Quantum Algorithm for Low Energy Effective Hamiltonian and Quasi-Degenerate Eigenvalue Problem
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866918400818675712 |
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| author | Li, Chun-Tse Ong, Tzen Lin, Chih-Yun Chen, Yu-Cheng Lin, Hsin Hsieh, Min-Hsiu |
| author_facet | Li, Chun-Tse Ong, Tzen Lin, Chih-Yun Chen, Yu-Cheng Lin, Hsin Hsieh, Min-Hsiu |
| contents | Quasi-degenerate eigenvalue problems are central to quantum chemistry and condensed-matter physics, where low-energy spectra often form manifolds of nearly degenerate states that determine physical properties. Standard quantum algorithms, such as phase estimation and QSVT-based eigenvalue filtering, work well when a unique ground state is separated by a moderate spectral gap, but in the quasi-degenerate regime they require resolution finer than the intra-manifold splitting; otherwise, they return an uncontrolled superposition within the low-energy span and fail to detect or resolve degeneracies. In this work, we propose a quantum algorithm that directly diagonalizes such quasi-degenerate manifolds by solving an effective-Hamiltonian eigenproblem in a low-dimensional reference subspace. This reduced problem is exactly equivalent to the full eigenproblem, and its solutions are lifted to the full Hilbert space via a block-encoded wave operator. Our analysis provides provable bounds on eigenvalue accuracy and subspace fidelity, together with total query complexity, demonstrating that quasi-degenerate eigenvalue problems can be solved efficiently without assuming any intra-manifold splitting. We benchmark the algorithm on several systems (the Fermi-Hubbard model, LiH, and the transition-metal complex [Ru(bpy)$_3$]$^{2+}$), demonstrating robust performance and reliable resolution of (quasi-)degeneracies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_08088 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Algorithm for Low Energy Effective Hamiltonian and Quasi-Degenerate Eigenvalue Problem Li, Chun-Tse Ong, Tzen Lin, Chih-Yun Chen, Yu-Cheng Lin, Hsin Hsieh, Min-Hsiu Quantum Physics Quasi-degenerate eigenvalue problems are central to quantum chemistry and condensed-matter physics, where low-energy spectra often form manifolds of nearly degenerate states that determine physical properties. Standard quantum algorithms, such as phase estimation and QSVT-based eigenvalue filtering, work well when a unique ground state is separated by a moderate spectral gap, but in the quasi-degenerate regime they require resolution finer than the intra-manifold splitting; otherwise, they return an uncontrolled superposition within the low-energy span and fail to detect or resolve degeneracies. In this work, we propose a quantum algorithm that directly diagonalizes such quasi-degenerate manifolds by solving an effective-Hamiltonian eigenproblem in a low-dimensional reference subspace. This reduced problem is exactly equivalent to the full eigenproblem, and its solutions are lifted to the full Hilbert space via a block-encoded wave operator. Our analysis provides provable bounds on eigenvalue accuracy and subspace fidelity, together with total query complexity, demonstrating that quasi-degenerate eigenvalue problems can be solved efficiently without assuming any intra-manifold splitting. We benchmark the algorithm on several systems (the Fermi-Hubbard model, LiH, and the transition-metal complex [Ru(bpy)$_3$]$^{2+}$), demonstrating robust performance and reliable resolution of (quasi-)degeneracies. |
| title | Quantum Algorithm for Low Energy Effective Hamiltonian and Quasi-Degenerate Eigenvalue Problem |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.08088 |