Quantum Algorithms for the Jones Polynomial

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.

11 pages, 4 figures, LaTeX document

References in corpus (4)

• Non-Abelian Anyons and Topological Quantum Computation
• The BQP-hardness of approximating the Jones Polynomial
• NMR Quantum Calculations of the Jones Polynomial
• A 3-Stranded Quantum Algorithm for the Jones Polynomial

Cited by in corpus (1)

• End-to-End Quantum Algorithms for the Jones Polynomial