Title: Quantum Computing and Quantum Topology
Speaker: Louis H. Kauffman, UIC
Abstract:
This talk will discuss the construction of sets of universal
gates for quantum computing and quantum information theory and their
relationship with topological computing, quantum algorithms for computing
quantum link invariants such as the Jones polynomial and questions about
the relationship between quantum entanglement and topological
entanglement. We will discuss the creation of universal gates (in the
presence of local unitary transformations) by using solutions to the
Yang-Baxter equation and we will discuss the use of braided recoupling
theory (q-deforemed spin networks) to create unitary representations of
the braid group rich enough to support quantum information theory and
quantum computing. In particular we give quantum algorithms for
computing the colored Jones polynomials and the Witten-Reshetikhin-Turaev
invariants.