稀疏量子码的迭代译码
On the iterative decoding of sparse quantum codes
摘要：
本文研究了稀疏量子纠错码的译码问题。对于泡利信道，这个任务可以通过用于解码稀疏经典码的置信传播算法的一个版本来完成。然而，量子编码提出了两个新的挑战。首先，他们的Tanner图不可避免地包含小循环，这通常会破坏置信传播的性能。其次，稀疏量子码根据定义是高度简并的。标准的信念传播算法不利用这一功能，而是它受损it.We提出了启发式的方法来改善信念传播解码，专门针对这两个问题。虽然我们的结果显示出明显的改善，由于所提出的启发式方法，他们也表明，在量子编码方案中的错误的主要来源仍然在解码。
英文摘要：
We address the problem of decoding sparse quantum error correction codes. For Pauli channels, this task can be accomplished by a version of the belief propagation algorithm used for decoding sparse classical codes. Quantum codes pose two new challenges however. Firstly, their Tanner graph unavoidably contain small loops which typically undermines the performance of belief propagation. Secondly, sparse quantum codes are by definition highly degenerate. The standard belief propagation algorithm does not exploit this feature, but rather it is impaired by it. We propose heuristic methods to improve belief propagation decoding, specifically targeted at these two problems. While our results exhibit a clear improvement due to the proposed heuristic methods, they also indicate that the main source of errors in the quantum coding scheme remains in the decoding.
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