Abstract
Quantum Surface codes are a kind of quantum topological stabilizer codes whose stabilizers and qubits are geometrically related. Due to their special structures, surface codes have great potential to lead people to large-scale quantum computation. In the minimum weight perfect matching (MWPM) decoding of surface codes, the bit-flip errors and phase-flip errors are assumed to be independent for simplicity. However, these two kinds of errors are likely to be correlated in the real world. In this paper, we propose a modification to MWPM decoding for surface codes to deal with the noises in depolarizing channels where bit-flip errors and phase-flip errors are correlated. With this modification, we obtain thresholds of 17% and 15.3% for the surface codes with mixed boundaries and the surface codes with a hole, respectively
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