Generalized randomized compiling for non-Clifford gates

Randomized compiling is a circuit compilation technique with noise-tailoring and suppression effects. The standard implementation of this technique requires all two-qubit gates in the circuit to be Clifford gates. In this paper we extend randomized compiling to circuits containing non-Clifford two-qubit gates, two-qutrit gates , as well as certain k-qubit gates for k > 2. This is achieved by twirling using random gates from suitable subgroups of the unitary group, generalizing the Pauli-twirling method in standard randomized compiling. We give a theoretical characterization of the noise-tailoring effect of twirling using these groups, and provide numerical and experimental evidence of the noise reduction effect due to this technique in various example circuits.