The BP-LCOSD Algorithm for Toric Codes

The ordered statistics decoding with local constraints (LCOSD) algorithm is an OSD-like decoding algorithm that has been shown to have better performance than the conventional OSD algorithm in classical error-correcting codes. As for quantum error-correcting codes (QECCs), inspired by the post-processing for the quantum LDPC codes, we have proposed a new post-processing decoding algorithm based on the classical LCOSD algorithm for the toric codes, referred to as the BP-LCOSD algorithm. We show by simulations that the BP-LCOSD algorithm has a better logical error rate and a higher fault-tolerance threshold compared to the minimum-weight perfect matching (MWPM) algorithm in decoding toric codes.