  We review an experimental technique used to correct state preparation and
measurement errors on gate-based quantum computers, and discuss its rigorous
justification. Within a specific biased quantum measurement model, we prove
that nonideal measurement of an arbitrary $n$-qubit state is equivalent to
ideal projective measurement followed by a classical Markov process $\Gamma$
acting on the output probability distribution. Measurement errors can be
removed, with rigorous justification, if $\Gamma$ can be learned and inverted.
We show how to obtain $\Gamma$ from gate set tomography (R. Blume-Kohout et
al., arXiv:1310.4492) and apply the error correction technique to single IBM Q
superconducting qubits.
