For N > 4r, every 1D quantum cellular automaton of causality radius r is exactly a routed unitary circuit of nearest-neighbour interactions, and translation-invariant automata get translation-invariant circuits.
Causal structure in the presence of sectorial constraints, with application to the quantum switch,
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Causal Decompositions of 1D Quantum Cellular Automata
For N > 4r, every 1D quantum cellular automaton of causality radius r is exactly a routed unitary circuit of nearest-neighbour interactions, and translation-invariant automata get translation-invariant circuits.