Quantum cellular automata are a coarse homology theory

Abstract

We show that quantum cellular automata naturally form the degree-zero part of a coarse homology theory. The recent result of Ji and Yang that the space of QCA forms an Omega-spectrum in the sense of algebraic topology is a direct consequence of the formal properties of coarse homology theories.

arXiv comment31 pages, gabe more general definition of QCA group using the new notion of coarsely local automorphisms