  Quantum error mitigation (QEM) is a class of promising techniques for
reducing the computational error of variational quantum algorithms. In general,
the computational error reduction comes at the cost of a sampling overhead due
to the variance-boosting effect caused by the channel inversion operation,
which ultimately limits the applicability of QEM. Existing sampling overhead
analysis of QEM typically assumes exact channel inversion, which is unrealistic
in practical scenarios. In this treatise, we consider a practical channel
inversion strategy based on Monte Carlo sampling, which introduces additional
computational error that in turn may be eliminated at the cost of an extra
sampling overhead. In particular, we show that when the computational error is
small compared to the dynamic range of the error-free results, it scales with
the square root of the number of gates. By contrast, the error exhibits a
linear scaling with the number of gates in the absence of QEM under the same
assumptions. Hence, the error scaling of QEM remains to be preferable even
without the extra sampling overhead. Our analytical results are accompanied by
numerical examples.
