  We describe a practical experimental protocol for robustly characterizing the
error rates of non-Clifford gates associated with dihedral groups, including
gates in SU(2) associated with arbitrarily small angle rotations. Our dihedral
benchmarking protocol is a generalization of randomized benchmarking that
relaxes the usual unitary 2-design condition. Combining this protocol with
existing randomized benchmarking schemes enables an efficient means of
characterizing universal gate sets for quantum information processing in a way
that is independent of state-preparation and measurement errors. In particular,
our protocol enables direct benchmarking of the $T$ gate (sometime called
$\pi/8$-gate) even for the gate-dependent error model that is expected in
leading approaches to fault-tolerant quantum computation.
