Robust characterization of leakage errors

Leakage errors arise when the quantum state leaks out of some subspace of interest, for example, the two-level subspace of a multi-level system defining a computational 'qubit', the logical code space of a quantum error-correcting code, or a decoherence-free subspace. Leakage errors pose a distinct challenge to quantum control relative to the more well-studied decoherence errors and can be a limiting factor to achieving fault-tolerant quantum computation. Here we present a scalable and robust randomized benchmarking protocol for quickly estimating the leakage rate due to an arbitrary Markovian noise process on a larger system. We illustrate the reliability of the protocol through numerical simulations.