Coarse-grained quantum cellular automata

One can think of some physical evolutions as being the emergent-effective result a microscopic discrete model. Inspired by classical coarse-graining procedures, we provide simple procedure to coarse-grain color-blind quantum cellular automata that follow Goldilocks rules. The consists in (i) space-time grouping automaton (QCA) cells size $N$; (ii) projecting states cell onto its borders, connecting them with fine dynamics; (iii) describing overall dynamics border states, call signals; and (iv) constructing coarse-grained for different sizes $N$ cells. A byproduct this toy-model is general analog Stokes law. Moreover prove spacetime limit, converges Dirac free Hamiltonian. QCA introduce here be implemented present-day platforms, such Rydberg arrays, trapped ions, superconducting qbits. We hope our study pave way richer understanding those systems limited resolution.