Unitary R-matrices for topological quantum computing

The main problem with current approaches to quantum computing is the difficulty of establishing and maintaining entanglement. A Topological Quantum Computer (TQC) aims to overcome this by using different physical processes that are topological in nature and which are less susceptible to disturbance by the environment. In a (2+1)-dimensional system, pseudoparticles called anyons have statistics that fall somewhere between bosons and fermions. The exchange of two anyons, an effect called braiding from knot theory, can occur in two different ways. The quantum states corresponding to the two elementary braids constitute a two-state system allowing the definition of a computational basis. Quantum gates can be built up from patterns of braids and for quantum computing it is essential that the operator describing the braiding-the R-matrix-be described by a unitary operator. The physics of anyonic systems is governed by quantum groups, in particular the quasi-triangular Hopf algebras obtained from finite groups by the application of the Drinfeld quantum double construction. Their representation theory has been described in detail by Gould and Tsohantjis, and in this review article we relate the work of Gould to TQC schemes, particularly that of Kauffman.

Guiding intellectual and personal growth across educational contexts

This book recognizes the importance of cooperative learning, in contrast to the traditional classroom, as an effective approach to learning. Its coverage of the subject ranges across the educational spectrum, from pre-school years to university, and offers a fresh perspective on a topic that has gained increasing interest worldwide. With contributions from an international panel of leading experts in the field, this engaging text succeeds in providing key insights, linking the theories that underpin the study of group dynamics to their practical application in the classroom. It presents a comprehensive overview of this alternative educative approach, illustrating how cooperative learning experiences can promote socialisation and friendships, and facilitate learning. The editors assemble a range of well-researched essays, covering such aspects as: * The importance of teacher and student interaction * Small group, virtual and non-virtual teaching environments * Assessment practices for measuring the outcomes of individual and group progress * The effect of cooperative learning on relationships amongst students with diverse cultural, social and learning needs. Illustrated with practical examples throughout, this book will be a crucial read for teacher educators, educational psychologists, student teachers, academics and researchers who want to realize the significant potential of cooperative learning in all educational settings.