A universal variational quantum eigensolver for non-Hermitian systems

• Published in: Scientific reports 2023-12, Vol.13 (1), p.22313-15, Article 22313
• Main Authors: Zhao, Huanfeng, Zhang, Peng, Wei, Tzu-Chieh
• Format: Article
• Language: English
• Subjects: 639/166; 639/166/987; 639/705/117; 639/766/483/481; Algorithms; Computers; Eigenvalues; Humanities and Social Sciences; multidisciplinary; Science; Science (multidisciplinary)
• ISSN: 2045-2322; 2045-2322
• DOI: 10.1038/s41598-023-49662-5

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 ( l o g 2 N ) 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.