  Error mitigation techniques are crucial to achieving near-term quantum
advantage. Classical post-processing of quantum computation outcomes is a
popular approach for error mitigation, which includes methods such as Zero
Noise Extrapolation, Virtual Distillation, and learning-based error mitigation.
However, these techniques have limitations due to the propagation of
uncertainty resulting from a finite shot number of the quantum measurement. To
overcome this limitation, we propose general and unbiased methods for
quantifying the uncertainty and error of error-mitigated observables by
sampling error mitigation outcomes. These methods are applicable to any
post-processing-based error mitigation approach. In addition, we present a
systematic approach for optimizing the performance and robustness of these
error mitigation methods under uncertainty, building on our proposed
uncertainty quantification methods. To illustrate the effectiveness of our
methods, we apply them to Clifford Data Regression in the ground state of the
XY model simulated using IBM's Toronto noise model.
