Subspace benchmarking high-fidelity entangling operations with trapped ions

Abstract

We present a new and simplified two-qubit randomized benchmarking procedure that operates only in the symmetric subspace of a pair of qubits and is well suited for benchmarking trapped-ion systems. By performing benchmarking only in the symmetric subspace, we drastically reduce the experimental complexity, a number of gates required, and run time. The protocol is demonstrated on trapped ions using collective single-qubit rotations and the Mølmer-Sørenson (MS) interaction to estimate an entangling gate error of 2(1)×10^{−3}. We analyze the expected errors in the MS gate and find that the population remains mostly in the symmetric subspace. The errors that mix symmetric and antisymmetric subspaces appear as leakage and we characterize them by combining our protocol with recently proposed leakage benchmarking. Generalizations and limitations of the protocol are also discussed.