Hypothesis Testing for Error Mitigation: How to Judge Error Mitigation

There is a plethora of error mitigation (EM) techniques available in the literature to combat errors in Noisy Intermediate-Scale Quantum (NISQ) machines. In an experiment one then uses a set of EM techniques to mitigate errors, which we refer to as an EM pipeline. Although EM pipelines successfully mitigate errors in theory, we observe in practice that for a modest number of qubits EM does not always improve results while moreover also incurring circuit and/or shots overhead.

These observations provoke three key questions:

(a) How to determine if an EM pipeline mitigates error more often than not?

(b) How to compare multiple EM pipelines? and

(c) How to capture mitigation efficiency and resource overhead succinctly with a single metric?

In this work, we utilize a statistical hypothesis testing procedure to answer questions (a) and (b). Particularly, one-sample test of proportions to evaluate a single EM pipeline and two-sample test of proportions to compare multiple pipelines while for the last question we propose an entropic figure of merit. Finally, we demonstrate the use case of the hypothesis testing and the figure merit by conducting hardware experiments with several EM pipelines.

Our proposed approach and the metric will enable researchers to evaluate both existing and novel EM methods boosting NISQ applications as well.