Randomized benchmarking with non-Markovian noise and realistic finite-time gates

We analyze the impact of non-Markovian classical noise on single-qubit randomized benchmarking experiments, in a manner that explicitly models the realization of each gate via realistic finite-duration pulses. Our new framework exploits the random nature of each gate sequence to derive expressions for the full survival probability decay curve which are nonperturbative in the noise strength. In the presence of non-Markovian noise, our approach shows that the decay curve can exhibit a strong dependence on the gate implementation method, with regimes of both exponential and power law decays. We discuss how these effects can complicate the interpretation of a randomized benchmarking experiment, but also how to leverage them to probe non-Markovianity.