Mitigating Quantum Errors via Truncated Neumann Series

TL;DR

This paper introduces a scalable quantum error mitigation framework using truncated Neumann series to effectively reduce gate and measurement errors in quantum computations, improving accuracy without extensive error characterization.

Contribution

The paper proposes a unified, scalable error mitigation method that does not require detailed error models or tomography, enhancing near-term quantum device capabilities.

Findings

Error estimation error decays exponentially with truncated order

Error mitigation overhead is independent of system size under moderate noise

Numerical tests show substantial improvement in computation accuracy

Abstract

Quantum gates and measurements on quantum hardware are inevitably subject to hardware imperfections that lead to quantum errors. Mitigating such unavoidable errors is crucial to explore the power of quantum hardware better. In this paper, we propose a unified framework that can mitigate quantum gate and measurement errors in computing quantum expectation values utilizing the truncated Neumann series. The essential idea is to cancel the effect of quantum error by approximating its inverse via linearly combining quantum errors of different orders produced by sequential applications of the quantum devices with carefully chosen coefficients. Remarkably, the estimation error decays exponentially in the truncated order, and the incurred error mitigation overhead is independent of the system size, as long as the noise resistance of the quantum device is moderate. We numerically test this framework for different quantum errors and find that the computation accuracy is substantially improved. Our framework possesses several vital advantages: it mitigates quantum gate and measurement errors in a unified manner, it neither assumes any error structure nor requires the tomography procedure to completely characterize the quantum errors, and most importantly, it is scalable. These advantages empower our quantum error mitigation framework to be efficient and practical and extend the ability of near-term quantum devices to deliver quantum applications.