Lifting multiplicity in randomized benchmarking with applications to Mølmer-Sørensen gates

Clifford randomized benchmarking measures the average fidelity of a set of quantum operations that are an approximate representation of the n-qubit Clifford group, and character randomized benchmarking provides one approach to analyze non-Clifford benchmarking groups. However, character randomized benchmarking fails to adequately address situations where there is multiplicity in the representation of the benchmarking group. In such cases, the resulting signals appear as multi-exponential decays that are difficult to fit. In this work, we propose to lift multiplicity by expanding the benchmarking group with a set of fiducial operations that allow us to address particular isotypic components of the representation. Simply put, we perform tomography on irreps that appear with multiplicity. We apply this technique to design characterization experiments for MS gates. One direct application of this technique is that we can resolve isolated leakage and seepage rates between invariant subspaces of the action of the MS gate.