论文标题

通过机器学习的重型六边形QECC的高效综合征解码器

Efficient Syndrome Decoder for Heavy Hexagonal QECC via Machine Learning

论文作者

Bhoumik, Debasmita, Majumdar, Ritajit, Madan, Dhiraj, Vinayagamurthy, Dhinakaran, Raghunathan, Shesha, Sur-Kolay, Susmita

论文摘要

重型六角形代码和其他拓扑代码(例如表面代码)的错误综合征通常是通过基于最小重量匹配(MWPM)方法来解码的。最近的进步表明,可以通过部署机器学习(ML)技术,尤其是神经网络来有效地解码拓扑代码。在这项工作中,我们首先提出了一个基于ML的重型六边形代码的解码器,并在各种噪声模型的阈值和阈值阈值的值方面确定了其效率。我们表明,所提出的基于ML的解码方法可实现$ \ sim5 \ times $ $ threshold的阈值值。 接下来,利用子系统代码的属性,我们为重六角形代码定义了量规等值,这两个不同的错误可以属于同一错误类。提出了一种基于线性搜索的方法来确定等效误差类。这提供了二次减少误差类别的数量,以考虑到位flip和相位翻转错误,从而进一步改善了基本ML解码器的阈值中$ \ sim 14 \%$。最后,提出了基于等级的新技术,以确定等效误差类别,其经验上比基于线性搜索的误差类别更快。

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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