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[in Journal: Nankai Tracts in Mathematics] AND [Keyword: Spin Networks] (1)	27 Mar 2025	Run
[in Journal: Journal of Developmental Entrepreneurship] AND [Keyword: United States] (2)	27 Mar 2025	Run
[in Journal: Biophysical Reviews and Letters] AND [Keyword: Microorganism] (1)	27 Mar 2025	Run
[in Journal: Journal of Algebra and Its Applications] AND [Keyword: Modular Forms] (2)	27 Mar 2025	Run
[in Journal: Surface Review and Letters] AND [Keyword: Nanomaterials] (7)	27 Mar 2025	Run

chapterNo Access
Unitary Representations of the Artin Braid Groups and Quantum Algorithms for Colored Jones Polynomials and the Witten-Reshetikhin Invariant
- Louis H. Kauffman and
- Samuel J. Lomonaco, Jr.
Topology and Physics01 Aug 2008
Preview Abstract
We review the q-deformed spin network approach to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. The simplest case of these models is the Fibonacci model, itself universal for quantum computation. We here formulate these braid group representations in a form suitable for computation and algebraic work. In particular, we give quantum algorithms for computing colored Jones polynomials and the Witten-Reshetikhin-Turaev invariant of three-manifolds.

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