We introduce a parallel decoding algorithm for recently discovered families of asymptotically good quantum low-density parity-check codes. This algorithm provably corrects arbitrary errors of weight linear in the code length, with a logarithmic number of steps. This decoder applies directly to the family of quantum Tanner codes, and serves as a subroutine for expander lifted product codes. Along the way, we exploit recently established bounds on the robustness of random tensor codes to give a tight bound on the minimum distance of quantum Tanner codes.

翻译：我们引入了一种平行的解码算法, 用于最近发现的、 零星好的量子值低密度对等检查代码。 这个算法可以用一个对数步骤来纠正代码长度中任意的重量线性错误。 这个解码器直接适用于量子坦纳代码家族, 并且作为扩展器解除产品代码的子常规。 与此同时, 我们利用最近建立的随机气压代码的坚固度, 来给量子坦纳代码的最低距离设定一个紧紧的界限 。