Fidelity; Matrix completion; NISQ; Pauli operators; Quantum state tomography; Singular value decomposition; Benchmarking tools; Low-rank matrix completions; Post-processing; Quantum device; Quantum state; Quantum Information
Abstract :
[en] 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 2n+1 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.
Disciplines :
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Tariq, Shehbaz; Department of Electronics and Information Convergence Engineering, Kyung Hee University, Yongin-si, South Korea
Farooq, Ahmad; Department of Electronics and Information Convergence Engineering, Kyung Hee University, Yongin-si, South Korea ; Department of Electrical Engineering and Automation, Aalto University, Espoo, Finland
UR REHMAN, Junaid ; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > SigCom
Duong, Trung Q.; Department of Electrical and Computer Engineering, Memorial University of Newfoundland, St. John’s, Canada
Shin, Hyundong; Department of Electronics and Information Convergence Engineering, Kyung Hee University, Yongin-si, South Korea
External co-authors :
yes
Language :
English
Title :
Efficient quantum state estimation with low-rank matrix completion
Publication date :
August 2024
Journal title :
EPJ Quantum Technology
eISSN :
2196-0763
Publisher :
Springer Science and Business Media Deutschland GmbH
National Research Foundation of Korea Institute for Information & Communications Technology Planning & Evaluation
Funding text :
We acknowledge the use of the IBM Q for this work. The views expressed are those of the authors and do not reflect the official policy or position of IBM or the IBM Quantum team.This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1A4A3033401) and by the MSIT (Ministry of Science and ICT), Korea, under the ITRC (Information Technology Research Center) support program (IITP-2021-0-02046) supervised by the IITP (Institute for Information & Communications Technology Planning & Evaluation).
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