Fermionic quantum cellular automata in 2d are trivial

Abstract:Fermionic quantum cellular automata (QCA) are automorphisms of local fermionic operator algebras ($\mathbb Z_2$-graded superalgebras) that have bounded spread: they map local operators to nearby operators. We prove that every 2-dimensional fermionic QCA on a locally finite-dimensional algebra is a composition of local automorphisms and a fermionic shift. This is implied by our result that every locally finite-dimensional fermionic invertible subalgebra in a one-dimensional lattice is Brauer trivial, \textit{i.e.}, it is stably bounded-spread isomorphic to a tensor product fermionic algebra.

Mathematical Physics (math-ph); Strongly Correlated Electrons (cond-mat.str-el); Operator Algebras (math.OA); Quantum Physics (quant-ph)

arXiv:2609.09317 [math-ph]

(or arXiv:2609.09317v1 [math-ph] for this version)

https://doi.org/10.48550/arXiv.2609.09317 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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