Measuring Leakage Rates using Randomized Benchmarking

Leakage errors are those that move the state out of the computational subspace. It has been shown that an adaptation of randomized benchmarking can be used to simultaneously infer bounds on the logical error rate and the leakage rate. Here we show that one can use constraints on the state preparation and measurement errors to obtain orders of magnitude tighter bounds on the logical error rate than those obtained from previous protocols. We apply our procedure to infer the leakage and logical error rates in a superconducting qubit device, where the qubit is formed from a decoherence free subspace of two transmons. We found a 1-σ confidence interval for the logical error rate of [1.6 × 10^-3 , 2.1 × 10^-3 ].