Logical error growth in the presence of coherent physical errors

Coherent errors are unknown unitary rotations that can result from imperfections in experimental control and calibration. A key characteristic of coherent errors is that, when left to accumulate freely, they can constructively interfere in a circuit and quickly corrupt the system state. Fortunately, much like Pauli errors, coherent errors can be exponentially suppressed using stabilizer codes with increasing code distance. However, residual logical coherence can still constructively interfere over many error correction cycles. Moreover, constructive interference of physical coherent errors within a single error correction cycle can lead to elevated logical error rate per cycle in certain stabilizer eigenspaces. In this work we analyze how the logical error growth dynamics over repeated error correction cycles depend on the residual logical coherence and the stabilizer eigenspace chosen as the code space.