Improved Belief Propagation Decoding on Surface Codes with High Accuracy and Low Latency

Quantum error correction is crucial for universal quantum computing, requiring highly accurate and low-latency decoding algorithms. Belief Propagation (BP) is notable for its linear time complexity and general applicability to quantum LDPC codes. However, BP performs poorly on highly degenerate codes without Order Statistic Decoding (OSD) post-processing, which significantly increases time complexity. We focus on improving BP's performance on surface codes. We first propose Momentum-BP and AdaGrad-BP, inspired by machine learning optimization techniques, to reduce the oscillation of message updating and break the symmetric trapping sets. We further propose EWAInit-BP, which adaptively updates initial probabilities and exhibits aggressive exploration capabilities. EWAInit-BP achieves the highest accuracy among BP improvements without OSD post-processing on planar surface code, toric code, and XZZX surface code, providing a 1~3 orders of magnitude improvement compared to traditional BP, and demonstrating the error correction capability even under parallel scheduling. Its theoretical O(1) time complexity and high accuracy make it a promising candidate for high-precision real-time decoders.