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arXiv · 2309.10961

An index for quantum cellular automata on fusion spin chains

Corey Jones·Junhwi Lim
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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 $\mathbf{Fib}$, the index is a complete invariant for the group of QCA modulo finite depth circuits.

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Corey Jones, Junhwi Lim. 2024-03-18. An index for quantum cellular automata on fusion spin chains. https://arxiv.org/abs/2309.10961

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