  Achieving error rates that meet or exceed the fault-tolerance threshold is a
central goal for quantum computing experiments, and measuring these error rates
using randomized benchmarking is now routine. However, direct comparison
between measured error rates and thresholds is complicated by the fact that
benchmarking estimates average error rates while thresholds reflect worst-case
behavior when a gate is used as part of a large computation. These two measures
of error can differ by orders of magnitude in the regime of interest. Here we
facilitate comparison between the experimentally accessible average error rates
and the worst-case quantities that arise in current threshold theorems by
deriving relations between the two for a variety of physical noise sources. Our
results indicate that it is coherent errors that lead to an enormous mismatch
between average and worst case, and we quantify how well these errors must be
controlled to ensure fair comparison between average error probabilities and
fault-tolerance thresholds.
