Coherent errors and readout errors in the surface code

We consider the combined effect of readout errors and coherent errors, i.e., deterministic phase rotations, on surface code. use a recently developed numerical approach, via mapping physical qubits to Majorana fermions. show how this approach in presence treated phenomenological level: perfect projective measurements with potentially incorrectly recorded outcomes, multiple repeated measurement rounds. find threshold for combination an error rate close corresponding incoherent channel (random Pauli-Z errors). The value rate, using worst case fidelity as measure logical is 2.6%. Below threshold, scaling up code leads rapid loss coherence logical-level but rates that are greater than those channel. also vary independently, more sensitive errors. Our work extends recent results experimentally realistic situation where occur.