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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2505.22171 |
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| _version_ | 1866912403284819968 |
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| author | Ahmadi, Fatimah Rita |
| author_facet | Ahmadi, Fatimah Rita |
| contents | Unitary Ribbon Fusion Categories (URFC) formalize anyonic theories. It has been widely assumed that the same category formalizes a topological quantum computing model. However, in previous work, we addressed and resolved this confusion and demonstrated while the former could be any fusion category, the latter is always a subcategory of Hilb. In this paper, we argue that a categorical formalism that captures and unifies both anyonic theories (the Hardware of quantum computing) and a model of topological quantum computing is a braided (fusion) 2-category. In this 2-category, 0-morphisms describe anyonic types and Hom-categories describe different models of quantum computing. This picture provides an insightful perspective on superselection rules. It presents furthermore a clear distinction between fusion of anyons versus tensor products as defined in linear algebra, between vector spaces of 1-morphisms. The former represents a monoidal product and sum between 0-morphisms and the latter a tensor product and direct sum between 1-morphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22171 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The 2-Category of Topological Quantum Computation Ahmadi, Fatimah Rita Quantum Physics Unitary Ribbon Fusion Categories (URFC) formalize anyonic theories. It has been widely assumed that the same category formalizes a topological quantum computing model. However, in previous work, we addressed and resolved this confusion and demonstrated while the former could be any fusion category, the latter is always a subcategory of Hilb. In this paper, we argue that a categorical formalism that captures and unifies both anyonic theories (the Hardware of quantum computing) and a model of topological quantum computing is a braided (fusion) 2-category. In this 2-category, 0-morphisms describe anyonic types and Hom-categories describe different models of quantum computing. This picture provides an insightful perspective on superselection rules. It presents furthermore a clear distinction between fusion of anyons versus tensor products as defined in linear algebra, between vector spaces of 1-morphisms. The former represents a monoidal product and sum between 0-morphisms and the latter a tensor product and direct sum between 1-morphisms. |
| title | The 2-Category of Topological Quantum Computation |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2505.22171 |