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Randomized benchmarking (RB) protocols have become an essential tool forproviding a meaningful partial characterization of experimental quantumoperations. While the RB decay rate is known to enable estimates of the averagefidelity of those operations under gate-independent Markovian noise, undergate-dependent noise this rate is more difficult to interpret rigorously. Inthis paper, we prove that single-qubit RB decay parameter $p$ coincides withthe decay parameter of the gate-set circuit fidelity, a novel figure of meritwhich characterizes the expected average fidelity over arbitrary circuits ofoperations from the gate-set. We also prove that, in the limit of high-fidelitysingle-qubit experiments, the possible alarming disconnect between the averagegate fidelity and RB experimental results is simply explained by a basismismatch between the gates and the state-preparation and measurementprocedures, that is, to a unitary degree of freedom in labeling the Paulimatrices. Based on numerical evidence and physically motivated arguments, weconjecture that these results also hold for higher dimensions.

From randomized benchmarking experiments to gateset circuit fidelity: how to interpret randomized benchmarking decay parameters