https://doi.org/10.1140/epjqt/s40507-024-00261-x
Research
Efficient quantum state estimation with low-rank matrix completion
1
Department of Electronics and Information Convergence Engineering, Kyung Hee University, 1732 Deogyeong-daero, 17104, Yongin-si, Gyeonggi-do, Korea
2
Department of Electrical Engineering and Automation, Aalto University, 02150, Espoo, Finland
3
Interdisciplinary Centre for Security, Reliability and Trust (SnT), Univerity of Luxembourg, L-1855, Luxembourg
4
Department of Electrical and Computer Engineering, Memorial University of Newfoundland, St. John’s, NL, Canada
Received:
1
March
2023
Accepted:
29
July
2024
Published online:
5
August
2024
This paper introduces a novel and efficient technique for quantum state estimation, coined as low-rank matrix-completion quantum state tomography for characterizing pure quantum states, as it requires only non-entangling bases and 
local Pauli operators. This significantly reduces the complexity of the process and increases the accuracy of the state estimation, as it eliminates the need for the entangling bases, which are experimentally difficult to implement on quantum devices. The required minimal post-processing, improved accuracy and efficacy of this matrix-completion-based method make it an ideal benchmarking tool for investigating the properties of quantum systems, enabling researchers to verify the accuracy of quantum devices, characterize their performance, and explore the underlying physics of quantum phenomena. Our numerical results demonstrate that this method outperforms contemporary techniques in its ability to accurately reconstruct multi-qubit quantum states on real quantum devices, making it an invaluable contribution to the field of quantum state characterization and an essential step toward the reliable deployment of intermediate- and large-scale quantum devices.
Key words: NISQ / Quantum state tomography / Singular value decomposition / Fidelity / Matrix completion / Pauli operators
Shehbaz Tariq and Ahmad Farooq contributed equally to this work.
© The Author(s) 2024
Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
