Neural network decoders for large-distance 2d toric codes

Xiaotong Ni*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

14 Citations (Scopus)
50 Downloads (Pure)


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 [1]. The structure of our neural network decoder is inspired by the renormalization group decoder [2, 3]. 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 [4].

Original languageEnglish
Publication statusPublished - 2020


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