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We propose a sampling-based simulation for fault-tolerant quantum errorcorrection under coherent noise. A mixture of incoherent and coherent noise,possibly due to over-rotation, is decomposed into Clifford channels with aquasiprobability distribution. Then, an unbiased estimator of the logical errorprobability is constructed by sampling Clifford channels with an appropriatepostprocessing. We characterize the sampling cost via the channel robustnessand find that the proposed sampling-based method is feasible even for planarsurface codes with relatively large code distances intractable for fullstate-vector simulations. As a demonstration, we simulate repetitive faultysyndrome measurements on the planar surface code of distance 5 with 81 qubits.We find that the coherent error increases the logical error rate. This is apractical application of the quasiprobability simulation for a meaningful taskand would be useful to explore experimental quantum error correction on thenear-term quantum devices.

Sampling-based quasiprobability simulation for fault-tolerant quantum error correction on the surface codes under coherent noise