  In this work, we propose a two-stage procedure to systematically address
quantum noise inherent in quantum measurements. The idea behind it is
intuitive: we first detect and then eliminate quantum noise so that the
classical noise assumption is satisfied and measurement error mitigation works.
In the first stage, inspired by coherence witness in the resource theory of
quantum coherence, we design an efficient method to detect quantum noise. It
works by fitting the difference between two measurement statistics to the
Fourier series, where the statistics are obtained using maximally coherent
states with relative phase and maximally mixed states as inputs. The fitting
coefficients quantitatively benchmark quantum noise. In the second stage, we
design various methods to eliminate quantum noise, inspired by the Pauli
twirling technique. They work by executing randomly sampled Pauli gates before
the measurement device and conditionally flipping the measurement outcomes in
such a way that the effective measurement device contains only classical noise.
We demonstrate the feasibility of the two-stage procedure numerically on Baidu
Quantum Platform. Remarkably, the results show that quantum noise in
measurement devices is significantly suppressed, and the quantum computation
accuracy is substantially improved. We highlight that the two-stage procedure
complements existing measurement error mitigation techniques, and they together
form a standard toolbox for manipulating measurement errors in near-term
quantum devices.
