- 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

Parameter-efficient quantum anomaly detection method on a superconducting quantum processor

Maida Wang1, Jinyang Jiang2, and Peter V. Coveney1,3,4,*

  • *Contact author: p.v.coveney@ucl.ac.uk
PDF

Phys. Rev. Research 7, 043094 – Published 23 October, 2025

DOI: https://doi.org/10.1103/cv9y-2cnj

Abstract

Quantum machine learning has gained attention for its potential to address computational challenges. However, whether those algorithms can effectively solve practical problems and outperform their classical counterparts, especially on current quantum hardware, remains a critical question. In this work, we propose a quantum machine learning method, called Parameter-Efficient Quantum Anomaly Detection (PEQAD), for practical image anomaly detection, which aims to achieve both parameter efficiency and superior accuracy compared to classical models. Emulation results indicate that PEQAD demonstrates favorable recognition capabilities compared to classical baselines, achieving an average accuracy of over 90% on benchmarks with significantly fewer trainable parameters. Theoretical analysis suggests that PEQAD has a comparable expressivity to classical counterparts while requiring only a fraction of the parameters. Furthermore, we demonstrate the first implementation of a quantum anomaly detection method for general image datasets on a superconducting quantum processor. Specifically, we achieve an accuracy of over 80% with only 16 parameters on the device, providing initial evidence of PEQAD’s practical viability and highlighting its significant reduction in parameter requirements.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (69)

  1. E. Bernstein and U. Vazirani, Quantum complexity theory, in Proceedings of the 25th Annual ACM Symposium on Theory of Computing (ACM Press, New York, NY, 1993), pp. 11–20.
  2. L. K Grover, A fast quantum mechanical algorithm for database search, in Proceedings of the 28th Annual ACM Symposium on Theory of Computing (STOC) (ACM Press, New York, NY, 1996), pp. 212–219.
  3. P. W. Shor, Algorithms for quantum computation: Discrete logarithms and factoring, in Proceedings of the 35th Annual Symposium on Foundations of Computer Science (IEEE, New York, 1994), pp. 124–134.
  4. H.-S. Zhong et al., Quantum computational advantage using photons, Science 370, 1460 (2020).
  5. J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).
  6. J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, Quantum machine learning, Nature (London) 549, 195 (2017).
  7. J. Romero and A. Aspuru-Guzik, Variational quantum generators: Generative adversarial quantum machine learning for continuous distributions, Adv. Quantum Technol. 4, 2000003 (2021).
  8. 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).
  9. J. Kübler, S. Buchholz, and B. Schölkopf, The inductive bias of quantum kernels, Adv. Neural Inf. Process. Syst. 34, 12661 (2021).
  10. 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).
  11. A. Lavin and S. Ahmad, Evaluating real-time anomaly detection algorithms—The numenta anomaly benchmark, in Proceedings of the 2015 IEEE 14th International Conference on Machine Learning and Applications (ICMLA) (IEEE, Piscataway, NJ, 2015), pp. 38–44.
  12. P. Garcia-Teodoro, J. Diaz-Verdejo, G. Maciá-Fernández, and E. Vázquez, Anomaly-based network intrusion detection: Techniques, systems and challenges, Comput. Secur. 28, 18 (2009).
  13. C. Phua, V. Lee, K. Smith, and R. Gayler, A comprehensive survey of data mining-based fraud detection research, arXiv:1009.6119.
  14. T. Schlegl, P. Seeböck, S. M. Waldstein, U. Schmidt-Erfurth, and G. Langs, Unsupervised anomaly detection with generative adversarial networks to guide marker discovery, in Proceedings of the International Conference on Information Processing in Medical Imaging, IPMI 2017, edited by M. Niethammer et al., Lecture Notes in Computer Science Vol. 10265 (Springer, Cham, 2017).
  15. J. An and S. Cho, Variational autoencoder based anomaly detection using reconstruction probability, Special Lecture on IE 2, 1 (2015).
  16. L. Ruff, R. Vandermeulen, N. Goernitz, L. Deecke, S. A. Siddiqui, A. Binder, E. Müller, and M. Kloft, Deep one-class classification, in Proceedings of the International Conference on Machine Learning (PMLR, 2018), pp. 4393–4402.
  17. Q. Yu, C. Li, Y. Zhu, and T. Kurita, Convolutional autoencoder based on latent subspace projection for anomaly detection, Methods 214, 48 (2023).
  18. J. J. Engelsma and A. K. Jain, Generalizing fingerprint spoof detector: Learning a one-class classifier, in Proceedings of the 2019 International Conference on Biometrics (ICB) (IEEE, Piscataway, NJ, 2019), pp. 1–8.
  19. G. Park, J. Huh, and D. K. Park, Variational quantum one-class classifier, Mach. Learn.: Sci. Technol. 4, 015006 (2023).
  20. V. Belis, K. A. Woźniak, E. Puljak, P. Barkoutsos, G. Dissertori, M. Grossi, M. Pierini, F. Reiter, I. Tavernelli, and S. Vallecorsa, Quantum anomaly detection in the latent space of proton collision events at the LHC, Commun. Phys. 7, 334 (2024).
  21. A. Senokosov, V. Belis, M. Grossi, A. Hart, E. Kühn, M. Pierini, E. Puljak, F. Reiter, K. A. Wozniak, and S. Vallecorsa, Quantum-enhanced support vector machine for anomaly detection in high-energy physics, Mach. Learn.: Sci. Technol. 5, 015040 (2024).
  22. J. Romero, J. P. Olson, and A. Aspuru-Guzik, Quantum autoencoders for efficient compression of quantum data, Quantum Sci. Technol. 2, 045001 (2017).
  23. L. Lamata, U. Alvarez-Rodriguez, J. D. Martín-Guerrero, M. Sanz, and E. Solano, Quantum autoencoders via quantum adders with genetic algorithms, Quantum Sci. Technol. 4, 014007 (2018).
  24. Y. Ding, L. Lamata, M. Sanz, X. Chen, and E. Solano, Experimental implementation of a quantum autoencoder via quantum adders, Adv. Quantum Technol. 2, 1800065 (2019).
  25. M. Kieferová and N. Wiebe, Tomography and generative training with quantum Boltzmann machines, Phys. Rev. A 96, 062327 (2017).
  26. S. Jain, J. Ziauddin, P. Leonchyk, S. Yenkanchi, and J. Geraci, Quantum and classical machine learning for the classification of non-small-cell lung cancer patients, SN Appl. Sci. 2, 1088 (2020).
  27. P.-L. Dallaire-Demers and N. Killoran, Quantum generative adversarial networks, Phys. Rev. A 98, 012324 (2018).
  28. S. Lloyd and C. Weedbrook, Quantum generative adversarial learning, Phys. Rev. Lett. 121, 040502 (2018).
  29. J. Zeng, Y. Wu, J.-G. Liu, L. Wang, and J. Hu, Learning and inference on generative adversarial quantum circuits, Phys. Rev. A 99, 052306 (2019).
  30. P. Rebentrost, M. Mohseni, and S. Lloyd, Quantum support vector machine for big data classification, Phys. Rev. Lett. 113, 130503 (2014).
  31. R. Mengoni and A. Di Pierro, Kernel methods in quantum machine learning, Quantum Mach. Intell. 1, 65 (2019).
  32. H.-Y. Huang, M. Broughton, J. Cotler, S. Chen, J. Li, M. Mohseni, H. Neven, R. Babbush, R. Kueng, J. Preskill et al., Quantum advantage in learning from experiments, Science 376, 1182 (2022).
  33. J. Cotler, H.-Y. Huang, and J. R. McClean, Revisiting dequantization and quantum advantage in learning tasks, arXiv:2112.00811.
  34. S. Chen, J. Cotler, H.-Y. Huang, and J. Li, A hierarchy for replica quantum advantage, arXiv:2111.05874.
  35. E. Parzen, On estimation of a probability density function and mode, Ann. Math. Stat. 33, 1065 (1962).
  36. B. Schölkopf, J. C. Platt, J. Shawe-Taylor, A. J. Smola, and R. C. Williamson, Estimating the support of a high-dimensional distribution, Neural Comput. 13, 1443 (2001).
  37. D. M. J. Tax and R. P. W. Duin, Support vector data description, Mach. Learn. 54, 45 (2004).
  38. 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).
  39. V. Giovannetti, S. Lloyd, and L. Maccone, Quantum random access memory, Phys. Rev. Lett. 100, 160501 (2008).
  40. M. Schuld and N. Killoran, Quantum machine learning in feature Hilbert spaces, Phys. Rev. Lett. 122, 040504 (2019).
  41. S. Lloyd, M. Schuld, A. Ijaz, J. Izaac, and N. Killoran, Quantum embeddings for machine learning, arXiv:2001.03622.
  42. D. Silver, T. Patel, and D. Tiwari, Quilt: Effective multi-class classification on quantum computers using an ensemble of diverse quantum classifiers, in Proceedings of the AAAI Conference on Artificial Intelligence (AAAI Press, Reston, VA, 2022), Vol. 36, pp. 8324–8332.
  43. T. Patel, D. Silver, and D. Tiwari, Optic: A practical quantum binary classifier for near-term quantum computers, in 2022 Design, Automation & Test in Europe Conference & Exhibition (DATE) (IEEE, 2022), pp. 334–339.
  44. Román Orús, A practical introduction to tensor networks: Matrix product states and projected entangled pair states, Ann. Phys. 349, 117 (2014).
  45. M. Wang, A. Huang, Y. Liu, X. Yi, J. Wu, and S. Wang, A quantum-classical hybrid solution for deep anomaly detection, Entropy 25, 427 (2023).
  46. D. Wierichs, J. Izaac, C. Wang, and C. Y.-Y. Lin, General parameter-shift rules for quantum gradients, Quantum 6, 677 (2022).
  47. Y. Du, Z. Tu, X. Yuan, and D. Tao, Efficient measure for the expressivity of variational quantum algorithms, Phys. Rev. Lett. 128, 080506 (2022).
  48. Z. Holmes, K. Sharma, M. Cerezo, and P. J. Coles, Connecting ansatz expressibility to gradient magnitudes and barren plateaus, PRX Quantum 3, 010313 (2022).
  49. V. Vapnik, The Nature of Statistical Learning Theory (Springer Science & Business Media, New York, 2013).
  50. M. Mohri, A. Rostamizadeh, and A. Talwalkar, Foundations of Machine Learning (MIT Press, Cambridge, MA, 2018).
  51. P. L. Bartlett, D. J. Foster, and M. J. Telgarsky, Spectrally-normalized margin bounds for neural networks, in Advances in Neural Information Processing Systems, edited by I. Guyon, U. Von Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (Curran Associates, Red Hook, NY, 2017), Vol. 30.
  52. Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, Gradient-based learning applied to document recognition, Proc. IEEE 86, 2278 (1998).
  53. H. Xiao, K. Rasul, and R. Vollgraf, Fashion-mnist: A novel image dataset for benchmarking machine learning algorithms, arXiv:1708.07747.
  54. A. Krizhevsky and G. Hinton, Learning multiple layers of features from tiny images, Technical report, University of Toronto, 2009.
  55. P. Perera, P. Oza, and V. M. Patel, One-class classification: A survey, arXiv:2101.03064.
  56. V. Bergholm, J. Izaac, M. Schuld, C. Gogolin, S. Ahmed, V. Ajith, M. S. Alam, G. Alonso-Linaje, B. AkashNarayanan, A. Asadi et al., Pennylane: Automatic differentiation of hybrid quantum-classical computations, arXiv:1811.04968.
  57. D. P. Kingma, J. Ba, Y. Bengio, and Y. LeCun, 3rd International Conference on Learning Representation (ICLR, San Diego, 2015).
  58. A. Sebastianelli, D. A. Zaidenberg, D. Spiller, B. L. Saux, and S. L. Ullo, On circuit-based hybrid quantum neural networks for remote sensing imagery classification, IEEE J. Sel. Top. Appl. 15, 565 (2021).
  59. Y. Zeng, H. Wang, J. He, Q. Huang, and S. Chang, A multi-classification hybrid quantum neural network using an all-qubit multi-observable measurement strategy, Entropy 24, 394 (2022).
  60. A. Mari, T. R. Bromley, J. Izaac, M. Schuld, and N. Killoran, Transfer learning in hybrid classical-quantum neural networks, Quantum 4, 340 (2020).
  61. Institute of quantum Information and chinese academy of sciences quantum technology innovation, oned12: A 12-qubit superconducting quantum processor.
  62. J. C. Spall, Multivariate stochastic approximation using a simultaneous perturbation gradient approximation, IEEE Trans. Autom. Control 37, 332 (1992).
  63. http://yann.lecun.com/exdb/mnist/.
  64. https://github.com/zalandoresearch/fashion-mnist.
  65. https://www.cs.toronto.edu/kriz/cifar.html.
  66. https://github.com/UCL-CCS/PEQAD.git.
  67. T. Barthel and J. Lu, Fundamental limitations for measurements in quantum many-body systems, Phys. Rev. Lett. 121, 080406 (2018).
  68. D. Weingarten, Asymptotic behavior of group integrals in the limit of infinite rank, J. Math. Phys. 19, 999 (1978).
  69. Y. Yao and Y. Hasegawa, Direct gradient computation of parameterized quantum circuits, arXiv:2503.05145.

Outline

Information

Phys. Rev. Research 7, 043094– Published 23 October, 2025
  • Received 31 March 2025
  • Accepted 22 September 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