通过量子极码的列表解码改进逻辑错误率
Improved Logical Error Rate via List Decoding of Quantum Polar Codes
AI总结：
本文将SCL解码器应用于基于极化权重方法的新型量子极码，展示了其在低复杂度和高性能方面的优势，并通过SCL-C解码器在逻辑错误率上取得显著提升。
摘要：
successive cancellation list decoder (SCL) 是一种高效的经典极码解码器，具有低解码错误率，可近似最大似然解码器（MLD）在小列表大小下。本文将SCL应用于量子极码解码，证明其继承了经典情况的高性能和低复杂度，并可在某些信道中近似量子MLD。我们应用SCL解码器到基于极化权重（PW）方法的新型量子极码，完全避免了先前量子极码构造中显而易见的小量纠缠帮助需求。当用于查找精确错误模式时，量子SCL解码器（SCL-E）在性能上与相同大小和速率的表面码和低密度奇偶校验码具有竞争力。SCL解码器可能用于近似每个等价类错误的概率，然后选择最可能的类。我们对SCL-E解码器和SCL-C解码器进行基准测试，发现逻辑错误率有显著提升。这一提升源于仅低重量错误的贡献可合理近似错误类概率。SCL-E和SCL-C保持了SCL的复杂度O(LN logN)，其中代码大小为N，列表大小为L。我们还展示了列表解码器可用于了解码的重量分布及其对退化错误的影响。
英文摘要：
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.
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