Physics-Inspired Extrapolation for efficient error mitigation and hardware certification
Quantum error mitigation (QEM) is essential for the noisy intermediate-scale quantum era, and will remain relevant for early fault-tolerant quantum computers, where logical error rates are still significant. However, most QEM methods incur an exponential sampling overhead to achieve unbiased estimates, limiting their practical applicability. Recently, error mitigation by restricted evolution (EMRE) was shown to estimate expectation values with constant sampling overhead, albeit with a small bias that grows with circuit size and noise level. Building upon the EMRE framework, here, we propose physics-inspired extrapolation (PIE), a linear circuit runtime protocol that achieves enhanced accuracy without incurring substantial overhead. Unlike traditional heuristic zero-noise extrapolation methods, PIE provides a theoretical foundation for the operational interpretation of its fitting parameters and demonstrates convergence to unbiased estimates as noise decreases. Distinctively, the slope of the extrapolation fit corresponds to the max-relative entropy between the ideal and noisy circuits, enabling quantitative hardware certification alongside error mitigation, with no additional computational overhead. We also demonstrate the efficacy of this method on IBMQ hardware and apply it to simulate 84-qubit quantum dynamics efficiently. Our results show that PIE yields accurate, low-variance error mitigated estimates, establishing it as a practical and scalable strategy for both error mitigation and hardware certification for near-term and early fault-tolerant quantum computers.