Fermionic quantum cellular automata in 2d are trivial

@misc{kwan2026fermionic,
  title = {{Fermionic quantum cellular automata in 2d are trivial}},
  author = {Jeffrey Kwan and David M. Long and Jeongwan Haah},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.09317},
  eprint = {2609.09317},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.09317},
}

TY  - UNPB
TI  - Fermionic quantum cellular automata in 2d are trivial
AU  - Jeffrey Kwan
AU  - David M. Long
AU  - Jeongwan Haah
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.09317
UR  - https://arxiv.org/abs/2609.09317
AB  - Fermionic quantum cellular automata (QCA) are automorphisms of local fermionic operator algebras (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.
ER  -