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

TL;DR

This paper establishes a rigorous connection between randomized benchmarking decay parameters and a new fidelity measure for quantum gates, clarifying interpretation issues under gate-dependent noise.

Contribution

It proves that the RB decay parameter equals the decay of the gateset circuit fidelity and explains discrepancies in fidelity estimates due to basis mismatch.

Findings

RB decay parameter matches gateset circuit fidelity decay

Discrepancies in fidelity are due to basis mismatch

Results likely extend to higher-dimensional systems

Abstract

Randomized benchmarking (RB) protocols have become an essential tool for providing a meaningful partial characterization of experimental quantum operations. While the RB decay rate is known to enable estimates of the average fidelity of those operations under gate-independent Markovian noise, under gate-dependent noise this rate is more difficult to interpret rigorously. In this paper, we prove that single-qubit RB decay parameter $p$ coincides with the decay parameter of the gate-set circuit fidelity, a novel figure of merit which characterizes the expected average fidelity over arbitrary circuits of operations from the gate-set. We also prove that, in the limit of high-fidelity single-qubit experiments, the possible alarming disconnect between the average gate fidelity and RB experimental results is simply explained by a basis mismatch between the gates and the state-preparation and measurement procedures, that is, to a unitary degree of freedom in labeling the Pauli matrices. Based on numerical evidence and physically motivated arguments, we conjecture that these results also hold for higher dimensions.