Tomasz Maciążek

Non-abelian anyons on graphs

I will introduce a general framework for describing quantum statistics of particles constrained to move in a topological space X. This framework involves a study of unitary representations of the braid group of space X, which can be achieved by determining homology groups of the configuration space of X. This formulation leads to a new connection between K-theory and the classification of anyons used in topological quantum computing. We apply this methodology for configuration spaces of graphs. As a conclusion, I will provide families of graphs, which are good candidates for simple models of quantum computation. I will also present a number of new results concerning topology of graph configuration spaces.