Disagreement-Gated Graph-Residual Correction for Mismatched MWPM Decoding in Surface Codes

Minimum-weight perfect matching (MWPM) is one of the most widely used decoders for surface-code quantum error correction. However, its performance deteriorates when the assumed detector error model is mismatched with correlated circuit-level noise. In this work, we propose a decoder-disagreement-gated graph-residual correction framework that enhances mismatched MWPM without replacing it. The proposed hybrid decoder preserves MWPM as the primary decoder and applies selective residual correction using detector syndromes, graph-structured detector features, and decoder-context information only when residual correction is expected to be beneficial. We use direct residual correction as a diagnostic baseline for d = 3 and d = 5, and evaluate the proposed disagreement-gated strategy across d = 3, 5, and 7 under structured correlated-noise mismatch. Results indicate that direct residual correction achieves the strongest improvement at d = 3, with an average logical error rate (LER) reduction of 48.64%. Its effectiveness diminishes at d = 5, with an average reduction of 12.76% over the retained test points. In contrast, the disagreement-gated method maintains positive gains at d = 3, with an average LER reduction of 14.57%, and demonstrates better scalability, achieving average reductions of 29.56% at d = 5 and 35.63% at d = 7. Additionally, the proposed approach consistently improves decoding performance across all evaluated gated configurations, reduces the performance gap relative to the true-DEM PyMatching reference, and maintains positive net correction by correcting more MWPM errors than it introduces. These results show that selective graph-residual correction can improve MWPM surface-code decoding under correlated detector-model mismatch while retaining MWPM as the primary decoder.

paperurl: ‘https://www.researchgate.net/publication/415517916_Disagreement-Gated_Graph-Residual_Correction_for_Mismatched_MWPM_Decoding_in_Surface_Codes’