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. 2023 Dec 15;13(1):22313.
doi: 10.1038/s41598-023-49662-5.

A universal variational quantum eigensolver for non-Hermitian systems

Huanfeng Zhao  1 , Peng Zhang  2 , Tzu-Chieh Wei  3
Affiliations

A universal variational quantum eigensolver for non-Hermitian systems

Huanfeng Zhao et al. Sci Rep. .

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 [Formula: see text] 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.

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Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1
Figure 1
Quantum process snapshot.
Figure 2
Figure 2
Schematic diagram of Variational quantum universal eigensolver (VQUE).
Figure 3
Figure 3
Example 1a: Simple illustrative example in noise-free quantum simulator.
Figure 4
Figure 4
VQUE accuracy study.
Figure 5
Figure 5
Example 1b: Illustrative example in real quantum machine.
Figure 6
Figure 6
Example 2: VQUE scalability demonstration.
Figure 7
Figure 7
Example 3: Eigenvalue evaluation of non-diagonalizable matrix.
Figure 8
Figure 8
Example 4: Verification of VQUE for power network stability and oscillation mode analysis.
See this image and copyright information in PMC

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