Advantages of versatile neural-network decoding for topological codes

Finding optimal correction of errors in generic stabilizer codes is a computationally hard problem, even for simple noise models. While this task can be simplified for codes with some structure, such as topological stabilizer codes, developing good and efficient decoders still remains a challenge. In our paper, we systematically study a very versatile class of decoders based on feedforward neural networks. To demonstrate adaptability, we apply neural decoders to the triangular color and toric codes under various noise models with realistic features, such as spatially correlated errors. We report that neural decoders provide a significant improvement over leading efficient decoders in terms of the error-correction threshold. In particular, the neural decoder threshold for the two-dimensional color code is very close to the toric code threshold. Using neural networks simplifies the design of decoders and does not require prior knowledge of the underlying noise.