Interplay between non-Markovian noise and finite-duration gates in randomized benchmarking experiments

Randomized benchmarking (RB) is a widely used protocol for characterizing errors in qubit systems. While RB is effective at extracting the average gate infidelity under Markovian and gate independent noise, the Markovian assumption breaks down in realistic systems (e.g. superconducting qubits subject to 1/f dephasing noise). Here, we model RB experiments in the presence of non-Markovian dephasing noise, using a physically motivated approach that incorporates the finite-duration pulse sequences used to implement gates. This approach captures the intricate dynamics that arise from the interplay between time-correlated noise and driving. Using a generalized cumulant expansion inspired by our recent work [1], we derive expressions for the survival probability decay curve that are non-perturbative in the noise strength. Our results reveal a range of decay behaviors going from exponential in the Markovian limit to power-law for quasistatic noise. Importantly, we find that in many experimentally relevant regimes the decay remains exponential with a rate that depends on gate implementation but that is not directly related to the average gate infidelity.

[1] P. Groszkowski, A. Seif, J. Koch, and A. A. Clerk, Simple master equations for describing driven systems subject to classical non-Markovian noise, Quantum 7, 972 (2023)