Phases and phase transition in Grover's algorithm with systematic noise

While limitations on quantum computation under Markovian environmental noise are well understood in generality, their behavior for different quantum circuits and noise realizations can be less universal. Here we consider a canonical quantum algorithm---Grover's algorithm for unordered search on $L$ qubits---in the presence of systematic noise. This allows us to write the evolution as a random Floquet unitary, which we show is well characterized by random matrix theory (RMT). The RMT analysis enables analytical predictions for different regimes and critical disorders of the many-body dynamics. We find two critical disorders. At small disorder, finite-dimensional manifold remains nonergodic as long as the noise is smaller than an ergodicity-breaking transition, which scales as $O({L}^{\ensuremath{-}1})$. Computational power is lost at a much smaller disorder that scales as $O({2}^{\ensuremath{-}L/2})$. We comment on relevance to nonsystematic noise in realistic quantum computers, including cold atom, trapped ion, and superconducting platforms.