Optimized Quantum Autoencoder (2404.08429v1)
Abstract: Quantum autoencoder (QAE) compresses a bipartite quantum state into its subsystem by a self-checking mechanism. How to characterize the lost information in this process is essential to understand the compression mechanism of QAE\@. Here we investigate how to decrease the lost information in QAE for any input mixed state. We theoretically show that the lost information is the quantum mutual information between the remaining subsystem and the ignorant one, and the encoding unitary transformation is designed to minimize this mutual information. Further more, we show that the optimized unitary transformation can be decomposed as the product of a permutation unitary transformation and a disentanglement unitary transformation, and the permutation unitary transformation can be searched by a regular Young tableau algorithm. Finally we numerically identify that our compression scheme outperforms the quantum variational circuit based QAE\@.
- M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge university press, 2010).
- M. M. Wilde, Quantum Information Theory, 2nd ed. (Cambridge University Press, 2017).
- C. E. Shannon, Bell System Technical Journal 27, 379 (1948), https://onlinelibrary.wiley.com/doi/pdf/10.1002/j.1538-7305.1948.tb01338.x .
- I. Devetak, A. W. Harrow, and A. Winter, Phys. Rev. Lett. 93, 230504 (2004).
- B. Schumacher, Phys. Rev. A 51, 2738 (1995).
- R. Jozsa and B. Schumacher, Journal of Modern Optics 41, 2343 (1994), https://doi.org/10.1080/09500349414552191 .
- M. Hayashi and K. Matsumoto, Phys. Rev. A 66, 022311 (2002).
- F. Fogelman-Soulié and Y. Le Cun, Intellectica 2, 114 (1987), included in a thematic issue : Apprentissage et machine.
- H. Bourlard and Y. Kamp, Biol. Cybern. 59, 291–294 (1988).
- G. E. Hinton and R. S. Zemel, in Neural Information Processing Systems (1993).
- J. Romero, J. P. Olson, and A. Aspuru-Guzik, Quantum Science and Technology 2, 045001 (2017).
- A. Pepper, N. Tischler, and G. J. Pryde, Phys. Rev. Lett. 122, 060501 (2019).
- D. F. Locher, L. Cardarelli, and M. Müller, Quantum 7, 942 (2023).
- D. Bondarenko and P. Feldmann, Phys. Rev. Lett. 124, 130502 (2020).
- K. Ch’ng, N. Vazquez, and E. Khatami, Phys. Rev. E 97, 013306 (2018).
- Y. Wu, P. Zhang, and H. Zhai, Phys. Rev. Res. 3, L032057 (2021).
- K. J. B. Ghosh and S. Ghosh, Phys. Rev. B 108, 165408 (2023).
- V. S. Ngairangbam, M. Spannowsky, and M. Takeuchi, Phys. Rev. D 105, 095004 (2022).
- M. Schmitt and Z. Lenarčič, Phys. Rev. B 106, L041110 (2022).
- C. Cao and X. Wang, Phys. Rev. Appl. 15, 054012 (2021).
- F. Hiai and D. Petz, Communications in mathematical physics 143, 99 (1991).
- A. Lesniewski and M. B. Ruskai, Journal of Mathematical Physics 40, 5702 (1999), https://pubs.aip.org/aip/jmp/article-pdf/40/11/5702/19013936/5702_1_online.pdf .
- M. Berta and C. Majenz, Phys. Rev. Lett. 121, 190503 (2018).
- A. Anshu, M.-H. Hsieh, and R. Jain, Phys. Rev. Lett. 121, 190504 (2018).
- D. S. P. Salazar, Phys. Rev. E 109, L012103 (2024).
- H. Mu and Y. Li, Phys. Rev. A 102, 022217 (2020).
- M. G. Genoni, M. G. A. Paris, and K. Banaszek, Phys. Rev. A 78, 060303 (2008).
- M. Yang, C.-Q. Xu, and D. L. Zhou, Phys. Rev. A 108, 052402 (2023).
- R. Bhatia, Matrix Analysis (Springer New York, NY, 2012).
- G. E. Andrews, The Theory of Partitions, Encyclopedia of Mathematics and its Applications (Cambridge University Press, 1984).
- See Supplemental Material.
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