Improved belief propagation decoding algorithm based on decoupling representation of Pauli operators for quantum stabilizer codes

The article delves into the critical role of decoding algorithms in the effectiveness of quantum error-correcting codes, particularly stabilizer codes. It highlights the challenges faced by current belief propagation (BP) algorithms, such as quaternary BP and binary BP, in handling Pauli Y errors and achieving scalable efficiency. The authors propose a novel decoupling representation of Pauli operators, which eliminates the correlations introduced by Pauli Y errors and enhances the decoding performance. This representation leads to the development of partially decoupled binary BP (PDBP) and fully decoupled binary BP (FDBP) algorithms. Simulation results demonstrate that PDBP and FDBP outperform traditional symplectic binary BP (SBP) in pure Y noise and depolarizing noise channels, showcasing a more balanced capability to decode Pauli X, Y, and Z errors. The article also discusses the potential of FDBP in practical implementations and addresses open questions regarding the time complexity and measurement noise. The detailed analysis and innovative approach make this article a significant contribution to the field of quantum error correction and decoding algorithms.