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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Main Authors: Lorenzo Siro Trezzini, Alessandro Bisio, Paolo Perinotti
Format: Article
Language:English
Published: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 2025-05-01
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