Renormalisation of Quantum Cellular Automata
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 evol...
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2025-05-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2025-05-28-1756/pdf/ |
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| author | Lorenzo Siro Trezzini Alessandro Bisio Paolo Perinotti |
| author_facet | Lorenzo Siro Trezzini Alessandro Bisio Paolo Perinotti |
| author_sort | Lorenzo Siro Trezzini |
| collection | DOAJ |
| description | 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 | Article |
| id | doaj-art-ca1445efaffb44e28ab13af4d22a2a13 |
| institution | DOAJ |
| issn | 2521-327X |
| language | English |
| publishDate | 2025-05-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj-art-ca1445efaffb44e28ab13af4d22a2a132025-08-20T03:05:34ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2025-05-019175610.22331/q-2025-05-28-175610.22331/q-2025-05-28-1756Renormalisation of Quantum Cellular AutomataLorenzo Siro TrezziniAlessandro BisioPaolo PerinottiWe 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.https://quantum-journal.org/papers/q-2025-05-28-1756/pdf/ |
| spellingShingle | Lorenzo Siro Trezzini Alessandro Bisio Paolo Perinotti Renormalisation of Quantum Cellular Automata Quantum |
| title | Renormalisation of Quantum Cellular Automata |
| title_full | Renormalisation of Quantum Cellular Automata |
| title_fullStr | Renormalisation of Quantum Cellular Automata |
| title_full_unstemmed | Renormalisation of Quantum Cellular Automata |
| title_short | Renormalisation of Quantum Cellular Automata |
| title_sort | renormalisation of quantum cellular automata |
| url | https://quantum-journal.org/papers/q-2025-05-28-1756/pdf/ |
| work_keys_str_mv | AT lorenzosirotrezzini renormalisationofquantumcellularautomata AT alessandrobisio renormalisationofquantumcellularautomata AT paoloperinotti renormalisationofquantumcellularautomata |