Quantum Tanner codes constitute a family of quantum low-density parity-check (LDPC) 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 Z\'emor. 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.

翻译：量子Tanner码构成了一族具有良好参数（即恒定编码率和相对距离）的量子低密度奇偶校验（LDPC）码。本文证明了量子Tanner码也能实现对抗噪声的单次量子纠错（QEC），即仅需一轮测量（由恒定权重的奇偶校验组成）即可在存在测量误差的情况下执行可靠的QEC。我们对Leverrier和Zémor提出的顺序和并行译码算法均建立了这一结论。此外，我们表明，在QEC的多轮重复过程中抑制误差时，每轮仅需运行恒定时间的并行译码算法即可。结合良好的码参数，由此带来的QEC恒定时间开销以及对（可能时间相关的）对抗噪声的鲁棒性，使得量子Tanner码在量子容错协议方面具有吸引力。