Finite-Basis Duality Estimate for the Surface-Code Threshold under Correlated Bit-Flip Errors

We apply finite-basis duality to a statistical-mechanical model introduced by Chubb and Flammia for the surface code under spatially correlated bit-flip noise, for which their mapping gives a random-bond Ising model with both two-body edge interactions and four-body face interactions, and obtain several estimations of the error thresholds via the duality analysis in conjunction with the replica method.