Mitigating Quantum Errors via Truncated Neumann Series

The degree of truncated Neumann series as a function of the noise resistance.


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.

Science China Information Sciences
Yu-Ao Chen
Yu-Ao Chen
Research Associate

I obtained my BS in Mathematics and Applied Mathematics from University of Science and Technology of China. I obtained my PhD degree in Applied Mathematics from University of Chinese Academy of Sciences under the supervision of Prof. Xiao-Shan Gao. My research interests include quantum computing, symbolic computation and cryptanalysis.

Xin Wang
Xin Wang
Associate Professor

Prof. Xin Wang founded the QuAIR lab at HKUST(Guangzhou) in June 2023. His research primarily focuses on better understanding the limits of information processing with quantum systems and the power of quantum artificial intelligence. Prior to establishing the QuAIR lab, Prof. Wang was a Staff Researcher at the Institute for Quantum Computing at Baidu Research, where he concentrated on quantum computing research and the development of the Baidu Quantum Platform. Notably, he spearheaded the development of Paddle Quantum, a Python library designed for quantum machine learning. From 2018 to 2019, Prof. Wang held the position of Hartree Postdoctoral Fellow at the Joint Center for Quantum Information and Computer Science (QuICS) at the University of Maryland, College Park. He earned his doctorate in quantum information from the University of Technology Sydney in 2018, under the guidance of Prof. Runyao Duan and Prof. Andreas Winter. In 2014, Prof. Wang obtained his B.S. in mathematics (with Wu Yuzhang Honor) from Sichuan University.