Randomized Benchmarking of Almost Any Gate Set

<!--StartFragment-->We propose and demonstrate a range of simple randomized benchmarking (RB) protocols that can be used to benchmark almost any gate set. The main RB protocol we propose consists of random circuits of gates from any gate set that generates the n-qubit Clifford group. We show that this ``generator RB'' protocol is well-behaved for all reasonably low-error gates, and that the error rate reported by generator RB is a sensible notion of the average error per gate in this gate set. The standard approach to RB consists of implementing random circuits of n-qubit Clifford gates, which, in practice, are necessarily compiled into sequences of the physically available ``primitive gates''. Our protocols have many advantages over this standard approach, including: generator RB directly reports an error per physical primitive gate, rather than an error per Clifford, and generator RB is more scalable, facilitating the benchmarking of a greater number of qubits. We demonstrate our protocols on a trapped ion qubit. <!--EndFragment-->