Dorit Aharonov

On the quantum algorithm for approximating the Jones polynomial.

The Jones polynomial is a knot invariant that plays an important role in various areas in mathematics and physics. It has been known for some time that the approximation of the Jones polynomial at certain roots of unity is complete for quantum computation: this means that there is an efficient quantum algorithm for it, and if you can do it you can do all of quantum computation. However, this result (due to several works of Freedman, Kitaev, Larsen and Wang) is hardly known to the quantum computing community since it was presented in the language of topological field theories. I will present an algorithm from first principles to approximate the Jones polynomial. Joint work with Vaughan Jones and Zeph Landau.