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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum algorithms for colored Jones polynomials

Louis Hirsch Kauffman, Samuel J. Lomonaco

Published Mar 30, 2009• 0 citations
Publisher

Abstract

We review the q-deformed spin networks 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 formulate these braid group representations in a form suitable for computation and algebraic work and apply them to quantum algorithms for the computation of colored Jones polynomials and the Witten-Reshetikhin-Turaev Invariants.

DOI
10.1117/12.821974

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