Quantum error correction is an essential technique for constructing a scalable quantum computer. In order to implement quantum error correction with near-term quantum devices, a fast and near-optimal decoding method is required. A decoder based on machine learning is considered one of the most viable solutions for this purpose since its prediction is fast once training has been done, and it is applicable to any quantum error-correcting code and any noise model. So far, various formulations of the decoding problem as the task of machine learning have been proposed. Here we discuss general constructions of machine-learning-based decoders. We find several conditions to achieve near-optimal performance and propose a criterion which should be optimized when the size of a training data set is limited. We also discuss preferable constructions of neural networks and propose a decoder using spatial structures of topological codes using a convolutional neural network. We numerically show that our method can improve the performance of machine-learning-based decoders in various topological codes and noise models.

中文翻译：

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构建快速稳定的基于机器学习的拓扑稳定器代码解码器的通用框架

量子纠错是构建可伸缩量子计算机的必不可少的技术。为了用近期量子装置实现量子误差校正，需要一种快速且接近最佳的解码方法。基于机器学习的解码器被认为是实现此目的最可行的解决方案之一，因为一旦完成训练，其预测速度很快，并且适用于任何量子纠错码和任何噪声模型。到目前为止，已经提出了将解码问题作为机器学习任务的各种表达。在这里，我们讨论基于机器学习的解码器的一般结构。我们找到了几种条件来达到接近最佳的性能，并提出了一个准则，当训练数据集的大小受到限制时，应该对其进行优化。我们还讨论了神经网络的优选结构，并提出了使用卷积神经网络使用拓扑代码的空间结构的解码器。我们从数值上证明了我们的方法可以在各种拓扑代码和噪声模型中提高基于机器学习的解码器的性能。