Combining hard and soft decoders for hypergraph product codes
Combining hard and soft decoders for hypergraph product codes
复制标题
结合超图产品代码的硬解码器和软解码器
作者：
Antoine Grospellier;Lucien Grouès;Anirudh Krishna;Anthony Leverrier
超图乘积码是一类具有线性译码的恒速率量子低密度奇偶校验(LDPC)码，称为小集合翻转(SSF)。这种解码器在实践中表现出次优性能，并且需要非常大的纠错码才能有效。在这项工作中，我们提出了新的混合解码器，它结合了信任传播(BP)算法和SSF解码器。我们给出了码受到独立的位翻转和相移误差影响时的数值模拟结果。我们提供的证据表明，假设一个理想的校正子提取，这些代码的阈值大约为7.5%，并且在存在校正子噪声的情况下保持接近3%。这一结果包含并显著改进了Grospellier和Krishna(arxiv：1810.03681)的早期工作。这些启发式译码的低复杂度和高性能表明，当从零码率表面码转移到恒码率LDPC码时，译码应该不是一个实质性的困难，并进一步暗示在构建大型通用量子计算机的背景下，这种码非常值得研究。
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.
影响因子：
16.6
作者：
Brown BJ;Nickerson NH;Browne DE
通讯作者：
Browne DE
超图积代码阈值错误率的数值和分析界限
影响因子：
2.9
作者：
Kovalev, Alexey A.;Prabhakar, Sanjay;Dumer, Ilya;Pryadko, Leonid P.
通讯作者：
Pryadko, Leonid P.
影响因子：
6.7
作者：
Breuckmann, Nikolas P.;Vuillot, Christophe;Terhal, Barbara M.
通讯作者：
Terhal, Barbara M.