  Unitarity randomized benchmarking (URB) is an experimental procedure for
estimating the coherence of implemented quantum gates independently of state
preparation and measurement errors. These estimates of the coherence are
measured by the unitarity. A central problem in this experiment is relating the
number of data points to rigorous confidence intervals. In this work we provide
a bound on the required number of data points for Clifford URB as a function of
confidence and experimental parameters. This bound has favorable scaling in the
regime of near-unitary noise and is asymptotically independent of the length of
the gate sequences used. We also show that, in contrast to standard randomized
benchmarking, a nontrivial number of data points is always required to overcome
the randomness introduced by state preparation and measurement errors even in
the limit of perfect gates. Our bound is sufficiently sharp to benchmark
small-dimensional systems in realistic parameter regimes using a modest number
of data points. For example, we show that the unitarity of single-qubit
Clifford gates can be rigorously estimated using few hundred data points under
the assumption of gate-independent noise. This is a reduction of orders of
magnitude compared to previously known bounds.
