Color codes present distinct advantages for fault-tolerant quantum computing, such as high encoding rates and the transversal implementation of Clifford gates. However, existing matching-based decoders for the color codes such as the restricted decoder (Kubica and Delfosse, 2023), suffer from limited decoding performance. Inspired by the global decoding insight of the unified decoder (Benhemou et al., 2023), this paper introduces a correlated decoder for the 4.8.8 color code, which improves upon the conventional restricted decoder by leveraging correlations between restricted lattices, and is derived by mapping the correlated matching decoder for the surface code onto the color code lattice. Analytical and numerical results show that the correlated decoder achieves higher thresholds than the restricted and unified decoders, while matching the performance of the unified decoder at very low physical error rates. Under the code capacity and phenomenological noise models, the estimated thresholds for the color code against bit-flip error are 10.38% and 3.13%, respectively. Furthermore, by applying the surface-color code mapping, the thresholds of 16.62% and 3.52% are obtained for the surface code against depolarizing noise.

翻译：颜色码在容错量子计算中展现出独特优势，例如高编码率与Clifford门的横向实现。然而，现有基于匹配的颜色码解码器（如受限解码器（Kubica与Delfosse，2023））的解码性能有限。受统一解码器（Benhemou等人，2023）全局解码思想的启发，本文针对4.8.8颜色码提出一种关联解码器，该解码器通过利用受限晶格间的关联性改进了传统受限解码器，其设计方法是将表面码的关联匹配解码器映射至颜色码晶格。理论与数值分析表明，关联解码器相较于受限解码器与统一解码器实现了更高的阈值，同时在极低物理错误率下与统一解码器性能相当。在码容量与唯象噪声模型下，颜色码对抗比特翻转错误的估计阈值分别为10.38%与3.13%。此外，通过应用表面-颜色码映射，得到表面码对抗去极化噪声的阈值为16.62%与3.52%。