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Recent developments in the field of deep learning have motivated manyresearchers to apply these methods to problems in quantum information. Torlaiand Melko first proposed a decoder for surface codes based on neural networks.Since then, many other researchers have applied neural networks to study avariety of problems in the context of decoding. An important development inthis regard was due to Varsamopoulos et al. who proposed a two-step decoderusing neural networks. Subsequent work of Maskara et al. used the same conceptfor decoding for various noise models. We propose a similar two-step neuraldecoder using inverse parity-check matrix for topological color codes. We showthat it outperforms the state-of-the-art performance of non-neural decoders forindependent Pauli errors noise model on a 2D hexagonal color code. Our finaldecoder is independent of the noise model and achieves a threshold of $10 \%$.Our result is comparable to the recent work on neural decoder for quantum errorcorrection by Maskara et al.. It appears that our decoder has significantadvantages with respect to training cost and complexity of the network forhigher lengths when compared to that of Maskara et al.. Our proposed method canalso be extended to arbitrary dimension and other stabilizer codes.

Neural Decoder for Topological Codes using Pseudo-Inverse of Parity Check Matrix