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

Recent developments in the field of deep learning have motivated many researchers to apply these methods to problems in quantum information. Torlai and Melko first proposed a decoder for surface codes based on neural networks. Since then, many other researchers have applied neural networks to study a variety of problems in the context of decoding. An important development in this regard was due to Varsamopoulos et at. who proposed a two-step decoder using neural networks. Subsequent work of Maskara et at. used the same concept for decoding for various noise models. We propose a similar two-step neural decoder using inverse parity-check matrix for topological color codes. We show that it outperforms the state-of-the-art performance of non-neural decoders for independent Pauli errors noise model on a 2D hexagonal color code. Our final decoder achieves a threshold of 10%. Our result is comparable to the recent work on neural decoder for quantum error correction by Maskara et at. It appears that our decoder has advantages with respect to training cost and complexity of the network for higher distances when compared to that of Maskara et at.