Neural Network Decoders for Large-Distance 2D Toric Codes

TL;DR

This paper demonstrates that neural network decoders can effectively handle large-distance 2D toric codes, outperforming traditional algorithms under certain conditions, and provides insights into their design and limitations.

Contribution

It introduces a neural network decoder inspired by renormalization group methods capable of decoding large 2D toric codes and compares its performance to existing algorithms.

Findings

Neural decoders perform better with increasing code distance at low error rates.

Achieves near-optimal performance close to minimum-weight perfect matching.

Successfully simulates code distances up to 64.

Abstract

We still do not have perfect decoders for topological codes that can satisfy all needs of different experimental setups. Recently, a few neural network based decoders have been studied, with the motivation that they can adapt to a wide range of noise models, and can easily run on dedicated chips without a full-fledged computer. The later feature might lead to fast speed and the ability to operate at low temperatures. However, a question which has not been addressed in previous works is whether neural network decoders can handle 2D topological codes with large distances. In this work, we provide a positive answer for the toric code. The structure of our neural network decoder is inspired by the renormalization group decoder. With a fairly strict policy on training time, when the bit-flip error rate is lower than $9\%$ and syndrome extraction is perfect, the neural network decoder performs better when code distance increases. With a less strict policy, we find it is not hard for the neural decoder to achieve a performance close to the minimum-weight perfect matching algorithm. The numerical simulation is done up to code distance $d=64$. Last but not least, we describe and analyze a few failed approaches. They guide us to the final design of our neural decoder, but also serve as a caution when we gauge the versatility of stock deep neural networks. The source code of our neural decoder can be found at https://github.com/XiaotongNi/toric-code-neural-decoder .