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Unitarity randomized benchmarking (URB) is an experimental procedure forestimating the coherence of implemented quantum gates independently of statepreparation and measurement errors. These estimates of the coherence aremeasured by the unitarity. A central problem in this experiment is relating thenumber of data points to rigorous confidence intervals. In this work we providea bound on the required number of data points for Clifford URB as a function ofconfidence and experimental parameters. This bound has favorable scaling in theregime of near-unitary noise and is asymptotically independent of the length ofthe gate sequences used. We also show that, in contrast to standard randomizedbenchmarking, a nontrivial number of data points is always required to overcomethe randomness introduced by state preparation and measurement errors even inthe limit of perfect gates. Our bound is sufficiently sharp to benchmarksmall-dimensional systems in realistic parameter regimes using a modest numberof data points. For example, we show that the unitarity of single-qubitClifford gates can be rigorously estimated using few hundred data points underthe assumption of gate-independent noise. This is a reduction of orders ofmagnitude compared to previously known bounds.

Efficient Unitarity Randomized Benchmarking of Few-qubit Clifford Gates