Surface codes are a promising method of quantum error correction and the basis of many proposed quantum computation implementations. However, their efficient decoding is still not fully explored. Recently, approaches based on machine learning techniques have been proposed by as well as . In these approaches, a so called high level decoder is used to post-correct an underlying decoder by correcting logical errors. A significant problem is that these methods require large amounts of training data even for relatively small code distances. The above-mentioned methods were tested on the rotated surface code which encodes one logical qubit. Here, we show that they are viable even for the toric surface code which encodes two logical qubits. Furthermore, we explain how symmetries of the toric code can be exploited to reduce the amount of training data that is required to obtain good decoding results. Finally, we compare different underlying decoders and show that the accuracy of high level decoding noticeably depends on the quality of the underlying decoder in the realistic case of imperfect training.

中文翻译：

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Toric代码上高级神经解码器的对称性

表面编码是一种有前途的量子误差校正方法，并且是许多提议的量子计算实现的基础。但是，它们的有效解码仍未得到充分探索。最近，以及提出了基于机器学习技术的方法。在这些方法中，所谓的高级解码器用于通过校正逻辑错误来对基础解码器进行后校正。一个重要的问题是，即使对于相对较小的代码距离，这些方法也需要大量的训练数据。在编码一个逻辑量子位的旋转表面码上测试了上述方法。在这里，我们表明，即使对于编码两个逻辑量子位的复曲面表面代码，它们也是可行的。此外，我们将说明如何利用复曲面代码的对称性来减少获得良好解码结果所需的训练数据量。最后，我们比较了不同的基础解码器，并表明在不完善训练的实际情况下，高级解码的准确性明显取决于基础解码器的质量。