Quantum Computation and Information Seminar 

03/07/2009, 15:00 — 16:00 — Room P4.35, Mathematics Building
Louis H. Kauffman, U Illinois at Chicago

Topological Quantum Information

This talk will discuss the role of quantum topology in quantum computing and quantum information theory. We will begin with a review of basic quantum information theory and the elements of diagrammatic and categorical approaches to quantum topology We then weave correspondences between these fields, discussing teleportation, topological gate construction, topological quantum computing and quantum knots. In particular, we shall discuss a construction of the Fibonacci model for topological quantum computing that is based on the properties of the Jones polynomial, and we shall present quantum algorithms for computing the Jones polynomial, colored Jones polynomials and the Witten-Reshetikhin-Turaev invariant.