Rotationally Invariant Randomized Benchmarking*

Noise characterization methods such as randomized benchmarking (RB) are critical for the development of fault-tolerant quantum computation. However, standard RB techniques become prohibitively inefficient for high-dimensional systems such as qudits or bosonic modes, where experimental control is limited to implementing a small subset of all possible unitary operations. We introduce a broad framework for enhancing the sample efficiency of RB that is sufficiently powerful to extend the practical reach of RB beyond the multiqubit setting. To demonstrate the efficacy of our approach, we develop a detailed theory of RB for systems with rotational symmetry. Such systems carry a natural action of the group SU(2), and they form the basis for several novel quantum error-correcting codes. We show that, for experimentally accessible high-spin systems, our RB protocols can reduce the complexity of measuring rotationally invariant error rates by more than two orders of magnitude relative to standard approaches such as character RB.