Data-driven adaptive quantum error mitigation for probability distribution

Quantum error mitigation (QEM) has been proposed as a class of hardware-friendly error suppression techniques. While QEM has been primarily studied for mitigating errors in the estimation of expectation values of observables, recent works have explored its application to estimating noiseless probability distributions. In this work, we propose two protocols to improve the accuracy of QEM for probability distributions, inspired by techniques in software engineering. The first is the N-version programming method, which compares probability distributions obtained via different QEM strategies and excludes the outlier distribution, certifying the feasibility of the error-mitigated distributions. The second is a consistency-based method for selecting an appropriate extrapolation strategy. Specifically, we prepare K data points at different error rates, choose L<K of them for extrapolation, and evaluate error-mitigated results for all binom{K}{L} possible choices. We then select the extrapolation method that yields the smallest variance in the error-mitigated results. This procedure can also be applied bitstring-wise, enabling adaptive error mitigation for each probability in the distribution.