Noise-Robust Estimation of Quantum Observables in Noisy Hardware

Abstract

Error mitigation is essential for extracting reliable results from quantum computations performed on noisy intermediate-scale quantum hardware. Here we introduce Noise-Robust Estimation (NRE), a noise-agnostic framework that suppresses estimation bias through a two-stage post-processing protocol. The method combines measurement data from a target circuit and a corresponding noise-canceling companion circuit to construct a baseline estimator with reduced sensitivity to noise. We show that the residual bias of this estimator is governed by the variation of an auxiliary quantity across amplified noise realizations, motivating the use of a measurable diagnostic quantity: the normalized dispersion of this auxiliary estimator. When the dispersion approaches zero, contributions arising from imperfect noise amplification vanish and the remaining bias terms are expected to diminish for smooth stationary noise profiles. Leveraging this relationship, NRE performs a final extrapolation to the zero-dispersion limit using bootstrapped measurement data. We experimentally validate the method on a 20-qubit IQM superconducting quantum processor using circuits containing up to 480 entangling CZ gates. Across a variety of circuits and noise levels, NRE consistently achieves substantially reduced bias compared to existing mitigation techniques while maintaining moderate sampling overhead. These results establish NRE as a practical and broadly applicable error-mitigation strategy for quantum computations on noisy hardware.