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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2412.20604 |
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| _version_ | 1866914122614964224 |
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| author | Chehade, Sarah Delgado, Andrea Wang, Shuzhou Wang, Zhenhua |
| author_facet | Chehade, Sarah Delgado, Andrea Wang, Shuzhou Wang, Zhenhua |
| contents | In quantum computing, Trotter estimates are critical for enabling efficient simulation of quantum systems and quantum dynamics, help implement complex quantum algorithms, and provide a systematic way to control approximate errors. In this paper, we extend the analysis of Trotter-Suzuki approximations, including third and higher orders, to Jordan-Banach algebras. We solve an open problem in our earlier paper on the existence of second-order Trotter formula error estimation in Jordan-Banach algebras. To illustrate our work, we apply our formula to simulate Trotter-factorized spins, and show improvements in the approximations. Our approach demonstrates the adaptability of Trotter product formulas and estimates to non-associative settings, which offers new insights into the applications of Jordan algebra theory to operator dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20604 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Error Estimates and Higher Order Trotter Product Formulas in Jordan-Banach Algebras Chehade, Sarah Delgado, Andrea Wang, Shuzhou Wang, Zhenhua Quantum Physics Mathematical Physics Functional Analysis 17C90, 81P45, 15A16(Primary), 17C65, 81R15, 46H70(Secondary) In quantum computing, Trotter estimates are critical for enabling efficient simulation of quantum systems and quantum dynamics, help implement complex quantum algorithms, and provide a systematic way to control approximate errors. In this paper, we extend the analysis of Trotter-Suzuki approximations, including third and higher orders, to Jordan-Banach algebras. We solve an open problem in our earlier paper on the existence of second-order Trotter formula error estimation in Jordan-Banach algebras. To illustrate our work, we apply our formula to simulate Trotter-factorized spins, and show improvements in the approximations. Our approach demonstrates the adaptability of Trotter product formulas and estimates to non-associative settings, which offers new insights into the applications of Jordan algebra theory to operator dynamics. |
| title | Error Estimates and Higher Order Trotter Product Formulas in Jordan-Banach Algebras |
| topic | Quantum Physics Mathematical Physics Functional Analysis 17C90, 81P45, 15A16(Primary), 17C65, 81R15, 46H70(Secondary) |
| url | https://arxiv.org/abs/2412.20604 |