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

Based on decoupling representation of Pauli operators, we propose partially decoupled belief propagation (PDBP) and fully decoupled belief propagation (FDBP) decoding algorithm for quantum LDPC codes. These two algorithms can handle the correlations between the X and Z components of the vectors in symplectic representation, which are introduced by Pauli Y errors. Hence, they can apply not only to CSS codes, but also to non-CSS codes. For planar surface code and XZZX planar surface code, compared with traditional BP based on symplectic representation, the decoding accuracy of PDBP and FDBP is significantly improved in pure Y noise and depolarizing noise, especially that of FDBP. The impressive performance of FDBP might promote the practical implementation of quantum error correcting codes in engineering.