Renormalisation of Quantum Cellular Automata
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916775877148672 |
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| author | Trezzini, Lorenzo Siro Bisio, Alessandro Perinotti, Paolo |
| author_facet | Trezzini, Lorenzo Siro Bisio, Alessandro Perinotti, Paolo |
| contents | We study a coarse-graining procedure for quantum cellular automata on hypercubic lattices that consists in grouping neighboring cells into tiles and selecting a subspace within each tile. This is done in such a way that multiple evolution steps applied to this subspace can be viewed as a single evolution step of a new quantum cellular automaton, whose cells are the subspaces themselves. We derive a necessary and sufficient condition for renormalizability and use it to investigate the renormalization flow of cellular automata on a line, where the cells are qubits and the tiles are composed of two neighboring cells. The problem is exhaustively solved, and the fixed points of the renormalization flow are highlighted. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12652 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Renormalisation of Quantum Cellular Automata Trezzini, Lorenzo Siro Bisio, Alessandro Perinotti, Paolo Quantum Physics Statistical Mechanics Mathematical Physics We study a coarse-graining procedure for quantum cellular automata on hypercubic lattices that consists in grouping neighboring cells into tiles and selecting a subspace within each tile. This is done in such a way that multiple evolution steps applied to this subspace can be viewed as a single evolution step of a new quantum cellular automaton, whose cells are the subspaces themselves. We derive a necessary and sufficient condition for renormalizability and use it to investigate the renormalization flow of cellular automata on a line, where the cells are qubits and the tiles are composed of two neighboring cells. The problem is exhaustively solved, and the fixed points of the renormalization flow are highlighted. |
| title | Renormalisation of Quantum Cellular Automata |
| topic | Quantum Physics Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2407.12652 |