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

• URL: http://arxiv.org/abs/2507.04783v1
• Date: Mon, 07 Jul 2025 08:59:16 GMT
• Title: Variational quantum algorithm for generalized eigenvalue problems of non-Hermitian systems
• Authors: Jiaxin Li, Zhaobing Fan, Hongmei Yao, Chunlin Yang, Shao-Ming Fei, Zi-Tong Zhou, Teng-Yang Ma,
• Abstract summary: We propose a variational quantum algorithm for solving generalized eigenvalue problems in non-Hermitian systems.<n>We numerically validate the algorithm's performance through simulations and demonstrate its application to generalized eigenvalue problems in ocean acoustics.
• Score: 6.752287704489559
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Most quantum algorithms for generalized eigenvalue problems focus on Hermitian systems, and few are applicable to non-Hermitian systems. Based on the generalized Schur decomposition, we propose a variational quantum algorithm for solving generalized eigenvalue problems in non-Hermitian systems. The algorithm transforms the generalized eigenvalue problem into a process of searching for unitary transformation matrices. Moreover, we develop a method for evaluating both the loss function and its gradients on near-term quantum devices. Finally, we numerically validate the algorithm's performance through simulations and demonstrate its application to generalized eigenvalue problems in ocean acoustics. The algorithm's robustness is further confirmed through noise simulations.

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