Fermionic quantum cellular automata in 2d are trivial

• URL: http://arxiv.org/abs/2609.09317v1
• Date: Tue, 08 Sep 2026 18:04:56 GMT
• Title: Fermionic quantum cellular automata in 2d are trivial
• Abstract summary: We prove that every 2-dimensional fermionic QCA on a locally finite-dimensional algebra is a composition of local automorphisms and a fermionic shift.<n>This is implied by our result that every locally finite-dimensional fermionic invertible subalgebra in a one-dimensional lattice is Brauer trivial.
• Score: 0.42481744176244507
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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