Braiding Fibonacci anyons
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929462395797504 |
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| author | Hadjiivanov, Ludmil Georgiev, Lachezar S. |
| author_facet | Hadjiivanov, Ludmil Georgiev, Lachezar S. |
| contents | Fibonacci anyons provide the simplest possible model of non-Abelian fusion rules: [1] x [1] = [0] + [1]. We propose a conformal field theory construction of topological quantum registers based on Fibonacci anyons realized as quasiparticle excitations in the Z_3 parafermion fractional quantum Hall state. To this end, the results of Ardonne and Schoutens for the correlation function of n = 4 Fibonacci fields are extended to the case of arbitrary n (and 3 r electrons). Special attention is paid to the braiding properties of the obtained correlators. We explain in details the construction of a monodromy representation of the Artin braid group acting on n-point conformal blocks of Fibonacci anyons. For low n (up to n = 8), the matrices of braid group generators are displayed explicitly. A simple recursion formula makes it possible to extend without efforts the construction to any n. Finally, we construct N qubit computational spaces in terms of conformal blocks of 2N + 2 Fibonacci anyons. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01778 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Braiding Fibonacci anyons Hadjiivanov, Ludmil Georgiev, Lachezar S. High Energy Physics - Theory Mathematical Physics Quantum Physics Fibonacci anyons provide the simplest possible model of non-Abelian fusion rules: [1] x [1] = [0] + [1]. We propose a conformal field theory construction of topological quantum registers based on Fibonacci anyons realized as quasiparticle excitations in the Z_3 parafermion fractional quantum Hall state. To this end, the results of Ardonne and Schoutens for the correlation function of n = 4 Fibonacci fields are extended to the case of arbitrary n (and 3 r electrons). Special attention is paid to the braiding properties of the obtained correlators. We explain in details the construction of a monodromy representation of the Artin braid group acting on n-point conformal blocks of Fibonacci anyons. For low n (up to n = 8), the matrices of braid group generators are displayed explicitly. A simple recursion formula makes it possible to extend without efforts the construction to any n. Finally, we construct N qubit computational spaces in terms of conformal blocks of 2N + 2 Fibonacci anyons. |
| title | Braiding Fibonacci anyons |
| topic | High Energy Physics - Theory Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2404.01778 |