Neural Network Decoder for topological PlanarSurface Codes with Depolarizing noise model

Abstract Decoding is the most important part of the error correction process. During thedecoding process, the main idea of this paper is to transfer the error measuredinside ancilla qubit to the boundary, and decompose the error into the productof stabilizer, logical error and pure error, stabilizer error do not affect logicalerror. Therefore, the result of error syndrome is only affected by pure error,while the error of stabilizer can be ignored. Decoding by neural network can takeadvantage of its high threshold and adaptability to training different codes. Thefocus of this work is to propose a suitable algorithm for neural network decodingof planar codes, so as to reduce the size of the neural network as much as possiblewithout compromising the decoding performance. Comparative experiments wereconducted using the minimum weight perfect matching(MWPM) decoder andthe neural network decoder to compare the decoding performance of planar codeswith code distances of 5, 7, and 9, respectively, demonstrating high threshold ofneural network decoder and its adaptability to training different codes. Takingthe planar code with code distance of 5 as an example, the pseudo-thresholdsobtained using the MWPM decoder and the neural network decoder are 0.005and 0.0068 respectively,increased by 36%. It shows that for planar code, theneural network decoder significantly outperforms the MWPM decoder.