Errors in heavy hexagonal code and other topological codes like surface code were usually decoded using the Minimum Weight Perfect Matching (MWPM) based decoders. Recent advances have shown that topological codes can be efficiently decoded by deploying machine learning (ML) techniques, for example, neural networks. In this work, we first propose an ML based decoder and show that this decoder can decode heavy hexagonal code efficiently, in terms of the values of threshold and pseudo-threshold, for various noise models. We show that the proposed ML based decoding method achieves $\sim 5$ times higher values of threshold than that by MWPM. Next, exploiting the property of subsystem codes, we define gauge equivalence in heavy hexagonal code, by which two different errors can belong to the same error class. We obtain a quadratic reduction in the number of error classes for both bit flip and phase flip errors, thus achieving a further improvement of $\sim 14\%$ in the threshold o ver the basic ML decoder. A novel technique of rank based gauge equivalence minimization to minimize the number of classes is further proposed, which is empirically faster than the previously mentioned gauge equivalence minimization.
翻译:在重六边码和其他表层代码(如表层代码)错误中,通常使用以最低重量完美匹配(MWPM)为基础的分解器解码。最近的进展显示,表层代码可以通过部署机器学习(ML)技术(例如神经网络)来有效解码。在这项工作中,我们首先提议以 ML 为基础的解码器,并表明,从门槛值和伪临界值的角度,这一解码可以有效地解码重六边码,用于各种噪音模型。我们显示,拟议的基于 ML 的解码方法比MWPM 的临界值高出5倍。接下来,我们利用子系统代码的属性,我们界定重六边形代码的等值,其中两个不同的错误可以属于相同的错误类别。我们从位翻和阶段翻差错误的角度,在错误类别的数量上都实现了四分解码减少,从而在基本 ML 解码中实现了14 $的进一步改进。基于级等同的新技术是先前提到的最短度等值,而最短于实验性等值的数值。