Validation of Attaining a Higher Threshold Using Double-Pass MWPM Decoding of CSS Codes Using X/Z Correlations

In this report we validate that Minimum Weight Perfect Matching (MWPM) decoding ofa surface code helps attain a higher code threshold than standard decoding by taking into account the correlations of errors that occur on the lattice. Correlated decoding cannot be directly performed using MWPM due to the presence of hyperedges in the graph. Decomposing correlated errors into simultaneous X and Z excitations, along with considering an asymmetric code for optimal performance of this scheme, yields a codecapacity threshold of 15% for standard depolarizing error by updating the weights of one decoding graph based on the corrections of another.