A universal variational quantum eigensolver for non-Hermitian systems

Journal Article · Fri Dec 15 00:00:00 EST 2023 · Scientific Reports

DOI:https://doi.org/10.1038/s41598-023-49662-5· OSTI ID:2234325

Zhao, Huanfeng; Zhang, Peng; Wei, Tzu-Chieh

Abstract Many quantum algorithms are developed to evaluate eigenvalues for Hermitian matrices. However, few practical approach exists for the eigenanalysis of non-Hermintian ones, such as arising from modern power systems. The main difficulty lies in the fact that, as the eigenvector matrix of a general matrix can be non-unitary, solving a general eigenvalue problem is inherently incompatible with existing unitary-gate-based quantum methods. To fill this gap, this paper introduces a Variational Quantum Universal Eigensolver (VQUE), which is deployable on noisy intermediate scale quantum computers. Our new contributions include: (1) The first universal variational quantum algorithm capable of evaluating the eigenvalues of non-Hermitian matrices—Inspired by Schur’s triangularization theory, VQUE unitarizes the eigenvalue problem to a procedure of searching unitary transformation matrices via quantum devices; (2) A Quantum Process Snapshot technique is devised to make VQUE maintain the potential quantum advantage inherited from the original variational quantum eigensolver—With additional $$$$O(log_{2}{N})$$$$ $O\left(lo{g}_{2}N\right)$ quantum gates, this method efficiently identifies whether a unitary operator is triangular with respect to a given basis; (3) Successful deployment and validation of VQUE on a real noisy quantum computer, which demonstrates the algorithm’s feasibility. We also undertake a comprehensive parametric study to validate VQUE’s scalability, generality, and performance in realistic applications.

• Sponsoring Organization: USDOE
• Grant/Contract Number: Office of Electricity under Award No. 37533,Office of Electricity under Award No. 37533,DE-SC0012704
• OSTI ID: 2234325
• Journal Information: Scientific Reports, Journal Name: Scientific Reports Vol. 13 Journal Issue: 1; ISSN 2045-2322
• Publisher: Nature Publishing Group
• Country of Publication: United Kingdom
• Language: English