Quantum low-density parity-check (QLDPC) codes are promising candidates for error correction in quantum computers. One of the major challenges in implementing QLDPC codes in quantum computers is the lack of a universal decoder. In this work, we first propose to decode QLDPC codes with a belief propagation (BP) decoder operating on overcomplete check matrices. Then, we extend the neural BP (NBP) decoder, which was originally studied for suboptimal binary BP decoding of QLPDC codes, to quaternary BP decoders. Numerical simulation results demonstrate that both approaches as well as their combination yield a low-latency, high-performance decoder for several short to moderate length QLDPC codes.

翻译：量子低密度奇偶校验码是量子计算机中极具前景的纠错方案。在量子计算机中实现量子LDPC码的主要挑战之一是缺乏通用译码器。本文首先提出采用基于过完备校验矩阵的置信传播译码器对量子LDPC码进行译码。随后，我们将最初针对量子LDPC码次优二进制BP译码所研究的神经BP译码器扩展至四态BP译码器。数值仿真结果表明，两种方法及其组合能够为若干短至中等码长的量子LDPC码提供低延迟、高性能的译码器。