Easy twirling gates provide more accurate fidelity estimation

Accurate benchmarking of quantum gates is crucial for understanding and enhancing the performance of quantum hardware. A standard method for this is interleaved benchmarking, a technique which estimates the error on an interleaved target gate by comparing cumulative error rates of randomized sequences implemented with the interleaved gate (interleaved sequence) and without it (reference sequence) . In this study, we show that the choice of randomization group, also called twirling group, has a significant impact on the accuracy of fidelity estimates. In particular, we find that more recent approaches based twirling groups with lower error rates, such as the Pauli group used in cycle benchmarking, provide significantly reduced systematic uncertainty relative to the standard approach of interleaved randomized benchmarking (IRB), which uses the 2-qubit Clifford group for randomization. Our analysis considers supplementing IRB with purity benchmarking, but while this provides some reduction to the systematic uncertainty, we find the approach still falls short of the higher accuracy of cycle benchmarking. We support our conclusions with a theoretical framework for bounding systematic errors, extensive numerical results comparing a range of interleaved protocols under fixed resource costs and experimental demonstrations on three quantum computing platforms. In order to compare the accuracy of fidelity estimation protocols on a rigorous basis, we also introduce a protocol for gauge-fixing of the fidelity. This protocol overcomes the gauge-ambiguity in the definition of fidelity and this for the first time allows for a precise theoretical statement regarding the `true infidelity' of an interleaved gate operation.