  Randomized benchmarking (RB) is an important protocol for robustly
characterizing the error rates of quantum gates. The technique is typically
applied to the Clifford gates since they form a group that satisfies a
convenient technical condition of forming a unitary 2-design, in addition to
having a tight connection to fault-tolerant quantum computing and an efficient
classical simulation. In order to achieve universal quantum computing one must
add at least one additional gate such as the T gate (also known as the $\pi$/8
gate). Here we propose and analyze a simple variation of the standard
interleaved RB protocol that can accurately estimate the average fidelity of
the T gate while retaining the many advantages of a unitary 2-design and the
fidelity guarantees that such a design delivers, as well as the efficient
classical simulation property of the Clifford group. Our work complements prior
methods that have succeeded in estimating T gate fidelities, but only by
relaxing the 2-design constraint and using a more complicated data analysis.
