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Beyond optimization: Harnessing quantum annealer dynamics for machine learning

Akitada Sakurai1,*, Aoi Hayashi1, Tadayoshi Matsumori2, Daisuke Kaji3, Tadashi Kadowaki4,3, and Kae Nemoto1,†

  • *Contact author: akitada.sakurai@oist.jp
  • †Contact author: kae.nemoto@oist.jp
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Phys. Rev. Research 8, 033161 – Published 10 August, 2026

DOI: https://doi.org/10.1103/dcvc-blqy

Abstract

Quantum annealing is typically regarded as a tool for combinatorial optimization, but its coherent dynamics also offer potential for machine learning. We present a model that encodes classical data into an Ising Hamiltonian, evolves it on a quantum annealer, and uses the resulting probability distributions as feature maps for classification. Experiments on the quantum annealer machine with the Digits dataset, together with simulations on MNIST, demonstrate that short annealing times yield higher classification accuracy, while longer times reduce accuracy but lower sampling costs. We introduce the participation ratio as a measure of the effective support of the output probability distribution and show its strong correlation with generalization.

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References (43)

  1. T. Kadowaki and H. Nishimori, Quantum annealing in the transverse Ising model, Phys. Rev. E 58, 5355 (1998).
  2. A. Das, B. K. Chakrabarti, and R. B. Stinchcombe, Quantum annealing in a kinetically constrained system, Phys. Rev. E 72, 026701 (2005).
  3. G. E. Santoro and E. Tosatti, Optimization using quantum mechanics: Quantum annealing through adiabatic evolution, J. Phys. A: Math. Gen. 39, R393 (2006).
  4. A. Das and B. K. Chakrabarti, Colloquium: Quantum annealing and analog quantum computation, Rev. Mod. Phys. 80, 1061 (2008).
  5. S. Morita and H. Nishimori, Mathematical foundation of quantum annealing, J. Math. Phys. 49, 125210 (2008).
  6. T. Albash and D. A. Lidar, Adiabatic quantum computation, Rev. Mod. Phys. 90, 015002 (2018).
  7. P. Hauke, H. G. Katzgraber, W. Lechner, H. Nishimori, and W. D. Oliver, Perspectives of quantum annealing: Methods and implementations, Rep. Prog. Phys. 83, 054401 (2020).
  8. C. C. McGeoch, Adiabatic Quantum Computation and Quantum Annealing: Theory and Practice, Synthesis Lectures on Quantum Computing (SLQC) (Springer Cham, Switzerland, 2014).
  9. D-Wave Systems Inc., D-Wave Leap Quantum Cloud Service, 2025, https://docs.dwavesys.com/docs/latest/index.html, accessed: 25 December 2025.
  10. J. Wurtz, P. Lopes, N. Gemelke, A. Keesling, and S. Wang, Industry applications of neutral-atom quantum computing solving independent set problems, arXiv:2205.08500.
  11. A. D. King et al., Quantum critical dynamics in a 5,000-qubit programmable spin glass, Nature (London) 617, 61 (2023).
  12. A. D. King et al., Beyond-classical computation in quantum simulation, Science 388, 199 (2025).
  13. H. Neven, V. S. Denchev, G. Rose, and W. G. Macready, Training a large scale classifier with the quantum adiabatic algorithm, arXiv:0912.0779.
  14. A. Mott, J. Job, J.-R. Vlimant, D. Lidar, and M. Spiropulu, Solving a Higgs optimization problem with quantum annealing for machine learning, Nature (London) 550, 375 (2017).
  15. D. Crawford, A. Levit, N. Ghadermarzy, J. S. Oberoi, and P. Ronagh, Reinforcement learning using quantum Boltzmann machines, Quantum Inf. Comput. 18, 51 (2018).
  16. J. Liu, F. M. Spedalieri, K.-T. Yao, T. E. Potok, C. Schuman, S. Young, R. Patton, G. S. Rose, and G. Chamka, Adiabatic quantum computation applied to deep learning networks, Entropy 20, 380 (2018).
  17. T. Sato, M. Ohzeki, and K. Tanaka, Assessment of image generation by quantum annealer, Sci. Rep. 11, 13523 (2021).
  18. R. Shibukawa, R. Tamura, and K. Tsuda, Boltzmann sampling with quantum annealers via fast Stein correction, Phys. Rev. Res. 6, 043050 (2024).
  19. R. Y. Li, R. Di Felice, R. Rohs, and D. A. Lidar, Quantum annealing versus classical machine learning applied to a simplified computational biology problem, npj Quantum Inf. 4, 14 (2018).
  20. H. Salloum, K. Sabbagh, V. Savchuk, R. Lukin, O. Orabi, M. Isangulov, and M. Mazzara, Performance of quantum annealing machine learning classification models on ADMET datasets, IEEE Access 13, 16263 (2025).
  21. K. Fujii and K. Nakajima, Harnessing disordered-ensemble quantum dynamics for machine learning, Phys. Rev. Appl. 8, 024030 (2017).
  22. K. Fujii, H. Kobayashi, T. Morimae, H. Nishimura, S. Tamate, and S. Tani, Impossibility of classically simulating one-clean-qubit model with multiplicative error, Phys. Rev. Lett. 120, 200502 (2018).
  23. K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii, Quantum circuit learning, Phys. Rev. A 98, 032309 (2018).
  24. K. Fujii and K. Nakajima, Quantum reservoir computing: A reservoir approach toward quantum machine learning on near-term quantum devices, in Reservoir Computing: Theory, Physical Implementations, and Applications, edited by K. Nakajima and I. Fischer (Springer, Singapore, 2021), pp. 423–450.
  25. K. Nakajima, K. Fujii, M. Negoro, K. Mitarai, and M. Kitagawa, Boosting computational power through spatial multiplexing in quantum reservoir computing, Phys. Rev. Appl. 11, 034021 (2019).
  26. Y. Suzuki, Q. Gao, K. C. Pradel, K. Yasuoka, and N. Yamamoto, Natural quantum reservoir computing for temporal information processing, Sci. Rep. 12, 1353 (2022).
  27. R. A. Bravo, K. Najafi, X. Gao, and S. F. Yelin, Quantum reservoir computing using arrays of Rydberg atoms, PRX Quantum 3, 030325 (2022).
  28. P. Pfeffer, F. Heyder, and J. Schumacher, Hybrid quantum-classical reservoir computing of thermal convection flow, Phys. Rev. Res. 4, 033176 (2022).
  29. P. Mujal, R. Martínez-Peña, G. L. Giorgi, M. C. Soriano, and R. Zambrini, Time-series quantum reservoir computing with weak and projective measurements, npj Quantum Inf. 9, 16 (2023).
  30. A. Hayashi, A. Sakurai, S. Nishio, W. J. Munro, and K. Nemoto, Impact of the form of weighted networks on the quantum extreme reservoir computation, Phys. Rev. A 108, 042609 (2023).
  31. M. Noori, S. S. Vedaie, I. Singh, D. Crawford, J. S. Oberoi, B. C. Sanders, and E. Zahedinejad, Analog-quantum feature mapping for machine-learning applications, Phys. Rev. Appl. 14, 034034 (2020).
  32. F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, and E. Duchesnay, Scikit-learn: Machine learning in Python, J. Mach. Learn. Res. 12, 2825 (2011).
  33. E. Alpaydin and C. Kaynak, Optical recognition of handwritten digits, UCI Machine Learning Repository, 1998, https://doi.org/10.24432/C50P49
  34. K. Boothby, P. Bunyk, J. Raymond, and A. Roy, Next-generation topology of D-Wave quantum processors, arXiv:2003.00133.
  35. D-Wave Systems Inc., D-Wave documentation, 2025, https://docs.dwavequantum.com/en/latest/quantum_research/solver_properties_specific.html.
  36. L. Deng, The MNIST database of handwritten digit images for machine learning research [Best of the Web], IEEE Signal Process. Mag. 29, 141 (2012).
  37. J. T. Edwards and D. J. Thouless, Numerical studies of localization in disordered systems, J. Phys. C 5, 807 (1972).
  38. V. Mehta, H. De Raedt, K. Michielsen, and F. Jin, Understanding the physics of D-Wave annealers: From Schrödinger to Lindblad to Markovian dynamics, Phys. Rev. A 112, 032616 (2025).
  39. A. Sakurai, A. Hayashi, W. J. Munro, and K. Nemoto, Simple Hamiltonian dynamics as a powerful resource for image classification, Phys. Rev. A 111, 052432 (2025).
  40. A. Sakurai, A. Hayashi, W. J. Munro, and K. Nemoto, Quantum optical reservoir computing powered by boson sampling, Opt. Quantum 3, 238 (2025).
  41. S. Haykin, Neural Networks and Learning Machines, 3rd ed. (Pearson, London, UK, 2010).
  42. A. Sakurai, M. P. Estarellas, W. J. Munro, and K. Nemoto, Quantum extreme reservoir computation utilizing scale-free networks, Phys. Rev. Appl. 17, 064044 (2022).
  43. J. Duchi, E. Hazan, and Y. Singer, Adaptive subgradient methods for online learning and stochastic optimization, J. Mach. Learn. Res. 12, 2121 (2011).

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Phys. Rev. Research 8, 033161– Published 10 August, 2026
  • Received 23 December 2025
  • Accepted 10 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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