Abstract
Fibonacci anyons ε provide the simplest possible model of non-Abelian fusion rules: [1] × [1] = [0] ⊕ [1]. We propose a conformal field theory construction of topological quantum registers based on Fibonacci anyons realized as quasiparticle excitations in the ℤ3 parafermion fractional quantum Hall state. To this end, the results of Ardonne and Schoutens for the correlation function of four Fibonacci fields are extended to the case of arbitrary number n of quasi-holes and N = 3r 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 \( \mathcal{B} \)n acting on n-point conformal blocks of Fibonacci anyons. The matrices of braid group generators are displayed explicitly for all n ≤ 8. A simple recursion formula makes it possible to extend without efforts the construction to any n. Finally, we construct \( \mathcal{N} \) qubit computational spaces in terms of conformal blocks of \( 2\mathcal{N} \) + 2 Fibonacci anyons.
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Acknowledgments
This work has been done under the project BG05M2OP001-1.002-0006 “Quantum Communication, Intelligent Security Systems and Risk Management” (QUASAR) financed by the Bulgarian Operational Programme “Science and Education for Smart Growth” (SESG) co-funded by the ERDF. Both LH and LSG thank the Bulgarian Science Fund for partial support under Contract No. DN 18/3 (2017). LSG has been also supported as a Research Fellow by the Alexander von Humboldt Foundation.
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Hadjiivanov, L., Georgiev, L.S. Braiding Fibonacci anyons. J. High Energ. Phys. 2024, 84 (2024). https://doi.org/10.1007/JHEP08(2024)084
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DOI: https://doi.org/10.1007/JHEP08(2024)084