Variational quantum algorithm for generalized eigenvalue problems of non-Hermitian systems
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arXiv
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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910036226211840 |
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| author | Li, Jiaxin Fan, Zhaobing Yao, Hongmei Yang, Chunlin Fei, Shao-Ming Zhou, Zi-Tong Dou, Meng-Han Ma, Teng-Yang |
| author_facet | Li, Jiaxin Fan, Zhaobing Yao, Hongmei Yang, Chunlin Fei, Shao-Ming Zhou, Zi-Tong Dou, Meng-Han Ma, Teng-Yang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04783 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Variational quantum algorithm for generalized eigenvalue problems of non-Hermitian systems Li, Jiaxin Fan, Zhaobing Yao, Hongmei Yang, Chunlin Fei, Shao-Ming Zhou, Zi-Tong Dou, Meng-Han Ma, Teng-Yang Quantum Physics 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. |
| title | Variational quantum algorithm for generalized eigenvalue problems of non-Hermitian systems |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2507.04783 |