Threshold theorem in quantum annealing with deterministic analog control errors

We investigate the effect of deterministic analog control errors in the time-dependent Hamiltonian on isolated quantum dynamics. Deterministic analog control errors are formulated as time-dependent operators in the Schrodinger equation. We give an upper bound on the distance between two states in time evolution with and without deterministic analog control errors. As a result, we prove that, if the strength of deterministic analog control errors is less than the inverse of computational time, the final state in quantum dynamics without deterministic analog control errors can be obtained through a constant-order number of measurements in quantum dynamics with deterministic analog control errors.