Title: A universal variational quantum eigensolver for non-Hermitian systems

Abstract

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.

Authors:

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

Publication Date:

Fri Dec 15 00:00:00 EST 2023

Sponsoring Org.:

USDOE

OSTI Identifier:

2234325

Grant/Contract Number:  

Office of Electricity under Award No. 37533,Office of Electricity under Award No. 37533,DE-SC0012704

Resource Type:

Published Article

Journal Name:

Scientific Reports

Additional Journal Information:

Journal Name: Scientific Reports Journal Volume: 13 Journal Issue: 1; Journal ID: ISSN 2045-2322

Publisher:

Nature Publishing Group

Country of Publication:

United Kingdom

Language:

English