  A new class of protocols called mirror benchmarking was recently proposed to
measure the system-level performance of quantum computers. These protocols
involve circuits with random sequences of gates followed by mirroring, that is,
inverting each gate in the sequence. We give a simple proof that mirror
benchmarking leads to an exponential decay of the survival probability with
sequence length, under the uniform noise assumption, provided the twirling
group forms a 2-design. The decay rate is determined by a quantity that is a
quadratic function of the error channel, and for certain types of errors is
equal to the unitarity. This result yields a new method for estimating the
coherence of noise. We present data from mirror benchmarking experiments run on
the Honeywell System Model H1. This data constitutes a set of performance
curves, indicating the success probability for random circuits as a function of
qubit number and circuit depth.
