- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

VQE-generated quantum circuit dataset for machine learning

Akimoto Nakayama1,*, Kosuke Mitarai1,2,†, Leonardo Placidi1,2, Takanori Sugimoto2,3,4, and Keisuke Fujii1,2,5,‡

  • *Contact author: akimoto.nakayama@gmail.com
  • †Contact author: mitarai.kosuke.es@osaka-u.ac.jp
  • ‡Contact author: fujii@qc.ee.es.osaka-u.ac.jp
PDF

Phys. Rev. Research 7, 033048 – Published 11 July, 2025

DOI: https://doi.org/10.1103/c43x-9866

Abstract

Quantum machine learning has the potential to computationally outperform classical machine learning, but it is not yet clear whether it will actually be valuable for practical problems. While some artificial scenarios have shown that certain quantum machine learning techniques may be advantageous compared to their classical counterpart, evidence does not yet suggest that quantum machine learning has surpassed conventional approaches in dealing with standard classical datasets, such as the MNIST dataset. In contrast, dealing with quantum data, such as quantum states or circuits, may be the task where we can benefit from quantum methods. Therefore, it is important to develop practically meaningful quantum datasets for which we expect quantum methods to be superior. In this paper, we propose a machine learning task that is likely to soon arise in the real world: clustering and classification of quantum circuits. We provide a dataset of quantum circuits optimized by the variational quantum eigensolver. We utilized six common types of Hamiltonians in condensed matter physics, with a range of 4–20 qubits, and applied ten different ansatz with varying depths (ranging from 3 to 32) to generate a quantum circuit dataset of six distinct classes, each containing 300 samples. We show that this dataset can be easily learned using quantum methods. In particular, we demonstrate a successful classification of our dataset using real four-qubit devices available through IBMQ. By providing a setting and an elementary dataset where quantum machine learning is expected to be beneficial, we hope to encourage and ease the advancement of the field.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (54)

  1. J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, Quantum machine learning, Nature (London) 549, 195 (2017).
  2. M. Cerezo, G. Verdon, H.-Y. Huang, L. Cincio, and P. J. Coles, Challenges and opportunities in quantum machine learning, Nat. Comput. Sci. 2, 567 (2022).
  3. E. Farhi and H. Neven, Classification with quantum neural networks on near term processors, arXiv:1802.06002
  4. K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii, Quantum circuit learning, Phys. Rev. A 98, 032309 (2018).
  5. M. Schuld and N. Killoran, Quantum machine learning in feature hilbert spaces, Phys. Rev. Lett. 122, 040504 (2019).
  6. J.-G. Liu and L. Wang, Differentiable learning of quantum circuit born machines, Phys. Rev. A 98, 062324 (2018).
  7. M. Benedetti, D. Garcia-Pintos, O. Perdomo, V. Leyton-Ortega, Y. Nam, and A. Perdomo-Ortiz, A generative modeling approach for benchmarking and training shallow quantum circuits, npj Quantum Inf. 5, 45 (2019).
  8. V. Havlíček, A. D. Córcoles, K. Temme, A. W. Harrow, A. Kandala, J. M. Chow, and J. M. Gambetta, Supervised learning with quantum-enhanced feature spaces, Nature (London) 567, 209 (2019).
  9. T. Kusumoto, K. Mitarai, K. Fujii, M. Kitagawa, and M. Negoro, Experimental quantum kernel trick with nuclear spins in a solid, npj Quantum Inf. 7, 94 (2021).
  10. K. Bartkiewicz, C. Gneiting, A. Černoch, K. Jiráková, K. Lemr, and F. Nori, Experimental kernel-based quantum machine learning in finite feature space, Sci. Rep. 10, 1 (2020).
  11. M. S. Rudolph, N. B. Toussaint, A. Katabarwa, S. Johri, B. Peropadre, and A. Perdomo-Ortiz, Generation of high-resolution handwritten digits with an ion-trap quantum computer, Phys. Rev. X 12, 031010 (2022).
  12. Y. Liu, S. Arunachalam, and K. Temme, A rigorous and robust quantum speed-up in supervised machine learning, Nat. Phys. 17, 1013 (2021).
  13. H.-Y. Huang, M. Broughton, M. Mohseni, R. Babbush, S. Boixo, H. Neven, and J. R. McClean, Power of data in quantum machine learning, Nat. Commun. 12, 2631 (2021).
  14. V. Dunjko, Y.-K. Liu, X. Wu, and J. M. Taylor, Exponential improvements for quantum-accessible reinforcement learning, arXiv:1710.11160.
  15. S. Jerbi, C. Gyurik, S. Marshall, H. Briegel, and V. Dunjko, Parametrized quantum policies for reinforcement learning, in Advances in Neural Information Processing Systems, edited by M. Ranzato, A. Beygelzimer, Y. Dauphin, P. Liang, and J. W. Vaughan (Curran Associates, Inc., 2021), Vol. 34, pp. 28362–28375.
  16. N. Pirnay, R. Sweke, J. Eisert, and J.-P. Seifert, A super-polynomial quantum-classical separation for density modelling, Phys. Rev. A 107, 042416 (2023).
  17. Y. Lecun, L. Bottou, Y. Bengio, and P. Haffner, Gradient-based learning applied to document recognition, Proc. IEEE 86, 2278 (1998).
  18. H. Xiao, K. Rasul, and R. Vollgraf, Fashion-mnist: a novel image dataset for benchmarking machine learning algorithms, arXiv:1708.07747.
  19. H.-Y. Huang, M. Broughton, J. Cotler, S. Chen, J. Li, M. Mohseni, H. Neven, R. Babbush, R. Kueng, J. Preskill, and J. R. McClean, Quantum advantage in learning from experiments, Science 376, 1182 (2022).
  20. L. Schatzki, A. Arrasmith, P. J. Coles, and M. Cerezo, Entangled datasets for quantum machine learning, arXiv:2109.03400.
  21. E. Perrier, A. Youssry, and C. Ferrie, Qdataset, quantum datasets for machine learning, Sci. Data 9, 582 (2022).
  22. L. Placidi, R. Hataya, T. Mori, K. Aoyama, H. Morisaki, K. Mitarai, and K. Fujii, Mnisq: A large-scale quantum circuit dataset for machine learning on/for quantum computers in the nisq era, arXiv:2306.16627 (2023).
  23. E. Bernstein and U. Vazirani, Quantum complexity theory, SIAM J. Comput. 26, 1411 (1997).
  24. A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O'Brien, A variational eigenvalue solver on a photonic quantum processor, Nat. Commun. 5, 4213 (2014).
  25. J. Tilly, H. Chen, S. Cao, D. Picozzi, K. Setia, Y. Li, E. Grant, L. Wossnig, I. Rungger, G. H. Booth, and J. Tennyson, The variational quantum eigensolver: A review of methods and best practices, Phys. Rep. 986, 1 (2022).
  26. N. Akimoto, M. Kosuke, P. Leonardo, S. Takanori, and F. Keisuke, Qulacs-Osaka, VQE-generated dataset, GitHub repository, https://github.com/Qulacs-Osaka/VQE-generated-datase.
  27. A. Cross, A. Javadi-Abhari, T. Alexander, N. De Beaudrap, L. S. Bishop, S. Heidel, C. A. Ryan, P. Sivarajah, J. Smolin, J. M. Gambetta, and B. R. Johnson, OpenQASM 3: A Broader and Deeper Quantum Assembly Language, ACM Trans. Quantum Comput. 3, 1 (2022).
  28. A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets, Nature (London) 549, 242 (2017).
  29. K. M. Nakanishi, K. Mitarai, and K. Fujii, Subspace-search variational quantum eigensolver for excited states, Phys. Rev. Res. 1, 033062 (2019).
  30. J. M. Kübler, A. Arrasmith, L. Cincio, and P. J. Coles, An adaptive optimizer for measurement-frugal variational algorithms, Quantum 4, 263 (2020).
  31. K. M. Nakanishi, K. Fujii, and S. Todo, Sequential minimal optimization for quantum-classical hybrid algorithms, Phys. Rev. Res. 2, 043158 (2020).
  32. J. R. McClean, S. Boixo, V. N. Smelyanskiy, R. Babbush, and H. Neven, Barren plateaus in quantum neural network training landscapes, Nat. Commun. 9, 4812 (2018).
  33. R. M. Parrish, E. G. Hohenstein, P. L. McMahon, and T. J. Martínez, Quantum computation of electronic transitions using a variational quantum eigensolver, Phys. Rev. Lett. 122, 230401 (2019).
  34. L. Slattery, B. Villalonga, and B. K. Clark, Unitary block optimization for variational quantum algorithms, Phys. Rev. Res. 4, 023072 (2022).
  35. J. Dborin, F. Barratt, V. Wimalaweera, L. Wright, and A. G. Green, Matrix product state pre-training for quantum machine learning, Quantum Sci. Technol. 7, 035014 (2022).
  36. M. S. Rudolph, J. Miller, J. Chen, A. Acharya, and A. Perdomo-Ortiz, Synergy between quantum circuits and tensor networks: Short-cutting the race to practical quantum advantage, arXiv:2208.13673.
  37. D. Wecker, M. B. Hastings, and M. Troyer, Progress towards practical quantum variational algorithms, Phys. Rev. A 92, 042303 (2015).
  38. R. Wiersema, C. Zhou, Y. de Sereville, J. F. Carrasquilla, Y. B. Kim, and H. Yuen, Exploring entanglement and optimization within the hamiltonian variational ansatz, PRX Quantum 1, 020319 (2020).
  39. P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S. J. van der Walt, M. Brett, J. Wilson, K. J. Millman, N. Mayorov, A. R. J. Nelson, E. Jones, R. Kern, E. Larson, C. J. Carey et al., SciPy 1.0: Fundamental algorithms for scientific computing in python, Nat. Methods 17, 261 (2020).
  40. Y. Suzuki, Y. Kawase, Y. Masumura, Y. Hiraga, M. Nakadai, J. Chen, K. M. Nakanishi, K. Mitarai, R. Imai, S. Tamiya, T. Yamamoto, T. Yan, T. Kawakubo, Y. O. Nakagawa, Y. Ibe, Y. Zhang, H. Yamashita, H. Yoshimura, A. Hayashi, and K. Fujii, Qulacs: a fast and versatile quantum circuit simulator for research purpose, Quantum 5, 559 (2021).
  41. L. van der Maaten and G. Hinton, Visualizing data using t-SNE, J. Mach. Learn. Res. 9, 2579 (2008).
  42. J. Kruskal, Nonmetric multidimensional scaling: A numerical method, Psychometrika 29, 115 (1964).
  43. A. Novikov, PyClustering: Data Mining Library, J. Open Source Softw. 4, 1230 (2019).
  44. L. Hubert and P. Arabie, Comparing partitions, J. Classif. 2, 193 (1985).
  45. H. Wang, P. Liu, J. Cheng, Z. Liang, J. Gu, Z. Li, Y. Ding, W. Jiang, Y. Shi, X. Qian, D. Z. Pan, F. T. Chong, and S. Han, Quest: Graph transformer for quantum circuit reliability estimation, arXiv:2210.16724 v1 [quant-ph].
  46. T. N. Kipf and M. Welling, Semi-supervised classification with graph convolutional networks, arXiv:1609.02907 [cs.LG].
  47. P. Veličković, G. Cucurull, A. Casanova, A. Romero, P. Liò, and Y. Bengio, Graph attention networks, arXiv:1710.10903.
  48. K. Xu, W. Hu, J. Leskovec, and S. Jegelka, How powerful are graph neural networks? arXiv:1810.00826.
  49. W. L. Hamilton, R. Ying, and J. Leskovec, Inductive representation learning on large graphs, arXiv:1706.02216.
  50. J. Platt, Probabilistic outputs for support vector machines and comparison to regularized likelihood methods, in Advances in Large Margin Classifiers (MIT Press, Cambridge, MA, 2000).
  51. E. Grant, L. Wossnig, M. Ostaszewski, and M. Benedetti, An initialization strategy for addressing barren plateaus in parametrized quantum circuits, Quantum 3, 214 (2019).
  52. A. Skolik, J. R. McClean, M. Mohseni, P. van der Smagt, and M. Leib, Layerwise learning for quantum neural networks, Quantum Mach. Intell. 3, 5 (2021).
  53. M. S. Rudolph, J. Miller, D. Motlagh, J. Chen, A. Acharya, and A. Perdomo-Ortiz, Synergy between quantum circuits and tensor networks: Short-cutting the race to practical quantum advantage, Nat. Commun. 14, 8367 (2023).
  54. R. Watanabe, K. Fujii, and H. Ueda, Variational quantum eigensolver with embedded entanglement using a tensor-network ansatz, Phys. Rev. Res. 6, 023009 (2024).

Outline

Information

Phys. Rev. Research 7, 033048– Published 11 July, 2025
  • Received 15 June 2023
  • Accepted 17 June 2025
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation