Randomized Benchmarking for Continuosly Parametrized Entangling Gates

We present a variation of the randomized benchmarking (RB) protocol in which random sequences are drawn from a twirling group containing entangling gates with arbitrary rotation angles. Under standard RB assumptions, the average noise channel twirls to a sum of projectors onto the irreducible representations (irreps) of the group. The decay parameters associated with the irreps are isolated by measuring a suitable POVM and applying a transformation to the outcome distribution. We apply this technique to several groups, including the group generated by the two-qubit Pauli operators and continuously parametrized Molmer-Sorenson (MS) gates, which are realizable as the native entangling gates in a trapped ion architecture. The protocol estimates the average fidelity and determines the block-diagonal components of the noise on the MS gates projected onto each irrep. We simulate this method and show that the precision of the noise estimates compares favorably to joint process and measurement tomography, indicating that the tomographic information can be extracted in a manner that is robust to state prep and measurement errors.