Slow convergence of Trotter decomposition for rotations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916043906088960 |
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| author | Facchi, Paolo Perrini, Francesco Viesti, Vito |
| author_facet | Facchi, Paolo Perrini, Francesco Viesti, Vito |
| contents | We study the Trotter approximation for a pair of orbital angular momentum operators, $L_x$ and $L_y$. In particular, we investigate the scaling behavior of the state-dependent Trotter error. We show that for states in the domains of the orbital angular momentum operators the Trotter error scales as $n^{-1}$, where $n$ is the number of time steps. Instead, the convergence rate can be arbitrarily slow for states that do not belong to the domains of the angular momentum operators. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_15421 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Slow convergence of Trotter decomposition for rotations Facchi, Paolo Perrini, Francesco Viesti, Vito Quantum Physics Mathematical Physics We study the Trotter approximation for a pair of orbital angular momentum operators, $L_x$ and $L_y$. In particular, we investigate the scaling behavior of the state-dependent Trotter error. We show that for states in the domains of the orbital angular momentum operators the Trotter error scales as $n^{-1}$, where $n$ is the number of time steps. Instead, the convergence rate can be arbitrarily slow for states that do not belong to the domains of the angular momentum operators. |
| title | Slow convergence of Trotter decomposition for rotations |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2507.15421 |