Renormalisation of Quantum Cellular Automata
The study develops a coarse-graining procedure for quantum cellular automata by grouping neighboring cells into tiles and selecting a subspace within them, allowing multiple evolution steps to be viewed as one step of a new automaton. This leads to necessary and sufficient conditions for renormalizability. Applied to 1D QCAs with qubit cells, the work shows that renormalizability is very restrictive, with most models failing unless they exhibit trivial dynamics or information propagation.