Fault-tolerant quaternary belief propagation decoding based on a neural network - Ji, Naihua; Chen, Zhao; Qu, Yingjie; Bao, Rongyi; Yang, Xin; Wang, Shumei (Frontiers in Physics, 2023)
Quantum computing offers significant advantages over classical computing in terms of increasing computing power. A major challenge is finding an efficient decoder suitable for quantum error correction codes for fault-tolerant experiments. In this paper, we aim to find a better decoding scheme based on the flag-bridge fault tolerance experiment and through the comparative study of two decoding algorithms. Firstly, we improve the syndrome extraction circuit based on the flag-bridge method to satisfy the requirements of fault-tolerant experiments better. Then, we study two decoding schemes: a combination scheme based on deep neural network decoding and simple decoder, and a design of RNN structure decoding scheme based on the belief propagation algorithm variant MBP4 algorithm. In deep learning schemes, neural networks are used to assist simple decoders in determining whether additional logical corrections need to be added. In the second scheme, the recurrent neural network structure is designed through the variant MBP4 algorithm and post-processing method is adopted. The error qubit position can be pinpointed by syndrome information for decoding. Our experimental results indicate that our decoding scheme improves the pseudo-threshold by 39.52% compared to the MWPM decoder. We observed thresholds of approximately 15.8% and 16.4% for the two decoders, respectively.