Suzuki Type Estimates for Exponentiated Sums and Generalized Lie-Trotter Formulas in Banach Algebras
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910876171239424 |
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| author | Wang, Zhenhua |
| author_facet | Wang, Zhenhua |
| contents | The Lie-Trotter formula has been a fundamental tool in quantum mechanics, quantum computing, and quantum simulations. The error estimations for the Lie-Trotter product formula play a crucial role in achieving scalability and computational efficiency. In this note, we present two error estimates of Lie-Trotter product formulas, utilizing Jordan product within Banach algebras. Additionally, we introduce two generalized Lie-Trotter formula and provide two explicit estimation formulas. Consequently, the renowned Suzuki symmetrized approximation for the exponentiated sums follows directly from our main Theorem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_13791 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Suzuki Type Estimates for Exponentiated Sums and Generalized Lie-Trotter Formulas in Banach Algebras Wang, Zhenhua Quantum Physics Mathematical Physics Functional Analysis 47A58, 47N50, 17C65(Primary), 15A16, 81R15, 81P45(Secondary) The Lie-Trotter formula has been a fundamental tool in quantum mechanics, quantum computing, and quantum simulations. The error estimations for the Lie-Trotter product formula play a crucial role in achieving scalability and computational efficiency. In this note, we present two error estimates of Lie-Trotter product formulas, utilizing Jordan product within Banach algebras. Additionally, we introduce two generalized Lie-Trotter formula and provide two explicit estimation formulas. Consequently, the renowned Suzuki symmetrized approximation for the exponentiated sums follows directly from our main Theorem. |
| title | Suzuki Type Estimates for Exponentiated Sums and Generalized Lie-Trotter Formulas in Banach Algebras |
| topic | Quantum Physics Mathematical Physics Functional Analysis 47A58, 47N50, 17C65(Primary), 15A16, 81R15, 81P45(Secondary) |
| url | https://arxiv.org/abs/2306.13791 |