Single-Shot Decoding of Good Quantum LDPC Codes

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...

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Bibliographic Details
Published in:Communications in mathematical physics Vol. 405; no. 3; p. 85
Main Authors: Gu, Shouzhen, Tang, Eugene, Caha, Libor, Choe, Shin Ho, He, Zhiyang, Kubica, Aleksander
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2024
Springer Nature B.V
Springer Science + Business Media
Subjects:
Algorithms
Classical and Quantum Gravitation
Codes
Complex Systems
Decoding
Error correcting codes
Error correction
Fault tolerance
Mathematical and Computational Physics
Mathematical Physics
Noise measurement
Parameters
Parity
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
ISSN:0010-3616, 1432-0916
Online Access:Get full text
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Summary: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.
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USDOE
AC02-07CH11359
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-024-04951-6