Quantum Computing and the Jones Polynomial

Details Quantum Computing and the Jones Polynomial Quantum Computing and the Jones Polynomial

2001-05-31

arxiv.org/abs/math/0105255v1

Mathematics

Quantum Algebra

51 pages, 20 figures, LaTeX manuscript

Scientific paper

This paper is an exploration of relationships between the Jones polynomial and quantum computing. We discuss the structure of the Jones polynomial in relation to representations of the Temperley Lieb algebra, and give an example of a unitary representation of the braid group. We discuss the evaluation of the polynomial as a generalized quantum amplitude and show how the braiding part of the evaluation can be construed as a quantum computation when the braiding representation is unitary. The question of an efficient quantum algorithm for computing the whole polynomial remains open.

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