  Extrapolating physical error rates to logical error rates requires many
assumptions and thus can radically under- or overestimate the performance of an
error correction implementation. We introduce logical randomized benchmarking,
a characterization procedure that directly assesses the performance of a
quantum error correction implementation at the logical level, and is motivated
by a reduction to the well-studied case of physical randomized benchmarking. We
show that our method reliably reports logical performance and can estimate the
average probability of correctable and uncorrectable errors for a given code
and physical channel.
