An index for quantum cellular automata on fusion spin chains

2023/09/19 by Corey Jones, Jones, Corey, Junhwi Lim +1 · 2 citations
Computer Science · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #Physics of Superconductivity and Magnetism #Quantum Algebra (math.QA) #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Quantum-Dot Cellular Automata

paper · pdf · doi:10.48550/arxiv.2309.10961

openalex publication_date 2023/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Interpreting the GNVW index for 1D quantum cellular automata (QCA) in terms of the Jones index for subfactors leads to a generalization of the index defined for QCA on more general abstract spin chains. These include fusion spin chains, which arise as the local operators invariant under a global (categorical/MPO) symmetry, and as the boundary operators of 2D topological codes. We show that for the fusion spin chains built from the fusion category Fib, the index is a complete invariant for the group of QCA modulo finite depth circuits.

Cited by

• The zipper condition for 4-tensors in two-dimensional topological order and the higher relative commutants of a subfactor arising from a commuting square
• Causal Decompositions of 1D Quantum Cellular Automata

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