  Randomized benchmarking is a technique for estimating the average fidelity of
a set of quantum gates. For general gatesets, however, it is difficult to draw
robust conclusions from the resulting data. Here we propose a new method based
on representation theory that has little experimental overhead and applies to a
broad class of benchmarking problems. As an example, we apply our method to a
gateset that includes the $T$-gate, and analyze a new interleaved benchmarking
protocol that extracts the average fidelity of a 2-qubit Clifford gate using
only single-qubit Clifford gates as reference.
