Character randomized benchmarking for non-multiplicity-free groups with applications to subspace, leakage, and matchgate randomized benchmarking

Randomized benchmarking (RB) is a powerful method for determining the error rate of quantum gates. However, classical RB is restricted to gatesets like the Clifford group that form a unitary 2-design. The recently introduced character RB can benchmark more general gates using techniques from representation theory; however, this method has only been explored for “multiplicity-free” groups, limiting its applicability. In this talk, I’ll present a generalization of character RB that explicitly includes non-multiplicity-free groups, and three example applications. First, I’ll give a rigorous version of the recently introduced subspace RB[1] for characterizing the Honeywell entangling gate. Second, I present a leakage RB that applies to more general gates than the original[2]. Finally, I’ll demonstrate a scalable RB protocol for the matchgate group. This represents one of the few examples of a scalable non-Clifford RB. I’ll also discuss the potential of using character RB to characterize specific gates and find new examples of scalable RB.
[1] C. Baldwin et al., Subspace benchmarking high-fidelity entangling operations with trapped ions, Phys. Rev. Res. 2, 013317 (2020).
[2] C. Wood and J. Gambetta, Quantification and characterization of leakage errors, Phys. Rev. A 97, 032306 (2018).