Renormalisation of Quantum Cellular Automata
- URL: http://arxiv.org/abs/2407.12652v1
- Date: Wed, 17 Jul 2024 15:33:33 GMT
- Title: Renormalisation of Quantum Cellular Automata
- Authors: Lorenzo Siro Trezzini, Alessandro Bisio, Paolo Perinotti,
- Abstract summary: We study a coarse-graining procedure for quantum cellular automata on hypercubic lattices.
Multiple evolution steps applied to a subspace in each tile can be viewed as a single evolution step of a new quantum cellular automaton.
We derive a necessary and sufficient condition for renormalizability and use it to investigate the renormalization flow of cellular automata on a line.
- Score: 45.279573215172285
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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.
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