论文标题
结合使用高图产品代码的硬和软解码器
Combining hard and soft decoders for hypergraph product codes
论文作者
论文摘要
HyperGraph产品代码是一类恒定量量子量子低密度均衡检查（LDPC）代码，该代码配备了线性时间解码器，称为Small-Set-Flip（SSF）。该解码器在实践中显示了亚最佳性能，并且需要非常大的错误校正代码才能有效。在这项工作中，我们提出了将信念传播（BP）算法与SSF解码器相结合的新混合解码器。当代码受到独立的位叉和相叉错误时，我们介绍了数值模拟的结果。我们提供的证据表明，假设理想的综合征提取，这些代码的阈值约为7.5％，并且在存在综合征噪声的情况下保持接近3％。这一结果取决于Grospellier和Krishna（Arxiv：1810.03681）的早期工作。这些启发式解码器的低复杂性高性能表明，从零速率的表面代码转变为恒定速率LDPC代码时，解码并不是一个重大困难，并进一步提示此类代码是在构建大型通用量子计算机的背景下进行的井值调查。
Hypergraph product codes are a class of constant-rate quantum low-density parity-check (LDPC) codes equipped with a linear-time decoder called small-set-flip (SSF). This decoder displays sub-optimal performance in practice and requires very large error correcting codes to be effective. In this work, we present new hybrid decoders that combine the belief propagation (BP) algorithm with the SSF decoder. We present the results of numerical simulations when codes are subject to independent bit-flip and phase-flip errors. We provide evidence that the threshold of these codes is roughly 7.5% assuming an ideal syndrome extraction, and remains close to 3% in the presence of syndrome noise. This result subsumes and significantly improves upon an earlier work by Grospellier and Krishna (arXiv:1810.03681). The low-complexity high-performance of these heuristic decoders suggests that decoding should not be a substantial difficulty when moving from zero-rate surface codes to constant-rate LDPC codes and gives a further hint that such codes are well-worth investigating in the context of building large universal quantum computers.
