  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.
