The successive cancellation list decoder (SCL) is an efficient decoder for classical polar codes with low decoding error, approximating the maximum likelihood decoder (MLD) for small list sizes. Here we adapt the SCL to the task of decoding quantum polar codes and show that it inherits the high performance and low complexity of the classical case, and can approximate the quantum MLD for certain channels. We apply SCL decoding to a novel version of quantum polar codes based on the polarization weight (PW) method, which entirely avoids the need for small amounts of entanglement assistance apparent in previous quantum polar code constructions. When used to find the precise error pattern, the quantum SCL decoder (SCL-E) shows competitive performance with surface codes of similar size and low-density parity check codes of similar size and rate. The SCL decoder may instead be used to approximate the probability of each equivalence class of errors, and then choose the most likely class. We benchmark this class-oriented decoder (SCL-C) against the SCL-E decoder and find a noticeable improvement in the logical error rate. This improvement stems from the fact that the contributions from just the low-weight errors give a reasonable approximation to the error class probabilities. Both SCL-E and SCL-C maintain the complexity O(LN logN) of SCL for code size N and list size L. We also show that the list decoder can be used to gain insight into the weight distribution of the codes and how this impacts the effect of degenerate errors.

翻译：逐次相消列表解码器（SCL）是一种高效的低误码经典极化码解码器，在较小列表大小时可近似最大似然解码器（MLD）。本文将SCL算法适配于量子极化码解码任务，证明其继承了经典情形的高性能与低复杂度特性，并能在特定信道下近似量子MLD。我们基于极化权重（PW）方法将SCL解码应用于新型量子极化码，该构造完全避免了此前量子极化码方案中所需的少量纠缠辅助。当用于精确错误模式识别时，量子SCL解码器（SCL-E）在同等规模的曲面码及同等规模与码率的低密度奇偶校验码中展现出具有竞争力的性能。此外，SCL解码器可通过近似各错误等价类概率，选择最可能的错误类。我们将这种面向类别的解码器（SCL-C）与SCL-E进行基准测试，发现逻辑误码率显著改善。该改进源于仅利用低权重错误的贡献即可对错误类概率进行合理近似。SCL-E与SCL-C均保持SCL算法复杂度O(LN logN)（码长N，列表大小L）。我们还证明了列表解码器可用于揭示码重分布特征及其对简并错误效应的影响。