The space of all global unitaries that has lightcones displays an interesting topology, which leads to study of so-called quantum cellular automata. Connected components of this space correspond to local unitary circuits, and the existence of distinct connected components has been found and conjectured. I am going to discuss that a class of local measurement circuits, which includes those of Floquet codes, induce a strictly larger class of locality-preserving unitaries than that of local unitary circuits.
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