q-deformed Spin Networks and Anyonic Topological Quantum Computing

Louis Kauffman
University of Illinois at Chicago

Abstract: This talk will discuss how the Fibonacci model for topological quantum computing and generalizations of that model to other roots of unity can be constructed using the bracket polynomial model for the Jones polynomial as a base and using the q-deformed spin network approach to the recoupling theory that underlies the resulting unitary representations of the braid group. We will discuss,as well, quantum algorithms for computing colored Jones polynomials and the Witten-Reshetikhin-Turaev invariant. This talk represents joint work with Sam Lomonaco.

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