We introduce sequential and parallel decoders for quantum Tanner codes. When the Tanner code construction is applied to a sufficiently expanding square complex with robust local codes, we obtain a family of asymptotically good quantum low-density parity-check codes. In this case, our decoders provably correct arbitrary errors of weight linear in the code length, respectively in linear or logarithmic time. The same decoders are easily adapted to the expander lifted product codes of Panteleev and Kalachev. Along the way, we exploit recently established bounds on the robustness of random tensor codes to give a tighter bound on the minimum distance of quantum Tanner codes.

翻译：我们引入了量子坦纳代码的相继和平行解码器。 当坦纳代码的构建被应用到一个足够扩大的、具有强健本地代码的正方形结构时, 我们获得了一个基本良好的量子低密度对等检查代码组。 在这种情况下, 我们的解码器可以分别用线性或对数性时间来纠正代码长度中的任意重量线错误。 同样的解码器很容易适应Panteleev 和 Kalachev 的扩展产品代码。 与此同时, 我们利用最近建立的随机高压代码的稳健性界限, 以便更严格地限制量坦纳代码的最小距离 。