Branch-Assisted Sign-Flipping Belief Propagation Decoding for Topological Quantum Codes Based on Hypergraph Product Structure

Topological codes, a kind of quantum error correction code, have been used for current quantum computers due to their local qubit layout and high threshold. With nearly linear complexity, syndrome-based belief propagation (BP) can be considered as a decoding candidate for topological codes. However, such highly degenerate codes will lead to multiple low-weight errors where the syndrome is identical so that the BP decoding is not able to distinguish it, resulting in degradation in performance. In this article, we propose a branch-assisted sign-flipping belief propagation (BSFBP) decoding method for topological codes based on the hypergraph product structure. In our algorithm, we introduce the criteria to enter the new decoding path branched from BP combined with a syndrome residual, which is obtained from the syndrome-pruning process. A sign-flipping process is also conducted to disturb the log-likelihood ratio of the selected variable nodes, which provides diversity in the syndrome residual. Simulation results show that using the proposed BSFBP decoding is able to outperform the BP decoding by about two orders of magnitude.