Subspace benchmarking high-fidelity entangling operations with trapped ions

TL;DR

This paper introduces a simplified symmetric subspace randomized benchmarking method for trapped-ion systems, significantly reducing experimental complexity while accurately estimating entangling gate errors.

Contribution

The authors develop a new benchmarking protocol that operates solely within the symmetric subspace, streamlining the process for trapped-ion quantum systems.

Findings

Estimated entangling gate error of 2(1)×10^{-3}

Reduced experimental complexity and run time

Characterized leakage errors between symmetric and anti-symmetric subspaces

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, number of gates required, and run time. The protocol is demonstrated on trapped ions using collective single-qubit rotations and the Molmer-Sorenson (MS) interaction to estimate an entangling gate error of $2(1) \times 10^{-3}$. We analyze the expected errors in the MS gate and find that population remains mostly in the symmetric subspace. The errors that mix symmetric and anti-symmetric 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.