Quantum Algorithms for the Jones Polynomial

Details Quantum Algorithms for the Jones Polynomial Quantum Algorithms for the Jones Polynomial

2010-03-29

arxiv.org/abs/1003.5426v1

Mathematics

Geometric Topology

11 pages, 4 figures, LaTeX document

Scientific paper

This paper gives a generalization of the AJL algorithm and unitary braid group representation for quantum computation of the Jones polynomial to continuous ranges of values on the unit circle of the Jones parameter. We show that our 3-strand algorithm for the Jones polynomial is a special case of this generalization of the AJL algorithm. The present paper uses diagrammatic techniques to prove these results. The techniques of this paper have been used and will be used in the future in work with R. Marx, A. Fahmy, L. H. Kauffman, S. J. Lomonaco Jr.,A. Sporl, N. Pomplun, T. Schulte Herbruggen, J. M. Meyers, and S. J. Glaser on NMR quantum computation of the Jones polynomial.

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