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arXiv · 2507.04783

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

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

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Jiaxin Li, Zhaobing Fan, Hongmei Yao, Chunlin Yang, Shao-Ming Fei, Zi-Tong Zhou, Meng-Han Dou, Teng-Yang Ma. 2025-07-07. Variational quantum algorithm for generalized eigenvalue problems of non-Hermitian systems. https://arxiv.org/abs/2507.04783

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