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  • Letter
  • Open Access

Error-mitigated photonic quantum circuit Born machine

Alexia Salavrakos1,*, Tigran Sedrakyan1, James Mills1,2, Shane Mansfield1, and Rawad Mezher1

  • *Contact author: alexia.salavrakos@quandela.com
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Phys. Rev. A 111, L030401 – Published 18 March, 2025

DOI: https://doi.org/10.1103/PhysRevA.111.L030401

Abstract

In this Letter, we study quantum circuit Born machines (QCBMs) in the context of photonic quantum computing. QCBMs are a popular choice of quantum generative machine learning models, and we present a QCBM designed for linear optics. We show that a recently developed error mitigation technique called recycling mitigation greatly improves the training of QCBMs in realistic scenarios with photon loss, which is the primary source of noise in photonic systems. We demonstrate this through numerical simulations and through an experiment on a quantum photonic integrated processor. We expect our work to pave the way towards more demonstrations of error mitigation techniques tailored to photonic devices which can enhance the performance of a quantum algorithm.

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References (65)

  1. D. P. Kingma and M. Welling, in Proceedings of the 2nd International Conference on Learning Representations, ICLR 2014, Banff, AB, Canada, April 14–16, 2014, Conference Track Proceedings, edited by Y. Bengio and Y. LeCun, arXiv:1312.6114.
  2. I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, in Advances in Neural Information Processing Systems, edited by Z. Ghahramani, M. Welling, C. Cortes, N. Lawrence, and K. Weinberger (Curran Associates, Red Hook, NY, 2014), Vol. 27.
  3. J. Sohl-Dickstein, E. Weiss, N. Maheswaranathan, and S. Ganguli, in Proceedings of the 32nd International Conference on Machine Learning, edited by F. Bach and D. Blei, Proceedings of Machine Learning Research Vol. 37 (PMLR, Lille, France, 2015), pp. 2256–2265.
  4. M. Cerezo, A. Arrasmith, R. Babbush, S. C. Benjamin, S. Endo, K. Fujii, J. R. McClean, K. Mitarai, X. Yuan, L. Cincio, and P. J. Coles, Nat. Rev. Phys. 3, 625 (2021).
  5. J. Preskill, Quantum 2, 79 (2018).
  6. M. Schuld, A. Bocharov, K. M. Svore, and N. Wiebe, Phys. Rev. A 101, 032308 (2020).
  7. E. Farhi and H. Neven, arXiv:1802.06002.
  8. J. Tian, X. Sun, Y. Du, S. Zhao, Q. Liu, K. Zhang, W. Yi, W. Huang, C. Wang, X. Wu, M.-H. Hsieh, T. Liu, W. Yang, and D. Tao, arXiv:2206.03066.
  9. S. Lloyd and C. Weedbrook, Phys. Rev. Lett. 121, 040502 (2018).
  10. P.-L. Dallaire-Demers and N. Killoran, Phys. Rev. A 98, 012324 (2018).
  11. A. Khoshaman, W. Vinci, B. Denis, E. Andriyash, H. Sadeghi, and M. H. Amin, Quantum Sci. Technol. 4, 014001 (2018).
  12. M. H. Amin, E. Andriyash, J. Rolfe, B. Kulchytskyy, and R. Melko, Phys. Rev. X 8, 021050 (2018).
  13. N. Wiebe and L. Wossnig, arXiv:1905.09902.
  14. M. Benedetti, D. Garcia-Pintos, O. Perdomo, V. Leyton-Ortega, Y. Nam, and A. Perdomo-Ortiz, npj Quantum Inf. 5, 45 (2019).
  15. J.-G. Liu and L. Wang, Phys. Rev. A 98, 062324 (2018).
  16. D. Zhu, N. M. Linke, M. Benedetti, K. A. Landsman, N. H. Nguyen, C. H. Alderete, A. Perdomo-Ortiz, N. Korda, A. Garfoot, C. Brecque, L. Egan, O. Perdomo, and C. Monroe, Sci. Adv. 5, eaaw9918 (2019).
  17. M. S. Rudolph, N. B. Toussaint, A. Katabarwa, S. Johri, B. Peropadre, and A. Perdomo-Ortiz, Phys. Rev. X 12, 031010 (2022).
  18. K. E. Hamilton, E. F. Dumitrescu, and R. C. Pooser, Phys. Rev. A 99, 062323 (2019).
  19. B. Coyle, M. Henderson, J. C. J. Le, N. Kumar, M. Paini, and E. Kashefi, Quantum Sci. Technol. 6, 024013 (2021).
  20. V. Leyton-Ortega, A. Perdomo-Ortiz, and O. Perdomo, Quantum Mach. Intell. 3, 17 (2021).
  21. N. Maring, A. Fyrillas, M. Pont, E. Ivanov, P. Stepanov, N. Margaria, W. Hease, A. Pishchagin, T. H. Au, S. Boissier, E. Bertasi, A. Baert, M. Valdivia, M. Billard, O. Acar, A. Brieussel, R. Mezher, S. C. Wein, A. Salavrakos, P. Sinnott et al., Nat. Photon. 18, 603 (2024).
  22. QUANDELA Cloud (2022), https://cloud.quandela.com.
  23. H.-S. Zhong, H. Wang, Y.-H. Deng, M.-C. Chen, L.-C. Peng, Y.-H. Luo, J. Qin, D. Wu, X. Ding, Y. Hu, P. Hu, X.-Y. Yang, W.-J. Zhang, H. Li, Y. Li, X. Jiang, L. Gan, G. Yang, L. You, Z. Wang et al., Science 370, 1460 (2020).
  24. L. S. Madsen, F. Laudenbach, M. F. Askarani, F. Rortais, T. Vincent, J. F. F. Bulmer, F. M. Miatto, L. Neuhaus, L. G. Helt, M. J. Collins, A. E. Lita, T. Gerrits, S. W. Nam, V. D. Vaidya, M. Menotti, I. Dhand, Z. Vernon, N. Quesada, and J. Lavoie, Nature (London) 606, 75 (2022).
  25. C. S. Hamilton, R. Kruse, L. Sansoni, S. Barkhofen, C. Silberhorn, and I. Jex, Phys. Rev. Lett. 119, 170501 (2017).
  26. D. A. Lidar and T. A. Brun, Quantum Error Correction (Cambridge University Press, Cambridge, UK, 2013).
  27. S. Endo, S. C. Benjamin, and Y. Li, Phys. Rev. X 8, 031027 (2018).
  28. S. Endo, Z. Cai, S. C. Benjamin, and X. Yuan, J. Phys. Soc. Jpn. 90, 032001 (2021).
  29. J. Mills and R. Mezher, arXiv:2405.02278.
  30. S. Aaronson and A. Arkhipov, in STOC ‘11: Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing (ACM, New York, 2011), pp. 333–342.
  31. R. Berkowitz and P. Devlin, Isr. J. Math. 224, 437 (2018).
  32. W. R. Clements, P. C. Humphreys, B. J. Metcalf, W. S. Kolthammer, and I. A. Walmsley, Optica 3, 1460 (2016).
  33. S. Shankar and D. Towsley, Joint European Conference on Machine Learning and Knowledge Discovery in Databases (Springer, Berlin, 2022).
  34. J. Shi, Y. Tang, Y. Lu, Y. Feng, R. Shi, and S. Zhang, IEEE Trans. Knowl. Data Eng. 35, 1965 (2023).
  35. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevA.111.L030401 for more information on recycling mitigation and the no-collision regime, for more details on the model training and hyperparameters, for a description of the experimental setup, and for two theorems on the approximation of output probabilities in a boson sampling experiment, which also includes Refs. [58, 59, 60, 61, 62, 63, 64, 65].
  36. S. Kullback and R. A. Leibler, Ann. Math. Stat. 22, 79 (1951).
  37. D. A. Levin, Y. Peres, and E. L. Wilmer, Markov Chains and Mixing Times, 2nd ed. (American Mathematical Society, Providence, RI, 2017), p. 48.
  38. K. Gili, M. Hibat-Allah, M. Mauri, C. Ballance, and A. Perdomo-Ortiz, Quantum Sci. Technol. 8, 035021 (2023).
  39. M. Heusel, H. Ramsauer, T. Unterthiner, B. Nessler, and S. Hochreiter, in Advances in Neural Information Processing Systems, edited by I. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (Curran Associates, Red Hook, NY, 2017), Vol. 30.
  40. Z. Wang, A. Bovik, H. Sheikh, and E. Simoncelli, IEEE Trans. Image Process. 13, 600 (2004).
  41. A. Gretton, K. M. Borgwardt, M. J. Rasch, B. Schölkopf, and A. Smola, J. Mach. Learn. Res. 13, 723 (2012).
  42. B. Coyle, D. Mills, V. Danos, and E. Kashefi, npj Quantum Inf. 6, 60 (2020).
  43. N. Heurtel, A. Fyrillas, G. de Gliniasty, R. L. Bihan, S. Malherbe, M. Pailhas, E. Bertasi, B. Bourdoncle, P.-E. Emeriau, R. Mezher, L. Music, N. Belabas, B. Valiron, P. Senellart, S. Mansfield, and J. Senellart, Quantum 7, 931 (2023).
  44. C. Zoufal, arXiv:2111.12738.
  45. V. S. Shchesnovich, Phys. Rev. A 91, 013844 (2015).
  46. M. C. Tichy, Phys. Rev. A 91, 022316 (2015).
  47. O. V. Borzenkova, G. I. Struchalin, I. V. Kondratyev, A. D. Moiseevskiy, N. N. Skryabin, I. V. Dyakonov, and S. S. Straupe, Opt. Lett. 49, 4453 (2024).
  48. A. Fyrillas, O. Faure, N. Maring, J. Senellart, and N. Belabas, Optica 11, 427 (2024).
  49. B. Y. Gan, D. Leykam, and D. G. Angelakis, EPJ Quantum Technol. 9, 16 (2022).
  50. L. Gurvits, in Mathematical Foundations of Computer Science 2005, edited by J. Jedrzejowicz and A. Szepietowski (Springer, Berlin, 2005), pp. 447–458.
  51. S. Aaronson and T. Hance, arXiv:1212.0025.
  52. W. Hoeffding, The Collected Works of Wassily Hoeffding (Springer, Berlin, 2012).
  53. S. Aaronson and D. J. Brod, Phys. Rev. A 93, 012335 (2016).
  54. A. Bouland, D. Brod, I. Datta, B. Fefferman, D. Grier, F. Hernandez, and M. Oszmaniec, arXiv:2312.00286.
  55. M. S. Rudolph, S. Lerch, S. Thanasilp et al., npj Quantum Inf. 10, 116 (2024).
  56. A. Angrisani, A. Schmidhuber, M. S. Rudolph, M. Cerezo, Z. Holmes, and H.-Y. Huang, arXiv:2409.01706.
  57. A. Salavrakos, T. Sedrakyan, J. Mills, S. Mansfield, and R. Mezher (2024), https://github.com/Quandela/photonic-qcbm.
  58. M. Schuld, V. Bergholm, C. Gogolin, J. Izaac, and N. Killoran, Phys. Rev. A 99, 032331 (2019).
  59. J. G. Vidal and D. O. Theis, arXiv:1812.06323.
  60. G. de Felice and C. Cortlett, arXiv:2401.07997.
  61. G. Facelli, D. D. Roberts, H. Wallner, A. Makarovskiy, Z. Holmes, and W. R. Clements, arXiv:2409.16369.
  62. A. Pappalardo, P.-E. Emeriau, G. de Felice, B. Ventura, H. Jaunin, R. Yeung, B. Coecke, and S. Mansfield, arXiv:2410.02726.
  63. J. C. Spall, Johns Hopkins APL Tech. Dig. 19 (4), 482 (1998).
  64. M. C. Caro, H.-Y. Huang, M. Cerezo, K. Sharma, A. Sornborger, L. Cincio, and P. J. Coles, Nat. Commun. 13, 4919 (2022).
  65. R. Mezher, A. F. Carvalho, and S. Mansfield, Phys. Rev. A 108, 032405 (2023).

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Phys. Rev. A 111, L030401– Published 18 March, 2025
  • Received 9 October 2024
  • Accepted 27 February 2025
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