Quantum Algorithms for the Jones Polynomial
Geometric Topology
2015-05-18 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1003.5426,
title = {Quantum Algorithms for the Jones Polynomial},
author = {Louis H. Kauffman and Samuel J. Lomonaco},
journal= {arXiv preprint arXiv:1003.5426},
year = {2015}
}
Comments
11 pages, 4 figures, LaTeX document