Randomized benchmarking in the presence of non-Markovian noise

Detecting and characterizing the noise features aids us in suppressing the error rates in qubit operations, which will allow us to advance the realization of a fault-tolerant quantum computer. Among the various methods established to address this issue, randomized benchmarking (RB) is the most prominent protocol used to characterize the gate errors in a quantum processor due to its ease of implementation and interpretation. However, RB protocols rely on the assumption of temporally uncorrelated (i.e., Markovian) noise in the system. Unfortunately, many real systems suffer from non-Markovian noise, and so neglecting such processes can lead to inaccurate results. In this work, we go beyond this assumption and study the impact of non-Markovian noise in single-qubit RB experiments. Despite the exponentially decaying nature of the RB curves, our results demonstrate that the RB performance strongly depends on the gate implementation as well as the correlation time of the noise in the system, which is in contrast with the well-known features of a truly Markovian noise. We further discuss how RB protocols can be utilized to probe the non-Markovianity of the noise in a qubit processor.