Topology from the Quantum Computation Viewpoint
Speaker: Uwe Kaiser (Boise State University)
Abstract: The talk will give an elementary introduction into the models of classical respectively quantum computation as information processing by classical logic gates respectively quantum gates.
Quantum information processing is distinguished by interference and entanglement in informationally isolated systems. These properties give rise to the well known "quantum weirdness". I will briefly
discuss the mathematical description of quantum information processing (the axioms of quantum mechanics) by unitary operators acting on complex vector spaces. Some examples for the resulting apparent
improvement in computational power of quantum over classical computation will be described. Quantum information processing systems involve the wave functions of composite system and the statistics of
the particle exchange of identical particles. Understanding this particle exchange is been known for a long time to be related to the topology of particles moving in space. Interesting examples are so called anyons, quasi-particles moving in 2-space and known to appear e.g. in the fractional quantum Hall effect. Then quantum computation naturally asks to understand the mathematical model of anyons, which
is a well-known subject in the field of quantum topology.
Bio: Dr. Uwe Kaiser received his PhD and habilitation from the University of Siegen in Germany. Additionally he also holds a K12-teaching certificate for Mathematics and Physics in Germany. Currently he is
Associate Professor in the Mathematics Department at Boise State University, where he also serves as Associate Chair. His research interests are in Geometric and Algebraic Topology, more recently in
Low Dimensional Topology and Quantum Topology, in particular in theory of skein modules. He is also working on several projects and grants related to STEM Education at Boise State University.