We introduce and analyse an efficient decoder for the quantum Tanner codes of that can correct adversarial errors of linear weight. Previous decoders for quantum low-density parity-check codes could only handle adversarial errors of weight $O(\sqrt{n \log n})$. We also work on the link between quantum Tanner codes and the Lifted Product codes of Panteleev and Kalachev, and show that our decoder can be adapted to the latter. The decoding algorithm alternates between sequential and parallel procedures and converges in linear time.

翻译：我们引入并分析能够纠正线性重量对抗差错的量子坦纳编码的有效解码器。 之前的量子低密度对等检查编码解码器只能处理重量对称差错$O( sqrt{n\log n})美元。 我们还在研究量坦纳编码与Panteleev和Kalachev的提振产品编码之间的联系,并表明我们的解码器可以适应后者。 解码算法在顺序和平行程序之间互换,在线性时间趋同。