# Jerusalem Mathematics Colloquium

Thursday, 8th December 2005, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Dorit Aharonov

(Computer Science Dept, Hebrew University)

"The Jones polynomial and Quantum Computation"

** Abstract: **
I will explain a very intriguing connection between low dimensional
topology, knot invariants, and quantum computation: It turns out that in
some well defined sense, quantum computation is *equivalent* to certain
approximations of the Jones polynomial. This means that:

- There is an efficient quantum algorithm to approximate the Jones
polynomial of any given link;
- The approximation of the Jones polynomial is the hardest problem a
quantum computer can possibly solve;
- Shor's factoring algorithm can be presented as the
approximation of the Jones polynomial of a certain link.

The results are based on works of Kitaev, Freedman, Larsen and Wang, as
well as on a recent paper by myself, together with Jones and Landau. I
will concentrate in my talk mainly on our recent paper. The goal is to
give a feel of how quantum computation can be viewed through the lense of
beautiful pictorial objects such as the braid group and Temperley-Lieb
algebras. No prior knowledge of quantum computation will be assumed.

Light refreshments will be served in the faculty lounge at 3:30.

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