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Advantage of Quantum Neural Networks as Quantum Information Decoders (2401.06300v1)

Published 11 Jan 2024 in quant-ph, cond-mat.dis-nn, cs.AI, and cs.LG

Abstract: A promising strategy to protect quantum information from noise-induced errors is to encode it into the low-energy states of a topological quantum memory device. However, readout errors from such memory under realistic settings is less understood. We study the problem of decoding quantum information encoded in the groundspaces of topological stabilizer Hamiltonians in the presence of generic perturbations, such as quenched disorder. We first prove that the standard stabilizer-based error correction and decoding schemes work adequately well in such perturbed quantum codes by showing that the decoding error diminishes exponentially in the distance of the underlying unperturbed code. We then prove that Quantum Neural Network (QNN) decoders provide an almost quadratic improvement on the readout error. Thus, we demonstrate provable advantage of using QNNs for decoding realistic quantum error-correcting codes, and our result enables the exploration of a wider range of non-stabilizer codes in the near-term laboratory settings.

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References (26)
  1. C. Gross and I. Bloch, Quantum simulations with ultracold atoms in optical lattices, Science 357, 995 (2017).
  2. J. Preskill, Quantum computing in the nisq era and beyond, Quantum 2, 79 (2018).
  3. A. Y. Kitaev, Fault-tolerant quantum computation by anyons, Ann. Phys. (New York) 303, 2 (2003).
  4. S. B. Bravyi and A. Y. Kitaev, Quantum codes on a lattice with boundary, arXiv preprint quant-ph/9811052  (1998).
  5. R. Raussendorf and J. Harrington, Fault-tolerant quantum computation with high threshold in two dimensions, Phys. Rev. Lett. 98, 190504 (2007).
  6. P. W. Shor, Scheme for reducing decoherence in quantum computer memory, Phys. Rev. A 52, R2493 (1995).
  7. A. R. Calderbank and P. W. Shor, Good quantum error-correcting codes exist, Phys. Rev. A 54, 1098 (1996).
  8. A. M. Steane, Error correcting codes in quantum theory, Phys. Rev. Lett. 77, 793 (1996).
  9. D. Gottesman, Stabilizer codes and quantum error correction (California Institute of Technology, 1997).
  10. A. Krizhevsky, I. Sutskever, and G. E. Hinton, Imagenet classification with deep convolutional neural networks, Commun. ACM 60, 84 (2017).
  11. D. P. Kingma and M. Welling, Auto-encoding variational bayes, arXiv preprint arXiv:1312.6114  (2013).
  12. I. Goodfellow, Y. Bengio, and A. Courville, Deep learning (MIT press, 2016).
  13. G. Carleo and M. Troyer, Solving the quantum many-body problem with artificial neural networks, Science 355, 602 (2017).
  14. E. P. Van Nieuwenburg, Y.-H. Liu, and S. D. Huber, Learning phase transitions by confusion, Nat. Phys. 13, 435 (2017).
  15. J. Carrasquilla and R. G. Melko, Machine learning phases of matter, Nat. Phys. 13, 431 (2017).
  16. L. Wang, Discovering phase transitions with unsupervised learning, Phys. Rev. B 94, 195105 (2016).
  17. Y. Zhang and E.-A. Kim, Quantum loop topography for machine learning, Phys. Rev. Lett. 118, 216401 (2017).
  18. I. Cong, S. Choi, and M. D. Lukin, Quantum convolutional neural networks, Nat. Phys. 15, 1273 (2019).
  19. A. M. Gomez, S. F. Yelin, and K. Najafi, Reconstructing quantum states using basis-enhanced born machines, arXiv preprint arXiv:2206.01273  (2022).
  20. D. F. Locher, L. Cardarelli, and M. Müller, Quantum error correction with quantum autoencoders, Quantum 7, 942 (2023).
  21. R. Movassagh and Y. Ouyang, Constructing quantum codes from any classical code and their embedding in ground space of local hamiltonians, arXiv preprint arXiv:2012.01453  (2020).
  22. S. Bravyi, M. B. Hastings, and S. Michalakis, Topological quantum order: stability under local perturbations, J. Math. Phys. 51, 093512 (2010).
  23. M. Grassl, Bounds on the minimum distance of linear codes and quantum codes, Online available at http://www.codetables.de (2007), accessed on 2023-04-11.
  24. I. Hubač and S. Wilson, Brillouin-wigner methods for many-body systems, in Brillouin-Wigner Methods for Many-Body Systems (Springer, 2010) pp. 133–189.
  25. J. W. S. B. Rayleigh, The theory of sound, Vol. 2 (Macmillan, 1896).
  26. E. Schrödinger, Quantisierung als eigenwertproblem, Annalen der physik 385, 437 (1926).
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