基于机器学习的重六边形量子纠错码高效伴随式译码器
Efficient Syndrome Decoder for Heavy Hexagonal QECC via Machine Learning
AI总结：
本文提出基于机器学习的重六边形量子纠错码译码器，通过规范等价性和基于秩的错误类确定方法显著减少错误类数量，使译码阈值相比MWPM方法提高约5倍，并进一步获得约14%的阈值提升。
摘要：
重六边形码以及表面码等其他拓扑码的错误伴随式通常使用基于最小权重完美匹配（MWPM）的方法进行译码。近期进展表明，可以通过部署机器学习（ML）技术，特别是神经网络，对拓扑码进行高效译码。在本工作中，我们首先提出了一种基于ML的重六边形码译码器，并针对多种噪声模型，从阈值和伪阈值的取值角度确立了其效率。我们表明，所提出的基于ML的译码方法取得的阈值比MWPM方法高约$\sim5 \times$。接下来，利用子系统码的性质，我们为重六边形码定义了规范等价性，据此两个不同的错误可以属于同一个错误类。我们提出了一种基于线性搜索的方法来确定等价错误类。这使得比特翻转错误和相位翻转错误所需考虑的错误类数量实现了二次方级别的减少，从而使阈值在基础ML译码器的基础上进一步提高了约$\sim 14\\%$。最后，我们提出了一种基于秩来确定等价错误类的新技术，经验表明该技术比基于线性搜索的方法更快。
英文摘要：
Error syndromes for heavy hexagonal code and other topological codes such as surface code have typically been decoded by using Minimum Weight Perfect Matching (MWPM) based methods. Recent advances have shown that topological codes can be efficiently decoded by deploying machine learning (ML) techniques, in particular with neural networks. In this work, we first propose an ML based decoder for heavy hexagonal code and establish its efficiency in terms of the values of threshold and pseudo-threshold, for various noise models. We show that the proposed ML based decoding method achieves $\sim5 \times$ higher values of threshold than that for MWPM. Next, exploiting the property of subsystem codes, we define gauge equivalence for heavy hexagonal code, by which two distinct errors can belong to the same error class. A linear search based method is proposed for determining the equivalent error classes. This provides a quadratic reduction in the number of error classes to be considered for both bit flip and phase flip errors, and thus a further improvement of $\sim 14\%$ in the threshold over the basic ML decoder. Lastly, a novel technique based on rank to determine the equivalent error classes is presented, which is empirically faster than the one based on linear search.
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