Error-resilience Phase Transitions in Encoding-Decoding Quantum Circuits
Abstract: Understanding how errors deteriorate the information encoded in a many-body quantum system is a fundamental problem with practical implications for quantum technologies. Here, we investigate a class of encoding-decoding random circuits subject to local coherent and incoherent errors. We analytically demonstrate the existence of a phase transition from an error-protecting phase to an error-vulnerable phase occurring when the error strength is increased. This transition is accompanied by R\'enyi entropy transitions and by onset of multifractal features in the system. Our results provide a new perspective on storing and processing quantum information, while the introduced framework enables an analytic understanding of a dynamical critical phenomenon in a many-body system.
- J. Preskill, Quantum 2, 79 (2018).
- J. Fraxanet, T. Salamon, and M. Lewenstein, The coming decades of quantum simulation (2022), arXiv:2204.08905 [quant-ph] .
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).
- D. Gottesman, arXiv:9705052 (1997).
- B. Skinner, J. Ruhman, and A. Nahum, Phys. Rev. X 9, 031009 (2019).
- Y. Li, X. Chen, and M. P. A. Fisher, Phys. Rev. B 100, 134306 (2019).
- M. J. Gullans and D. A. Huse, Phys. Rev. X 10, 041020 (2020).
- Y. Bao, S. Choi, and E. Altman, Phys. Rev. B 101, 104301 (2020).
- F. Venn, J. Behrends, and B. Béri, Phys. Rev. Lett. 131, 060603 (2023).
- See the supplementary material.
- D. A. Roberts and B. Yoshida, Journal of High Energy Physics 2017 (2017).
- F. G. Brandao, A. W. Harrow, and M. Horodecki, Communications in Mathematical Physics 346, 397 (2016).
- X. Turkeshi and P. Sierant, Code and Analytical Expressions for ”Error- resilience Phase Transitions in Encoding-Decoding Quantum Circuits”, Zenodo [10.5281/zenodo.10302870] (2023).
- D. J. Luitz, F. Alet, and N. Laflorencie, Phys. Rev. Lett. 112, 057203 (2014a).
- J. Lindinger, A. Buchleitner, and A. Rodríguez, Phys. Rev. Lett. 122, 106603 (2019).
- N. Macé, F. Alet, and N. Laflorencie, Phys. Rev. Lett. 123, 180601 (2019).
- F. Pietracaprina and N. Laflorencie, Annals of Physics 435, 168502 (2021).
- S. Roy, Phys. Rev. B 106, L140204 (2022).
- P. Sierant and X. Turkeshi, Phys. Rev. Lett. 128, 130605 (2022).
- D. Aharonov and M. Ben-Or, SIAM J. Comput. (2008).
- P. Shor, in Proceedings of 37th Conference on Foundations of Computer Science (1996) pp. 56–65.
- E. Knill, R. Laflamme, and W. H. Zurek, Science 279, 342 (1998).
- E. Knill, Nature 434, 39 (2005).
- P. Sierant, and X. Turkeshi, To appear. (2023).
- P. Niroula, S. Gopalakrishnan, and M. J. Gullans, Error mitigation thresholds in noisy quantum circuits (2023b), arXiv:2302.04278 [quant-ph] .
- B. Schumacher and M. A. Nielsen, Phys. Rev. A 54, 2629 (1996).
- D. Gross, S. Nezami, and M. Walter, Communications in Mathematical Physics 385, 1325 (2021).
- D. J. Luitz, F. Alet, and N. Laflorencie, Phys. Rev. B 89, 165106 (2014b).
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