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arXiv · 2407.12652

Renormalisation of Quantum Cellular Automata

Lorenzo Siro Trezzini·Alessandro Bisio·Paolo Perinotti
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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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Lorenzo Siro Trezzini, Alessandro Bisio, Paolo Perinotti. 2024-07-17. Renormalisation of Quantum Cellular Automata. https://doi.org/10.22331/q-2025-05-28-1756

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