Topological Quantum Computing and the Jones Polynomial

Abstract

In this paper, we give a description of a recent quantum algorithm created by Aharonov, Jones, and Landau for approximating the values of the Jones polynomial at roots of unity of the form exp(2$\pi$i/k). This description is given with two objectives in mind. The first is to describe the algorithm in such a way as to make explicit the underlying and inherent control structure. The second is to make this algorithm accessible to a larger audience.

19 pages, 27 figures

References in corpus (2)

• The Jones polynomial: quantum algorithms and applications in quantum complexity theory
• Quantum automata, braid group and link polynomials

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