Accelerated spin-adapted ground state preparation with non-variational quantum algorithms
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913877547024384 |
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| author | Kobori, Takumi Kosugi, Taichi Nishi, Hirofumi Todo, Synge Matsushita, Yu-ichiro |
| author_facet | Kobori, Takumi Kosugi, Taichi Nishi, Hirofumi Todo, Synge Matsushita, Yu-ichiro |
| contents | Various methods have been explored to prepare the spin-adapted ground state, the lowest energy state within the Hilbert space constrained by externally specified values of the total spin magnitude and the spin-$z$ component. In such problem settings, variational and non-variational methods commonly incorporate penalty terms into the original Hamiltonian to enforce the desired constraints. While in variational approaches, only $O(n_{\textrm{spin}}^2)$ measurements are required for the calculation of the penalty terms for the total spin magnitude, non-variational approaches, such as probabilistic imaginary-time evolution or adiabatic time evolution, are expected to be more computationally intensive, requiring $O(n_{\textrm{spin}}^4)$ gates naively. This paper proposes a new procedure based on non-variational quantum algorithms to obtain the spin-adapted ground state. The proposed method consists of two steps: the first step is to prepare a spin-magnitude adapted state and the second step is post-processing for the desired $S_z$. By separating into two steps, the procedure achieves the desired spin-adapted ground state while reducing the number of penalty terms from $O(n_{\textrm{spin}}^4)$ to $O(n_{\textrm{spin}}^2)$. We conducted numerical experiments for spin-1/2 Heisenberg ring models and manganese trimer systems. The results confirmed the effectiveness of our method, demonstrating a significant reduction in gate complexity and validating its practical usefulness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04663 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Accelerated spin-adapted ground state preparation with non-variational quantum algorithms Kobori, Takumi Kosugi, Taichi Nishi, Hirofumi Todo, Synge Matsushita, Yu-ichiro Quantum Physics Various methods have been explored to prepare the spin-adapted ground state, the lowest energy state within the Hilbert space constrained by externally specified values of the total spin magnitude and the spin-$z$ component. In such problem settings, variational and non-variational methods commonly incorporate penalty terms into the original Hamiltonian to enforce the desired constraints. While in variational approaches, only $O(n_{\textrm{spin}}^2)$ measurements are required for the calculation of the penalty terms for the total spin magnitude, non-variational approaches, such as probabilistic imaginary-time evolution or adiabatic time evolution, are expected to be more computationally intensive, requiring $O(n_{\textrm{spin}}^4)$ gates naively. This paper proposes a new procedure based on non-variational quantum algorithms to obtain the spin-adapted ground state. The proposed method consists of two steps: the first step is to prepare a spin-magnitude adapted state and the second step is post-processing for the desired $S_z$. By separating into two steps, the procedure achieves the desired spin-adapted ground state while reducing the number of penalty terms from $O(n_{\textrm{spin}}^4)$ to $O(n_{\textrm{spin}}^2)$. We conducted numerical experiments for spin-1/2 Heisenberg ring models and manganese trimer systems. The results confirmed the effectiveness of our method, demonstrating a significant reduction in gate complexity and validating its practical usefulness. |
| title | Accelerated spin-adapted ground state preparation with non-variational quantum algorithms |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2506.04663 |