Spectra and phase transition in Grover's algorithm with systematic noise*

In this work, we present a study of Grover's search algorithm in the presence of systematic noise. By modeling the Grover operator within one timestep as a Floquet unitary, we showed that the bulk quasi-energy spectrum is well-captured by the first-order perturbation theory. Using the random matrix theory of an effective Hamiltonian, we obtain the scaling of the critical disorder for the algorithm. In addition, we also derive semi-analytical results for the oscillation frequency of the target state in the presence of noise.