Conditionally rigorous mitigation of multiqubit measurement errors
Several techniques have been recently introduced to mitigate errors in
near-term quantum computers without the overhead required by quantum error
correcting codes. While most of the focus has been on gate errors, measurement
errors are significantly larger than gate errors on some platforms. A widely
used {\it transition matrix error mitigation} (TMEM) technique uses measured
transition probabilities between initial and final classical states to correct
subsequently measured data. However from a rigorous perspective, the noisy
measurement should be calibrated with perfectly prepared initial states and the
presence of any state-preparation error corrupts the resulting mitigation. Here
we develop a measurement error mitigation technique, conditionally rigorous
TMEM, that is not sensitive to state-preparation errors and thus avoids this
limitation. We demonstrate the importance of the technique for high-precision
measurement and for quantum foundations experiments by measuring Mermin
polynomials on IBM Q superconducting qubits. An extension of the technique
allows one to correct for both state-preparation and measurement (SPAM) errors
in expectation values as well; we illustrate this by giving a protocol for
fully SPAM-corrected quantum process tomography.
Michael R. Geller