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arXiv · 2609.09317

Fermionic quantum cellular automata in 2d are trivial

Jeffrey Kwan·David M. Long·Jeongwan Haah
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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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Jeffrey Kwan, David M. Long, Jeongwan Haah. 2026-09-08. Fermionic quantum cellular automata in 2d are trivial. https://arxiv.org/abs/2609.09317

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