Error mitigated shadow estimation based on virtual distillation

Abstract

Shadow estimation is a method for deducing numerous properties of an unknown quantum state through a limited set of measurements, which suffers from noises in quantum devices. In this paper, we introduce an error-mitigated shadow estimation approach based on virtual distillation, tailored for applications in near-term quantum devices. Our methodology leverages the qubit reset technique, thereby reducing the associated qubit overhead. Crucially, our approach ensures that the required qubit resources remain independent of the desired accuracy and avoid an exponential measurement overhead, marking a substantial advancement in practical applications. Furthermore, our technique accommodates a mixed Clifford and Pauli-type shadow, which can result in a reduction in the number of required measurements across various scenarios. We also study the trade-off between circuit depth and measurement overhead quantitatively. Through numerical simulations, we substantiate the efficacy of our error mitigation method, establishing its utility in enhancing the robustness of shadow estimations on near-term quantum devices.