Fault-tolerant quaternary belief propagation decoding based on a neural network

Abstract

The article discusses the challenge of finding an efficient decoder for quantum error correction codes for fault-tolerant experiments in quantum computing. The study aims to develop a better decoding scheme based on the flag-bridge fault tolerance experiment. The research compares two decoding algorithms, a deep neural network decoding scheme and a simple decoder, and a recurrent neural network decoding scheme based on the belief propagation algorithm variant MBP4 algorithm. The study improved the syndrome extraction circuit based on the flag-bridge method to meet the requirements of fault-tolerant experiments better. Two decoding schemes were studied, a combination of a deep neural network and a simple decoder and a recurrent neural network structure based on the MBP4 algorithm. The first scheme used neural networks to assist simple decoders in determining whether additional logical corrections need to be added. The second scheme used a recurrent neural network structure designed through the variant MBP4 algorithm, along with a post-processing method to pinpoint the error qubit position for decoding. Experimental results showed that the decoding scheme developed in the study improved the pseudo-threshold by 39.52% compared to the minimum-weight perfect matching decoder. The two decoders had thresholds of approximately 15.8% and 16.4%, respectively. The study’s findings suggest that the proposed decoding schemes could improve quantum error correction and fault-tolerant experiments in quantum computing.