Quantum Optimization of Fully Connected Spin Glasses
Open accessAbstract
Quantum computing promises to be more efficient and significantly faster than today's classical computing. Researchers compare the performance of a quantum annealer with that of classical algorithms for the first time on hard spin-glass problems.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
For biclique inputs, since the number of random couplings scales as M^2, it is necessary to rescale the coupling strength to ensure extensive energy; couplers are rescaled as Jij → Jij sqrt(M/4).
“Since the number of random couplings scales as M 2 it is necessary to rescale the coupling strength to ensure extensive energy (correct scaling behavior) 71 ; we rescale couplers as J ij → Jij √ M/4 for every i in A and j in B.”
From Beyond-classical computation in quantum simulation (2025) · cites this paper as [71]
In “B. Replica exchange Monte Carlo method in ‘two dimensions’” (page unavailable), the paper says that ±1 logical couplings give energy scaling as N^(3/2), motivating size-dependent scaling for the embedded model. It does not discuss biclique inputs or prescribe the citing authors’ specific J_ij rescaling by √(M/4). (LLM, conf=0.86)
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Solvable Model of a Spin-Glass
Sherrington, D., & Kirkpatrick, S. (1975) · Physical Review Letters · doi:10.1103/physrevlett.35.1792 · Cited by 3,577 · see citing works
Collective Monte Carlo Updating for Spin Systems
Ulli Wolff, A. (1989) · Physical Review Letters · doi:10.1103/physrevlett.62.361 · Cited by 2,564 · see citing works
Ising formulations of many NP problems
Lucas, A. (2014) · Frontiers in Physics · doi:10.3389/fphy.2014.00005 · Cited by 2,512 · see citing works
Quantum annealing in the transverse Ising model
Kadowaki, T., & Nishimori, H. (1998) · Physical Review E · doi:10.1103/physreve.58.5355 · Cited by 2,339 · see citing works
Exchange Monte Carlo Method and Application to Spin Glass Simulations
Hukushima, K., & Nemoto, K. (1995) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.65.1604 · Cited by 2,223 · see citing works
Quantum annealing with manufactured spins
Johnson, M. W., Amin, M. H. S., Gildert, S., Lanting, T., Hamze, F., Dickson, N., Harris, R., Berkley, A. J., Johansson, J., Bunyk, P., et al. (2011) · Nature · doi:10.1038/nature10012 · Cited by 1,891 · see citing works
Exchange Monte Carlo method and application to spin glass simulationsPreprint
Hukushima, K., & Nemoto, K. (1996) · Cited by 1,645 · see citing works
Evidence for quantum annealing with more than one hundred qubits
Boixo, S., Rønnow, T. F., Isakov, S. V., Wang, Z., Wecker, D., Lidar, D. A., Martinis, J. M., & Troyer, M. (2014) · Nature Physics · doi:10.1038/nphys2900 · Cited by 810 · see citing works
Theory of Quantum Annealing of an Ising Spin Glass
Santoro, G. E., Martoňák, R., Tosatti, E., & Car, R. (2002) · Science · doi:10.1126/science.1068774 · Cited by 734 · see citing works
Defining and detecting quantum speedup
Rønnow, T. F., Wang, Z., Job, J., Boixo, S., Isakov, S. V., Wecker, D., Martinis, J. M., Lidar, D. A., & Troyer, M. (2014) · Science · doi:10.1126/science.1252319 · Cited by 601 · cited 5× · see citing works
“For these reasons groups around the world have started to experimentally benchmark the machine [9–11], nurturing a lively discussion on whether the device is making functional use of quantum mechanics for computation [12] and how to properly measure speedups between different computational/experimental algorithms [13,…”
BackgroundMethodInfluentialQuantum Annealing of a Disordered Magnet
Brooke, J., Bitko, D., F., T., Rosenbaum, & Aeppli, G. (1999) · Science · doi:10.1126/science.284.5415.779 · Cited by 518 · see citing works
Minor-embedding in adiabatic quantum computation: I. The parameter setting problem
Choi, V. (2008) · Quantum Information Processing · doi:10.1007/s11128-008-0082-9 · Cited by 410 · see citing works
Search for a transition in the three-dimensional J Ising spin-glass
Bhatt, R. N., & Young, A. P. (1985) · Physical Review Letters · doi:10.1103/physrevlett.54.924 · Cited by 395 · see citing works
Mathematical foundation of quantum annealing
Morita, S., & Nishimori, H. (2008) · Journal of Mathematical Physics · doi:10.1063/1.2995837 · Cited by 381 · cited 1× · see citing works
“While the founding principles of the technique have been investigated numerically [3], analytically [4,5], and experimentally [6] in the past decade, the disordered, interacting, time-dependent, and open nature of the many-body problem makes it very hard to draw universal conclusions about the power of the technique […”
BackgroundFinding low-energy conformations of lattice protein models by quantum annealing
Perdomo-Ortiz, A., Dickson, N., Drew-Brook, M., Rose, G., & Aspuru-Guzik, A. (2012) · Scientific Reports · doi:10.1038/srep00571 · Cited by 366 · see citing works
Architectural Considerations in the Design of a Superconducting Quantum Annealing Processor
Bunyk, P. I., Hoskinson, E., Johnson, M. W., Tolkacheva, E., Altomare, F., Berkley, A. J., Harris, R., Hilton, J. P., Lanting, T., Przybysz, A. J., et al. (2014) · IEEE Transactions on Applied Superconductivity · doi:10.1109/tasc.2014.2318294 · Cited by 356 · see citing works
Application of statistical mechanics to NP-complete problems in combinatorial optimisation
Fu, Y., & Anderson, P. W. (1986) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/19/9/033 · Cited by 325 · see citing works
Cluster Monte Carlo algorithms
Wang, J., & Swendsen, R. H. (1990) · Physica A Statistical Mechanics and its Applications · doi:10.1016/0378-4371(90)90275-w · Cited by 280 · see citing works
Minor-embedding in adiabatic quantum computation: II. Minor-universal graph design
Choi, V. (2011) · Quantum Information Processing · doi:10.1007/s11128-010-0200-3 · Cited by 278 · see citing works
Experimental investigation of an eight-qubit unit cell in a superconducting optimization processor
Harris, R., Johnson, M. W., Lanting, T. M., Berkley, A. J., Johansson, J., Bunyk, P., Tolkacheva, E., Ladizinsky, E., Ladizinsky, N., Oh, T., et al. (2010) · Physical Review B · doi:10.1103/physrevb.82.024511 · Cited by 268 · see citing works
A case study in programming a quantum annealer for hard operational planning problems
Rieffel, E. G., Venturelli, D., O’Gorman, B., Do, M. B., Prystay, E. M., & Smelyanskiy, V. (2014) · Quantum Information Processing · doi:10.1007/s11128-014-0892-x · Cited by 221 · see citing works
Self-citationError-corrected quantum annealing with hundreds of qubits
Pudenz, K. L., Albash, T., & Lidar, D. A. (2014) · Nature Communications · doi:10.1038/ncomms4243 · Cited by 194 · see citing works
A scalable control system for a superconducting adiabatic quantum optimization processor
Johnson, M. W., Bunyk, P., Maibaum, F., Tolkacheva, E., Berkley, A. J., Chapple, E. M., Harris, R., Johansson, J., Lanting, T. M., Perminov, I., et al. (2010) · Superconductor Science and Technology · doi:10.1088/0953-2048/23/6/065004 · Cited by 162 · see citing works
Katzgraber, H. G., Hamze, F., & Andrist, R. S. (2014) · Physical Review X · doi:10.1103/physrevx.4.021008 · Cited by 145 · see citing works
Consistency tests of classical and quantum models for a quantum annealer
Albash, T., Vinci, W., Mishra, A., Warburton, P. A., & Lidar, D. A. (2015) · Physical Review A · doi:10.1103/physreva.91.042314 · Cited by 134 · see citing works
Quantum Computing and Quantum Bits in Mesoscopic Systems
Leggett, A. J., Ruggiero, B., & Silvestrini, P. (2004) · Springer eBooks · doi:10.1007/978-1-4419-9092-1 · Cited by 134 · see citing works
Experimental Determination of Ramsey Numbers
Bian, Z., Chudak, F. A., Macready, W. G., Clark, L., & Gaitan, F. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.130505 · Cited by 101 · see citing works
Adiabatic quantum programming: minor embedding with hard faults
Klymko, C., Sullivan, B. D., & Humble, T. S. (2014) · Quantum Information Processing · doi:10.1007/s11128-013-0683-9 · Cited by 99 · cited 1× · see citing works
“Figure 1 shows an embedding of the SK model in a triangular portion [29,30] of the Vesuvius processor: each LB in the original problem of size N is represented by ðN=4Þ þ 1 qubits connected in a line.”
MethodBayesian network structure learning using quantum annealing
O’Gorman, B., Babbush, R., Perdomo‐Ortiz, A., Aspuru‐Guzik, A., & Smelyanskiy, V. (2015) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2015-02349-9 · Cited by 92 · see citing works
Self-citationAdiabatic quantum optimization with the wrong Hamiltonian
Young, K. C., Blume-Kohout, R., & Lidar, D. A. (2013) · Physical Review A · doi:10.1103/physreva.88.062314 · Cited by 60 · see citing works
Max 2-SAT with up to 108 qubits
Santra, S., Quiroz, G., Steeg, G. V., & Lidar, D. A. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/4/045006 · Cited by 60 · see citing works
Finding Large Clique Minors is Hard
Eppstein, D. (2009) · Journal of Graph Algorithms and Applications · doi:10.7155/jgaa.00183 · Cited by 27 · see citing works
Finite-size scaling analysis of the distributions of pseudo-critical temperatures in spin glasses
Billoire, A. H., Fernández, L. A., Maiorano, A., Marinari, E., Martín-Mayor, V., & Yllanes, D. (2011) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2011/10/p10019 · Cited by 22 · see citing works
How to test the “quantumness” of a quantum computer?
Zagoskin, A. M., Il’ichev, E. V., Grajcar, M., Betouras, J. J., & Nori, F. (2014) · Frontiers in Physics · doi:10.3389/fphy.2014.00033 · Cited by 21 · see citing works
Flagged first, then by citations
Research works printed but not linked: 8
- V. N. Smelyanskiy, E. G. Rieffel, S. I. Knysh, C. P. Williams, M. W. Johnson, M. C. Thom, W. G. Macready, and K. L. Pudenz, A Near-Term Quantum Computing Approach for Hard Computational Problems in Space Exploration, arXiv: 1204.2821. · arXiv
- S. Dash, A Note on QUBO Instances Defined on Chimera Graphs, arXiv:1306.1202v2. FIG. 5. Example of the intersection between two Binder ratio surfaces with, respectively, N ¼ 32 and N ¼ 64. The intersecting manifold is T 64 SG ðα F Þ (see Supplemental Material [36]). For α F ≫ 1, the logical SK model is recovered. · arXiv
- S. Boixo, V. N. Smelyanskiy, A. Shabani, S. V. Isakov, M. Dykman, V. S. Denchev, M. Amin, A. Smirnov, M. Mohseni, and H. Neven, Computational Role of Collective Tunneling in a Quantum Annealer, arXiv:1411.4036. · arXiv
- J. A. Smolin and G. Smith, Classical Signature of Quantum Annealing, arXiv:1305.4904. · arXiv
- J. Cai, B. Macready, and A. Roy, A Practical Heuristic for Finding Graph Minors, arXiv:1406.2741. · arXiv
- See Supplemental Material at http://link.aps.org/ supplemental/10.1103/PhysRevX.5.031040 for further de- tails on numerics and additional benchmarkings.
- A. D. King and C. C. McGeoch, Algorithm Engineering for a Quantum Annealing Platform, arXiv:1410.2628v2. · arXiv
- H. G. Katzgraber, Introduction to Monte Carlo Methods, arXiv:0905.1629. · arXiv
Cited by
Sorted by citations
Perspectives of quantum annealing: methods and implementations
Hauke, P., Katzgraber, H. G., Lechner, W., Nishimori, H., & Oliver, W. D. (2020) · Reports on Progress in Physics · doi:10.1088/1361-6633/ab85b8 · Cited by 507 · see citing works
Traffic Flow Optimization Using a Quantum Annealer
Neukart, F., Compostella, G., Seidel, C., Dollen, D. V., Yarkoni, S., & Parney, B. (2017) · Frontiers in ICT · doi:10.3389/fict.2017.00029 · Cited by 470 · see citing works
Physics-Inspired Optimization for Quadratic Unconstrained Problems Using a Digital Annealer
Aramon, M., Rosenberg, G., Valiante, E., Miyazawa, T., Tamura, H., & Katzgraber, H. G. (2019) · Frontiers in Physics · doi:10.3389/fphy.2019.00048 · Cited by 442 · see citing works
What is the Computational Value of Finite-Range Tunneling?
Denchev, V. S., Boixo, S., Isakov, S. V., Ding, N., Babbush, R., Smelyanskiy, V., Martinis, J., & Neven, H. (2016) · Physical Review X · doi:10.1103/physrevx.6.031015 · Cited by 399 · see citing works
Self-citationQuantum annealing for industry applications: introduction and review
Yarkoni, S., Raponi, E., Bäck, T., & Schmitt, S. (2022) · Reports on Progress in Physics · doi:10.1088/1361-6633/ac8c54 · Cited by 341 · see citing works
Hamerly, R., Inagaki, T., McMahon, P. L., Venturelli, D., Marandi, A., Onodera, T., Ng, E., Langrock, C., Inaba, K., Honjo, T., et al. (2019) · Science Advances · doi:10.1126/sciadv.aau0823 · Cited by 366 · see citing works
Self-citationHamerly, R., Inagaki, T., McMahon, P. L., Venturelli, D., Marandi, A., Onodera, T., Ng, E., Langrock, C., Inaba, K., Honjo, T., et al. (2019) · CaltechAUTHORS (California Institute of Technology) · Cited by 257 · see citing works
Self-citationZhang, Z., & Zhuang, Q. (2020) · Quantum Science and Technology · doi:10.1088/2058-9565/abd4c3 · Cited by 246 · see citing works
Computational multiqubit tunnelling in programmable quantum annealers
Boixo, S., Smelyanskiy, V., Shabani, A., Isakov, S. V., Dykman, M. I., Denchev, V. S., Amin, M. H. S., Smirnov, A. Y., Mohseni, M., & Neven, H. (2016) · Nature Communications · doi:10.1038/ncomms10327 · Cited by 232 · see citing works
Self-citationReverse quantum annealing approach to portfolio optimization problems
Venturelli, D., & Kondratyev, A. (2019) · Quantum Machine Intelligence · doi:10.1007/s42484-019-00001-w · Cited by 233 · see citing works
Self-citationA case study in programming a quantum annealer for hard operational planning problems
Rieffel, E. G., Venturelli, D., O’Gorman, B., Do, M. B., Prystay, E. M., & Smelyanskiy, V. (2014) · Quantum Information Processing · doi:10.1007/s11128-014-0892-x · Cited by 221 · see citing works
Self-citationLi, R. Y., Di Felice, R., Rohs, R., & Lidar, D. A. (2018) · npj Quantum Information · doi:10.1038/s41534-018-0060-8 · Cited by 202 · see citing works
Ajagekar, A., Humble, T., & You, F. (2020) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2019.106630 · Cited by 191 · see citing works
“The probability of recovering the global optimal solution is highly dependent on the embedding and annealing schedule [37, 38].”
BackgroundOpen source software in quantum computing
Fingerhuth, M., Babej, T., & Wittek, P. (2018) · PLoS ONE · doi:10.1371/journal.pone.0208561 · Cited by 188 · see citing works
Application of Quantum Annealing to Training of Deep Neural Networks
Adachi, S. H., & Henderson, M. P. (2015) · arXiv · doi:10.48550/arxiv.1510.06356 · Cited by 176 · see citing works
Quantum annealing: an overview
Rajak, A., Suzuki, S., Dutta, A., & Chakrabarti, B. K. (2022) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2021.0417 · Cited by 182 · see citing works
Probing for quantum speedup in spin-glass problems with planted solutions
Hen, I., Job, J., Albash, T., Rønnow, T. F., Troyer, M., & Lidar, D. A. (2015) · Physical Review A · doi:10.1103/physreva.92.042325 · Cited by 165 · see citing works
Fast clique minor generation in Chimera qubit connectivity graphs
Boothby, T., King, A. D., & Roy, A. (2015) · Quantum Information Processing · doi:10.1007/s11128-015-1150-6 · Cited by 161 · see citing works
Searching for quantum speedup in quasistatic quantum annealers
Amin, M. H. S. (2015) · Physical Review A · doi:10.1103/physreva.92.052323 · Cited by 154 · see citing works
Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models
Benedetti, M., Realpe-Gómez, J., Biswas, R., & Perdomo‐Ortiz, A. (2017) · Physical Review X · doi:10.1103/physrevx.7.041052 · Cited by 155 · see citing works
Self-citationApplication of Quantum Annealing to Nurse Scheduling Problem
Ikeda, K., Nakamura, Y., & Humble, T. S. (2019) · Scientific Reports · doi:10.1038/s41598-019-49172-3 · Cited by 139 · see citing works
Prospects for quantum enhancement with diabatic quantum annealing
Crosson, E., & Lidar, D. A. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00313-6 · Cited by 137 · see citing works
Beyond-classical computation in quantum simulation
King, A. D., Nocera, A., Rams, M. M., Dziarmaga, J., Wiersema, R., Bernoudy, W., Raymond, J., Kaushal, N., Heinsdorf, N., Harris, R., et al. (2025) · Science · doi:10.1126/science.ado6285 · Cited by 138 · see citing works
Mandrà, S., Zhu, Z., Wang, W., Perdomo‐Ortiz, A., & Katzgraber, H. G. (2016) · Physical Review A · doi:10.1103/physreva.94.022337 · Cited by 108 · see citing works
Self-citationQuantum annealing correction for random Ising problems
Pudenz, K. L., Albash, T., & Lidar, D. A. (2015) · Physical Review A · doi:10.1103/physreva.91.042302 · Cited by 99 · see citing works
Robust quantum optimizer with full connectivity
Nigg, S. E., Lörch, N., & Tiwari, R. P. (2017) · Science Advances · doi:10.1126/sciadv.1602273 · Cited by 101 · see citing works
Exponential Enhancement of the Efficiency of Quantum Annealing by Non-Stoquastic Hamiltonians
Nishimori, H., & Takada, K. (2017) · Frontiers in ICT · doi:10.3389/fict.2017.00002 · Cited by 95 · see citing works
Quantum annealing correction with minor embedding
Vinci, W., Albash, T., Paz-Silva, G. A., Hen, I., & Lidar, D. A. (2015) · Physical Review A · doi:10.1103/physreva.92.042310 · Cited by 96 · see citing works
A NASA perspective on quantum computing: Opportunities and challenges
Biswas, R., Zhang, J., Kechezhi, K., Knysh, S., Mandrà, S., O’Gorman, B., Perdomo‐Ortiz, A., Petukhov, A. G., Realpe-Gómez, J., Rieffel, E. G., et al. (2016) · Parallel Computing · doi:10.1016/j.parco.2016.11.002 · Cited by 96 · see citing works
Self-citationQuantum Annealing amid Local Ruggedness and Global Frustration
King, J., Yarkoni, S., Raymond, J., Ozfidan, I., King, A. D., Nevisi, M. M., Hilton, J., & McGeoch, C. C. (2019) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.88.061007 · Cited by 104 · see citing works
Bayesian network structure learning using quantum annealing
O’Gorman, B., Babbush, R., Perdomo‐Ortiz, A., Aspuru‐Guzik, A., & Smelyanskiy, V. (2015) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2015-02349-9 · Cited by 92 · see citing works
Self-citationA QUBO Model for the Traveling Salesman Problem with Time Windows
Papalitsas, C., Andronikos, T., Giannakis, K., Theocharopoulou, G., & Fanarioti, S. (2019) · Algorithms · doi:10.3390/a12110224 · Cited by 91 · see citing works
Mapping Constrained Optimization Problems to Quantum Annealing with Application to Fault Diagnosis
Bian, Z., Chudak, F. A., Israel, R. B., Lackey, B., Macready, W. G., & Roy, A. (2016) · Frontiers in ICT · doi:10.3389/fict.2016.00014 · Cited by 86 · see citing works
Seeking Quantum Speedup Through Spin Glasses: The Good, the Bad, and the Ugly
Katzgraber, H. G., Hamze, F., Zhu, Z., Ochoa, A. J., & Munoz-Bauza, H. (2015) · OakTrust (Texas A&M University Libraries) · Cited by 86 · see citing works
A deceptive step towards quantum speedup detection
Mandrà, S., & Katzgraber, H. G. (2018) · Quantum Science and Technology · doi:10.1088/2058-9565/aac8b2 · Cited by 82 · see citing works
Self-citationEfficiently embedding QUBO problems on adiabatic quantum computers
Date, P., Patton, R. M., Schuman, C. D., & Potok, T. E. (2019) · Quantum Information Processing · doi:10.1007/s11128-019-2236-3 · Cited by 76 · see citing works
Scaling and Diabatic Effects in Quantum Annealing with a D-Wave Device
Weinberg, P., Tylutki, M., Rönkkö, J., Westerholm, J., Åström, J. A., Manninen, P., Törmä, P., & Sandvik, A. W. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.090502 · Cited by 76 · see citing works
Benchmarking a quantum annealing processor with the time-to-target metric
King, J., Yarkoni, S., Nevisi, M. M., Hilton, J. P., & McGeoch, C. C. (2015) · arXiv · doi:10.48550/arxiv.1508.05087 · Cited by 77 · see citing works
Chancellor, N., Zohren, S., & Warburton, P. A. (2017) · npj Quantum Information · doi:10.1038/s41534-017-0022-6 · Cited by 72 · see citing works
Multivariable optimization: Quantum annealing and computation
Mukherjee, S., & Chakrabarti, B. K. (2015) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2015-02339-y · Cited by 77 · see citing works
Multiple query optimization on the D-Wave 2X adiabatic quantum computer
Trummer, I., & Koch, C. E. (2016) · Proceedings of the VLDB Endowment · doi:10.14778/2947618.2947621 · Cited by 81 · see citing works
A quantum annealing approach for fault detection and diagnosis of graph-based systems
Perdomo‐Ortiz, A., Fluegemann, J., Narasimhan, S., Biswas, R., & Smelyanskiy, V. (2015) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2015-02347-y · Cited by 78 · see citing works
Self-citationZhu, Z., Ochoa, A. J., Schnabel, S., Hamze, F., & Katzgraber, H. G. (2016) · Physical Review A · doi:10.1103/physreva.93.012317 · Cited by 74 · see citing works
Mandrà, S., Zhu, Z., & Katzgraber, H. G. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.070502 · Cited by 72 · see citing works
Self-citationDeploying a quantum annealing processor to detect tree cover in aerial imagery of California
Boyda, E., Basu, S., Ganguly, S., Michaelis, A., Mukhopadhyay, S., & Nemani, R. (2017) · PLoS ONE · doi:10.1371/journal.pone.0172505 · Cited by 63 · see citing works
Genome assembly using quantum and quantum-inspired annealing
Boev, A. S., Rakitko, A. S., Usmanov, S. R., Kobzeva, A. N., Popov, I. V., Ilinsky, V. V., Kiktenko, E. O., & Fedorov, A. K. (2021) · Scientific Reports · doi:10.1038/s41598-021-88321-5 · Cited by 63 · see citing works
Engineering Reflective Metasurfaces With Ising Hamiltonian and Quantum Annealing
Ross, C., Gradoni, G., Lim, Q. J., & Peng, Z. (2021) · IEEE Transactions on Antennas and Propagation · doi:10.1109/tap.2021.3137424 · Cited by 64 · see citing works
Towards practical applications in quantum computational biology
Fedorov, A. K., & Gelfand, M. S. (2021) · Nature Computational Science · doi:10.1038/s43588-021-00024-z · Cited by 62 · see citing works
Global Warming: Temperature Estimation in Annealers
Raymond, J., Yarkoni, S., & Andriyash, E. (2016) · Frontiers in ICT · doi:10.3389/fict.2016.00023 · Cited by 62 · see citing works
Dissipation in adiabatic quantum computers: lessons from an exactly solvable model
Keck, M., Montangero, S., Santoro, G. E., Fazio, R., & Rossini, D. (2017) · New Journal of Physics · doi:10.1088/1367-2630/aa8cef · Cited by 58 · see citing works
Nested quantum annealing correction
Vinci, W., Albash, T., & Lidar, D. A. (2016) · npj Quantum Information · doi:10.1038/npjqi.2016.17 · Cited by 57 · see citing works
Reverse quantum annealing of the p -spin model with relaxation
Passarelli, G., Yip, K.-W., Lidar, D. A., Nishimori, H., & Lucignano, P. (2020) · Physical Review A · doi:10.1103/physreva.101.022331 · Cited by 55 · see citing works
Quantum machine learning and quantum biomimetics: A perspective
Lamata, L. (2020) · Machine Learning Science and Technology · doi:10.1088/2632-2153/ab9803 · Cited by 58 · see citing works
Short-depth QAOA circuits and quantum annealing on higher-order ising models
Pelofske, E., Bärtschi, A., & Eidenbenz, S. (2024) · npj Quantum Information · doi:10.1038/s41534-024-00825-w · Cited by 49 · see citing works
Maximum-Entropy Inference with a Programmable Annealer
Chancellor, N., Szőke, S., Vinci, W., Aeppli, G., & Warburton, P. A. (2016) · Scientific Reports · doi:10.1038/srep22318 · Cited by 47 · see citing works
Uncertain fate of fair sampling in quantum annealing
Könz, M. S., Mazzola, G., Ochoa, A. J., Katzgraber, H. G., & Troyer, M. (2019) · Physical Review A · doi:10.1103/physreva.100.030303 · Cited by 49 · see citing works
Determination and correction of persistent biases in quantum annealers
Perdomo‐Ortiz, A., O’Gorman, B., Fluegemann, J., Biswas, R., & Smelyanskiy, V. (2016) · Scientific Reports · doi:10.1038/srep18628 · Cited by 45 · see citing works
Self-citationThermalization, Freeze-out, and Noise: Deciphering Experimental Quantum Annealers
Marshall, J., Rieffel, E. G., & Hen, I. (2017) · Physical Review Applied · doi:10.1103/physrevapplied.8.064025 · Cited by 44 · see citing works
Analog errors in Ising machines
Albash, T., Martin-Mayor, V., & Hen, I. (2019) · Quantum Science and Technology · doi:10.1088/2058-9565/ab13ea · Cited by 45 · see citing works
Enhancing quantum annealing performance for the molecular similarity problem
Hernandez, M., & Aramon, M. (2017) · Quantum Information Processing · doi:10.1007/s11128-017-1586-y · Cited by 42 · see citing works
Quantum-enhanced greedy combinatorial optimization solver
Dupont, M., Evert, B., Hodson, M. J., Sundar, B., Jeffrey, S., Yamaguchi, Y., Feng, D., Maciejewski, F. B., Hadfield, S., Alam, M. S., et al. (2023) · Science Advances · doi:10.1126/sciadv.adi0487 · Cited by 41 · see citing works
Self-citationCharged particle tracking with quantum annealing optimization
Zlokapa, A., Anand, A., Vlimant, J.-R., Duarte, J. M., Job, J., Lidar, D. A., & Spiropulu, M. (2021) · Quantum Machine Intelligence · doi:10.1007/s42484-021-00054-w · Cited by 42 · see citing works
Embedding Overhead Scaling of Optimization Problems in Quantum Annealing
Könz, M. S., Lechner, W., Katzgraber, H. G., & Troyer, M. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.040322 · Cited by 43 · see citing works
Constructing SAT Filters with a Quantum Annealer
Douglass, A., King, A. D., & Raymond, J. (2015) · Lecture notes in computer science · doi:10.1007/978-3-319-24318-4_9 · Cited by 41 · see citing works
Systematic and deterministic graph minor embedding for Cartesian products of graphs
Zaribafiyan, A., Marchand, D. J. J., & Rezaei, S. S. C. (2017) · Quantum Information Processing · doi:10.1007/s11128-017-1569-z · Cited by 39 · see citing works
Algorithm engineering for a quantum annealing platform
King, A. D., & McGeoch, C. C. (2014) · arXiv · doi:10.48550/arxiv.1410.2628 · Cited by 39 · see citing works
Mean Field Analysis of Quantum Annealing Correction
Matsuura, S., Nishimori, H., Albash, T., & Lidar, D. A. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.220501 · Cited by 38 · see citing works
Scaling Advantage in Approximate Optimization with Quantum Annealing
Munoz-Bauza, H., & Lidar, D. A. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.160601 · Cited by 46 · see citing works
Job, J., & Lidar, D. A. (2018) · Quantum Science and Technology · doi:10.1088/2058-9565/aabd9b · Cited by 33 · see citing works
A Fully-Connected Ising Model Embedding Method and Its Evaluation for CMOS Annealing Machines
Oku, D., Terada, K., HAYASHI, M., Yamaoka, M., Tanaka, S., & Togawa, N. (2019) · IEICE Transactions on Information and Systems · doi:10.1587/transinf.2018edp7411 · Cited by 33 · see citing works
Practical engineering of hard spin-glass instances
Marshall, J., Martín-Mayor, V., & Hen, I. (2016) · Physical Review A · doi:10.1103/physreva.94.012320 · Cited by 31 · see citing works
Towards quantum belief propagation for LDPC decoding in wireless networks
Kasi, S., & Jamieson, K. (2020) · ACM Annual International Conference on Mobile Computing and Networking (MobiCom) · doi:10.1145/3372224.3419207 · Cited by 33 · see citing works
Solving the resource constrained project scheduling problem with quantum annealing
Armas, L. F. P., Creemers, S., & Deleplanque, S. (2024) · Scientific Reports · doi:10.1038/s41598-024-67168-6 · Cited by 33 · see citing works
Quantum-Enhanced Reinforcement Learning for Finite-Episode Games with Discrete State Spaces
Neukart, F., Dollen, D. V., Seidel, C., & Compostella, G. (2018) · Frontiers in Physics · doi:10.3389/fphy.2017.00071 · Cited by 31 · see citing works
Combinatorial Optimization on Gate Model Quantum Computers: A Survey
Zahedinejad, E., & Zaribafiyan, A. (2017) · arXiv · doi:10.48550/arxiv.1708.05294 · Cited by 29 · see citing works
The pitfalls of planar spin-glass benchmarks: raising the bar for quantum annealers (again)
Mandrà, S., Katzgraber, H. G., & Thomas, C. (2017) · Quantum Science and Technology · doi:10.1088/2058-9565/aa7877 · Cited by 35 · see citing works
Self-citationImproving the Solving of Optimization Problems: A Comprehensive Review of Quantum Approaches
Volpe, D., Orlandi, G., & Turvani, G. (2025) · Quantum Reports · doi:10.3390/quantum7010003 · Cited by 32 · see citing works
Pelofske, E. (2025) · Quantum Science and Technology · doi:10.1088/2058-9565/adb029 · Cited by 31 · see citing works
Degeneracy, degree, and heavy tails in quantum annealing
King, A. D., Hoskinson, E., Lanting, T. M., Andriyash, E., & Amin, M. H. S. (2016) · Physical Review A · doi:10.1103/physreva.93.052320 · Cited by 27 · see citing works
Direct comparison of quantum and simulated annealing on a fully connected Ising ferromagnet
Wauters, M. M., Fazio, R., Nishimori, H., & Santoro, G. E. (2017) · Physical Review A · doi:10.1103/physreva.96.022326 · Cited by 29 · see citing works
Simulated-quantum-annealing comparison between all-to-all connectivity schemes
Albash, T., Vinci, W., & Lidar, D. A. (2016) · Physical Review A · doi:10.1103/physreva.94.022327 · Cited by 27 · see citing works
Open-System Quantum Annealing in Mean-Field Models with Exponential Degeneracy
Kechedzhi, K., & Smelyanskiy, V. (2016) · Physical Review X · doi:10.1103/physrevx.6.021028 · Cited by 28 · see citing works
Self-citationOptimally Stopped Optimization
Vinci, W., & Lidar, D. A. (2016) · Physical Review Applied · doi:10.1103/physrevapplied.6.054016 · Cited by 27 · see citing works
Benchmarking Adiabatic Quantum Optimization for Complex Network Analysis
Sandia National Laboratories (SNL), A., Parekh, O., Administration, U. A. S. F. H. R. A., Wendt, J., Shulenburger, L., Landahl, A. J., Moussa, J. E., & Aidun, J. B. (2015) · doi:10.2172/1459086 · Cited by 28 · see citing works
Sugie, Y., Yoshida, Y., Mertig, N., Takemoto, T., Teramoto, H., Nakamura, A., Takigawa, I., Minato, S.-I., Yamaoka, M., & Komatsuzaki, T. (2021) · Soft Computing · doi:10.1007/s00500-020-05502-6 · Cited by 26 · see citing works
Parameter setting for quantum annealers
Pudenz, K. L. (2016) · IEEE High Performance Extreme Computing Conference · doi:10.1109/hpec.2016.7761619 · Cited by 25 · see citing works
Equation Planting: A Tool for Benchmarking Ising Machines
Hen, I. (2019) · Physical Review Applied · doi:10.1103/physrevapplied.12.011003 · Cited by 25 · see citing works
A Hybrid Quantum-Classical Paradigm to Mitigate Embedding Costs in Quantum AnnealingPreprint
Abbott, A. A., Calude, C. S., Dinneen, M. J., & Hua, R. (2018) · ResearchSpace (University of Auckland) · doi:10.48550/arxiv.1803.04340 · Cited by 22 · see citing works
Quadratic Unconstrained Binary Optimization via Quantum-Inspired Annealing
Bowles, J., Dauphin, A., Huembeli, P., Martinez, J., & Acín, A. (2022) · Physical Review Applied · doi:10.1103/physrevapplied.18.034016 · Cited by 23 · see citing works
Advancing CMOS-Type Ising Arithmetic Unit into the Domain of Real-World Applications
Zhang, J., Chen, S., & Wang, Y. (2017) · IEEE Transactions on Computers · doi:10.1109/tc.2017.2775618 · Cited by 23 · see citing works
Jiang, D., Wang, X., Huang, Z., Yang, Y., & Yao, E. (2023) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2023.3263923 · Cited by 22 · see citing works
How to Reduce the Bit-Width of an Ising Model by Adding Auxiliary Spins
Oku, D., Tawada, M., Tanaka, S., & Togawa, N. (2020) · IEEE Transactions on Computers · doi:10.1109/tc.2020.3045112 · Cited by 24 · see citing works
Nested quantum annealing correction at finite temperature: p -spin models
Matsuura, S., Nishimori, H., Vinci, W., & Lidar, D. A. (2019) · Physical Review A · doi:10.1103/physreva.99.062307 · Cited by 21 · see citing works
Solving Set Cover with Pairs Problem using Quantum Annealing
Cao, Y., Jiang, S., Perouli, D., & Kais, S. (2016) · Scientific Reports · doi:10.1038/srep33957 · Cited by 21 · see citing works
Quantum adiabatic machine learning by zooming into a region of the energy surface
Zlokapa, A., Mott, A., Job, J., Vlimant, J.-R., Lidar, D. A., & Spiropulu, M. (2020) · Physical Review A · doi:10.1103/physreva.102.062405 · Cited by 22 · see citing works
Accelerating Scientific Computing in the Post-Moore’s Era
Hamilton, K. E., Schuman, C. D., Young, S. R., Bennink, R. S., Imam, N., & Humble, T. S. (2020) · ACM Transactions on Parallel Computing · doi:10.1145/3380940 · Cited by 22 · see citing works
Quantum-Assisted Cluster Analysis on a Quantum Annealing Device
Neukart, F., Dollen, D. V., & Seidel, C. (2018) · Frontiers in Physics · doi:10.3389/fphy.2018.00055 · Cited by 27 · see citing works
Benchmarking embedded chain breaking in quantum annealing *
Grant, E., & Humble, T. S. (2021) · Quantum Science and Technology · doi:10.1088/2058-9565/ac26d2 · Cited by 22 · see citing works
Perils of embedding for sampling problems
Marshall, J., Gioacchino, A. D., & Rieffel, E. G. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.023020 · Cited by 18 · see citing works
Quantum annealing for vehicle routing problem with weighted segment
Tambunan, T. D., Suksmono, A. B., Edward, I. J. M., & Mulyawan, R. (2023) · AIP conference proceedings · doi:10.1063/5.0178362 · Cited by 22 · see citing works
- Authors
- Venturelli, D., Mandrà, S., Knysh, S., O’Gorman, B., Biswas, R., & Smelyanskiy, V.
- Affiliations
- Ames Research Center (US)
- Google (United States) (US)
- Venue
- Physical Review X
- Publisher
- American Physical Society (APS)
- Published
- 2015-09-18
- Volume
- 5
- Issue
- 3
- ISSN
- 2160-3308 (ISSN-L)
- OpenAlex
- W1553502100
- Cited by
- 209
- References
- 35
- Citations by year
- 2026: 6 · 2025: 19 · 2024: 19 · 2023: 15 · 2022: 14 · 2021: 19 · 2020: 19 · 2019: 23 · 2018: 15 · 2017: 18 · 2016: 21 · 2015: 19 · 2014: 2
- FWCI
- 23.86
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Physical Review X (publishedVersion, cc-by)
- arXiv (Cornell University) (submittedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University)
- Funders
- National Aeronautics and Space Administration (NNX14AF62G, NNX12AK33A)
- Office of the Director of National Intelligence
- Intelligence Advanced Research Projects Activity
- AFRL Information Directorate (F4HBKC4162G001)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum annealing, spin glass, combinatorial optimization, quantum annealers, hard optimization problems
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
