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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.10167 |
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| _version_ | 1866912537301221376 |
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| author | Trabelsi, Rayan |
| author_facet | Trabelsi, Rayan |
| contents | This work introduces a quantum circuit synthesis framework for simulating the unitary time evolution under a subclass of symmetric Toeplitz Hamiltonians by decomposing them into specific diagonal matrices $M_k$. These matrices are then classified, to achieve significant simplification, into, $M_k$ when $k$ is a power of two, and congruence classes with constant coefficients. Finally, we construct the explicit quantum circuit for the one-dimensional discrete Poisson equation. This research was conducted under the supervision of Benoit Valiron during a Master's internship. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10167 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Symmetric Toeplitz Hamiltonians to Quantum Circuits Trabelsi, Rayan Quantum Physics This work introduces a quantum circuit synthesis framework for simulating the unitary time evolution under a subclass of symmetric Toeplitz Hamiltonians by decomposing them into specific diagonal matrices $M_k$. These matrices are then classified, to achieve significant simplification, into, $M_k$ when $k$ is a power of two, and congruence classes with constant coefficients. Finally, we construct the explicit quantum circuit for the one-dimensional discrete Poisson equation. This research was conducted under the supervision of Benoit Valiron during a Master's internship. |
| title | From Symmetric Toeplitz Hamiltonians to Quantum Circuits |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2508.10167 |