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码构成了一类具有优良参数的量子低密度奇偶校验（LDPC）码族，即恒定编码率和相对距离。本文证明了量子Tanner码同时支持对抗噪声下的单次量子纠错（QEC），其中一轮测量（由恒定权重的奇偶校验组成）足以在存在测量误差的情况下实现可靠的QEC。我们针对Leverrier和Zémor引入的串行与并行解码算法均建立了这一结论。此外，我们表明，为抑制多轮重复QEC过程中的误差，只需在每一轮中以常驻时间运行并行解码算法。结合优良的码参数，由此产生的QEC常驻时间开销以及对（可能时间相关的）对抗噪声的鲁棒性，使得量子Tanner码在量子容错协议领域具有吸引力。