  We propose a sampling-based simulation for fault-tolerant quantum error
correction under coherent noise. A mixture of incoherent and coherent noise,
possibly due to over-rotation, is decomposed into Clifford channels with a
quasiprobability distribution. Then, an unbiased estimator of the logical error
probability is constructed by sampling Clifford channels with an appropriate
postprocessing. We characterize the sampling cost via the channel robustness
and find that the proposed sampling-based method is feasible even for planar
surface codes with relatively large code distances intractable for full
state-vector simulations. As a demonstration, we simulate repetitive faulty
syndrome 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 a
practical application of the quasiprobability simulation for a meaningful task
and would be useful to explore experimental quantum error correction on the
near-term quantum devices.
