Hypothesis Testing for Error Mitigation: How to Evaluate Error Mitigation

TL;DR

This paper introduces hypothesis testing and a new figure of merit to evaluate and compare quantum error mitigation techniques, addressing the gap between theoretical models and real device performance in the NISQ era.

Contribution

It proposes a statistical framework and an inclusive metric for assessing the effectiveness and resource trade-offs of various error mitigation methods on real quantum hardware.

Findings

Hypothesis testing effectively evaluates error mitigation performance.

The figure of merit balances resource costs and mitigation efficiency.

Experimental evaluation of 16 error mitigation pipelines on IBM quantum computers.

Abstract

In the noisy intermediate-scale quantum (NISQ) era, quantum error mitigation will be a necessary tool to extract useful performance out of quantum devices. However, there is a big gap between the noise models often assumed by error mitigation techniques and the actual noise on quantum devices. As a consequence, there arises a gap between the theoretical expectations of the techniques and their everyday performance. Cloud users of quantum devices in particular, who often take the devices as they are, feel this gap the most. How should they parametrize their uncertainty in the usefulness of these techniques and be able to make judgement calls between resources required to implement error mitigation and the accuracy required at the algorithmic level? To answer the first question, we introduce hypothesis testing within the framework of quantum error mitigation and for the second question, we propose an inclusive figure of merit that accounts for both resource requirement and mitigation efficiency of an error mitigation implementation. The figure of merit is useful to weigh the trade-offs between the scalability and accuracy of various error mitigation methods. Finally, using the hypothesis testing and the figure of merit, we experimentally evaluate $16$ error mitigation pipelines composed of singular methods such as zero noise extrapolation, randomized compilation, measurement error mitigation, dynamical decoupling, and mitigation with estimation circuits. In total our data involved running $275,640$ circuits on two IBM quantum computers.