journal, April 1970
- Hastings, W. K.
- Biometrika, Vol. 57, Issue 1
Exponentially Biased Ground-State Sampling of Quantum Annealing Machines with Transverse-Field Driving Hamiltonians
journal, February 2017
- Mandrà, Salvatore; Zhu, Zheng; Katzgraber, Helmut G.
- Physical Review Letters, Vol. 118, Issue 7
Fault-Tolerant Quantum Computation with Long-Range Correlated Noise
journal, February 2006
- Aharonov, Dorit; Kitaev, Alexei; Preskill, John
- Physical Review Letters, Vol. 96, Issue 5
A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
journal, April 2001
- Farhi, E.; Goldstone, J.; Gutmann, S.
- Science, Vol. 292, Issue 5516
Strengths and weaknesses of weak-strong cluster problems: A detailed overview of state-of-the-art classical heuristics versus quantum approaches
journal, August 2016
- Mandrà, Salvatore; Zhu, Zheng; Wang, Wenlong
- Physical Review A, Vol. 94, Issue 2
Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models
journal, November 2017
- Benedetti, Marcello; Realpe-Gómez, John; Biswas, Rupak
- Physical Review X, Vol. 7, Issue 4
Entanglement in a Quantum Annealing Processor
journal, May 2014
- Lanting, T.; Przybysz, A. J.; Smirnov, A. Yu.
- Physical Review X, Vol. 4, Issue 2
Quantum annealing versus classical machine learning applied to a simplified computational biology problem
journal, February 2018
- Li, Richard Y.; Di Felice, Rosa; Rohs, Remo
- npj Quantum Information, Vol. 4, Issue 1
Advantages of Unfair Quantum Ground-State Sampling
journal, April 2017
- Zhang, Brian Hu; Wagenbreth, Gene; Martin-Mayor, Victor
- Scientific Reports, Vol. 7, Issue 1
Non-commuting two-local Hamiltonians for quantum error suppression
journal, February 2017
- Jiang, Zhang; Rieffel, Eleanor G.
- Quantum Information Processing, Vol. 16, Issue 4
Theory of Quantum Annealing of an Ising Spin Glass
journal, March 2002
- Santoro, G. E.
- Science, Vol. 295, Issue 5564
Efficient Cluster Algorithm for Spin Glasses in Any Space Dimension
journal, August 2015
- Zhu, Zheng; Ochoa, Andrew J.; Katzgraber, Helmut G.
- Physical Review Letters, Vol. 115, Issue 7
Simulating physics with computers
journal, June 1982
- Feynman, Richard P.
- International Journal of Theoretical Physics, Vol. 21, Issue 6-7
Tunneling and Speedup in Quantum Optimization for Permutation-Symmetric Problems
journal, July 2016
- Muthukrishnan, Siddharth; Albash, Tameem; Lidar, Daniel A.
- Physical Review X, Vol. 6, Issue 3
What is the Computational Value of Finite-Range Tunneling?
journal, August 2016
- Denchev, Vasil S.; Boixo, Sergio; Isakov, Sergei V.
- Physical Review X, Vol. 6, Issue 3
Collective Monte Carlo Updating for Spin Systems
journal, January 1989
- Wolff, Ulli
- Physical Review Letters, Vol. 62, Issue 4
Experimental Implementation of an Adiabatic Quantum Optimization Algorithm
journal, February 2003
- Steffen, Matthias; van Dam, Wim; Hogg, Tad
- Physical Review Letters, Vol. 90, Issue 6
Blossom V: a new implementation of a minimum cost perfect matching algorithm
journal, April 2009
- Kolmogorov, Vladimir
- Mathematical Programming Computation, Vol. 1, Issue 1
On the ground states of the frustration model of a spin glass by a matching method of graph theory
journal, August 1980
- Bieche, L.; Uhry, J. P.; Maynard, R.
- Journal of Physics A: Mathematical and General, Vol. 13, Issue 8
Glassy Chimeras Could Be Blind to Quantum Speedup: Designing Better Benchmarks for Quantum Annealing Machines
journal, April 2014
- Katzgraber, Helmut G.; Hamze, Firas; Andrist, Ruben S.
- Physical Review X, Vol. 4, Issue 2
Quantum Monte Carlo tunneling from quantum chemistry to quantum annealing
journal, October 2017
- Mazzola, Guglielmo; Smelyanskiy, Vadim N.; Troyer, Matthias
- Physical Review B, Vol. 96, Issue 13
Optimization by Simulated Annealing
journal, May 1983
- Kirkpatrick, S.; Gelatt, C. D.; Vecchi, M. P.
- Science, Vol. 220, Issue 4598
Temperature Scaling Law for Quantum Annealing Optimizers
journal, September 2017
- Albash, Tameem; Martin-Mayor, Victor; Hen, Itay
- Physical Review Letters, Vol. 119, Issue 11
Anisotropic Landau-Lifshitz-Gilbert models of dissipation in qubits
journal, December 2016
- Crowley, Philip J. D.; Green, A. G.
- Physical Review A, Vol. 94, Issue 6
Error suppression for Hamiltonian quantum computing in Markovian environments
journal, March 2017
- Marvian, Milad; Lidar, Daniel A.
- Physical Review A, Vol. 95, Issue 3
Goals and opportunities in quantum simulation
journal, April 2012
- Cirac, J. Ignacio; Zoller, Peter
- Nature Physics, Vol. 8, Issue 4
A blueprint for demonstrating quantum supremacy with superconducting qubits
journal, April 2018
- Neill, C.; Roushan, P.; Kechedzhi, K.
- Science, Vol. 360, Issue 6385
Quantum Boltzmann Machine
journal, May 2018
- Amin, Mohammad H.; Andriyash, Evgeny; Rolfe, Jason
- Physical Review X, Vol. 8, Issue 2
Error Suppression for Hamiltonian-Based Quantum Computation Using Subsystem Codes
journal, January 2017
- Marvian, Milad; Lidar, Daniel A.
- Physical Review Letters, Vol. 118, Issue 3
Solving a Higgs optimization problem with quantum annealing for machine learning
journal, October 2017
- Mott, Alex; Job, Joshua; Vlimant, Jean-Roch
- Nature, Vol. 550, Issue 7676
Optimally Stopped Optimization
journal, November 2016
- Vinci, Walter; Lidar, Daniel A.
- Physical Review Applied, Vol. 6, Issue 5
Reexamining classical and quantum models for the D-Wave One processor: The role of excited states and ground state degeneracy
journal, February 2015
- Albash, T.; Rønnow, T. F.; Troyer, M.
- The European Physical Journal Special Topics, Vol. 224, Issue 1
Quantum versus classical annealing of Ising spin glasses
journal, March 2015
- Heim, B.; Ronnow, T. F.; Isakov, S. V.
- Science, Vol. 348, Issue 6231
Minor-embedding in adiabatic quantum computation: I. The parameter setting problem
journal, September 2008
- Choi, Vicky
- Quantum Information Processing, Vol. 7, Issue 5
Works referencing / citing this record:
Finite temperature quantum annealing solving exponentially small gap problem with non-monotonic success probability
journal, July 2018
- Mishra, Anurag; Albash, Tameem; Lidar, Daniel A.
- Nature Communications, Vol. 9, Issue 1
Quantum annealing for systems of polynomial equations
journal, July 2019
- Chang, Chia Cheng; Gambhir, Arjun; Humble, Travis S.
- Scientific Reports, Vol. 9, Issue 1
A quantum engineer's guide to superconducting qubits
journal, June 2019
- Krantz, P.; Kjaergaard, M.; Yan, F.
- Applied Physics Reviews, Vol. 6, Issue 2
Dynamics of reverse annealing for the fully connected -spin model
journal, November 2019
- Yamashiro, Yu; Ohkuwa, Masaki; Nishimori, Hidetoshi
- Physical Review A, Vol. 100, Issue 5
Disorder-assisted graph coloring on quantum annealers
journal, December 2019
- Więckowski, Andrzej; Deffner, Sebastian; Gardas, Bartłomiej
- Physical Review A, Vol. 100, Issue 6
Nested quantum annealing correction at finite temperature: -spin models
journal, June 2019
- Matsuura, Shunji; Nishimori, Hidetoshi; Vinci, Walter
- Physical Review A, Vol. 99, Issue 6
Power of Pausing: Advancing Understanding of Thermalization in Experimental Quantum Annealers
journal, April 2019
- Marshall, Jeffrey; Venturelli, Davide; Hen, Itay
- Physical Review Applied, Vol. 11, Issue 4
Equation Planting: A Tool for Benchmarking Ising Machines
journal, July 2019
- Hen, Itay
- Physical Review Applied, Vol. 12, Issue 1
Scalable Emulation of Sign-Problem–Free Hamiltonians with Room-Temperature -bits
journal, September 2019
- Camsari, Kerem Y.; Chowdhury, Shuvro; Datta, Supriyo
- Physical Review Applied, Vol. 12, Issue 3
Improving quantum annealing of the ferromagnetic -spin model through pausing
journal, July 2019
- Passarelli, G.; Cataudella, V.; Lucignano, P.
- Physical Review B, Vol. 100, Issue 2
Obstacles to quantum annealing in a planar embedding of XORSAT
journal, August 2019
- Patil, Pranay; Kourtis, Stefanos; Chamon, Claudio
- Physical Review B, Vol. 100, Issue 5
Taming a nonconvex landscape with dynamical long-range order: Memcomputing Ising benchmarks
journal, November 2019
- Sheldon, Forrest; Traversa, Fabio L.; Di Ventra, Massimiliano
- Physical Review E, Vol. 100, Issue 5
Physics-Inspired Optimization for Quadratic Unconstrained Problems Using a Digital Annealer
journal, April 2019
- Aramon, Maliheh; Rosenberg, Gili; Valiante, Elisabetta
- Frontiers in Physics, Vol. 7