An index for quantum cellular automata on fusion spin chains
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914718913921024 |
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| author | Jones, Corey Lim, Junhwi |
| author_facet | Jones, Corey Lim, Junhwi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10961 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An index for quantum cellular automata on fusion spin chains Jones, Corey Lim, Junhwi Operator Algebras Mathematical Physics Quantum Algebra Quantum Physics 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. |
| title | An index for quantum cellular automata on fusion spin chains |
| topic | Operator Algebras Mathematical Physics Quantum Algebra Quantum Physics |
| url | https://arxiv.org/abs/2309.10961 |