Symmetries for a High Level Neural Decoder on the Toric Code

TL;DR

This paper explores how symmetries in the toric code can be used to reduce training data requirements for machine learning-based quantum error correction decoders, improving their efficiency and effectiveness.

Contribution

It demonstrates the viability of high level decoders for the toric code and introduces symmetry exploitation to decrease training data needs.

Findings

Symmetries can significantly reduce training data requirements.

High level decoders perform well on the toric code.

Decoder accuracy depends on the underlying decoder quality.

Abstract

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 Torlai and Melko as well as Varsamopoulos et al. 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.