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In the noisy intermediate-scale quantum (NISQ) era, quantum error mitigationwill 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 errormitigation techniques and the actual noise on quantum devices. As aconsequence, there arises a gap between the theoretical expectations of thetechniques and their everyday performance. Cloud users of quantum devices inparticular, who often take the devices as they are, feel this gap the most. Howshould they parametrize their uncertainty in the usefulness of these techniquesand be able to make judgement calls between resources required to implementerror mitigation and the accuracy required at the algorithmic level? To answerthe first question, we introduce hypothesis testing within the framework ofquantum error mitigation and for the second question, we propose an inclusivefigure of merit that accounts for both resource requirement and mitigationefficiency of an error mitigation implementation. The figure of merit is usefulto weigh the trade-offs between the scalability and accuracy of various errormitigation methods. Finally, using the hypothesis testing and the figure ofmerit, we experimentally evaluate $16$ error mitigation pipelines composed ofsingular methods such as zero noise extrapolation, randomized compilation,measurement error mitigation, dynamical decoupling, and mitigation withestimation circuits. In total our data involved running $275,640$ circuits ontwo IBM quantum computers.

Hypothesis Testing for Error Mitigation: How to Evaluate Error Mitigation