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Variational quantum algorithm for generalized eigenvalue problems of non-Hermitian systems

Year: 2025

Type: preprint

Abstract: Non-Hermitian generalized eigenvalue problems (GEPs) play a significant role in many practical applications, such as mechanical engineering. Based on the generalized Schur decomposition, we propose a variational quantum algorithm for solving the GEPs in non-Hermitian systems. The algorithm transforms the generalized eigenvalue problem into a process of searching for unitary transformation matrices. We demonstrate a method for evaluating both the loss function and its gradients on near-term quantum devices. We validate numerically the algorithm's performance through simulations, and demonstrate its application to GEPs in ocean acoustics. The algorithm's robustness is further confirmed through noise simulations.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2507.04783

Authors: Li, Jiaxin, Fan, Zhaobing, Yao, Hongmei, Yang, Chunlin, Fei, Shao-Ming, Zhou, Zi-Tong, Dou, Meng-Han, Ma, Teng-Yang

Institutions: Harbin Engineering University, Capital Normal University, Origin Quantum Computing Technology Company (China)

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7080337279

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