论文标题
解码量子制革商代码
Decoding quantum Tanner codes
论文作者
论文摘要
我们引入了量子制革商代码的顺序和并行解码器。当将制革商代码构建应用于具有稳健的本地代码的足够扩展的正方形复合体时，我们将获得一个渐近良好的量子低密度奇偶校验检查代码的家族。在这种情况下，我们的解码器在代码长度中分别在线性或对数时间中分别在代码长度中分别正确的任意权重错误。相同的解码器很容易适应Panteleev和Kalachev的扩展器提升的产品代码。一路上，我们利用最近建立了随机张量代码的鲁棒性的界限，以在量子制品代码的最小距离上更加紧密。
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.
