Certification and Classification of Linear Quantum Error Mitigation Methods

TL;DR

This paper introduces a framework of quantitative metrics and criteria for certifying and classifying linear quantum error mitigation methods, aiding future comparison and strategy development.

Contribution

It develops a set of metrics and a taxonomy for linear quantum error mitigation methods, enabling application-specific certification and evaluation.

Findings

Metrics account for continual hardware improvements.

Certification criteria include scalability, efficiency, robustness.

Framework applied to a mitigation strategy for stochastic noise and rotational errors.

Abstract

Numerous mitigation methods exist for quantum noise suppression, making it challenging to identify the optimum approach for a specific application; especially as ongoing advances in hardware tuning and error correction are expected to reduce logical error rates. In order to facilitate the future-proof application-dependent comparison of mitigation methods, we develop a set of quantitative metrics that account for continual improvements in logical gate quality. We use these metrics to define qualitative criteria (e.g. scalability, efficiency, and robustness to characterised imperfections in the mitigation implementation), which we combine into application-specific certifications. We then provide a taxonomy of linear mitigation methods, characterising them by their features and requirements. Finally, we use our framework to produce and evaluate a mitigation strategy. A mitigation strategy is a collections of mitigation methods and compilation procedures designed to mitigate all relevant errors for a given piece of characterised hardware. Our example mitigation strategy is targeted at mitigating the outputs of hardware suffering from stochastic noise and/or rotational errors. We find the most significant determinant of efficient mitigation is accurate and precise characterisation.