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.

• Received 30 August 2019
• Revised 21 April 2020
• Accepted 9 July 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.033399

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society