Single-Shot Decoding of Good Quantum LDPC Codes
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220_2024_Article_4951.pdf
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Author(s)
Gu, Shouzhen
Tang, Eugene
Caha, Libor
Choe, Shin Ho
He, Zhiyang
Kubica, Aleksander
Date Issued
March 2024
Publisher
Springer Science and Business Media LLC
Citation
Communications in Mathematical Physics. 2024 Mar 14;405(3):85
Version
Final published version
Abstract
Quantum Tanner codes constitute a family of quantum low-density parity-check codes with good parameters, i.e., constant encoding rate and relative distance. In this article, we prove that quantum Tanner codes also facilitate single-shot quantum error correction (QEC) of adversarial noise, where one measurement round (consisting of constant-weight parity checks) suffices to perform reliable QEC even in the presence of measurement errors. We establish this result for both the sequential and parallel decoding algorithms introduced by Leverrier and Zémor. Furthermore, we show that in order to suppress errors over multiple repeated rounds of QEC, it suffices to run the parallel decoding algorithm for constant time in each round. Combined with good code parameters, the resulting constant-time overhead of QEC and robustness to (possibly time-correlated) adversarial noise make quantum Tanner codes alluring from the perspective of quantum fault-tolerant protocols.
Subjects
Mathematical Physics
Statistical and Nonlinear Physics
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s00220-024-04951-6
