This volume contains a collection of papers, written by physicists, computer scientists, and mathematicians, from the Conference on Representation Theory, Quantum Field Theory, Category Theory, and Quantum Information Theory, which was held at the University of Texas at Tyler from October 1-4, 2009.

Quantum computing is a field at the interface of the physical sciences, computer sciences and mathematics. As such, advances in one field are often overlooked by practitioners in other fields. This volume brings together articles from each of these areas to make students, researchers and others interested in quantum computation aware of the most current advances. It is hoped that this work will stimulate future advances in the field.

Edited by: Kazem Mahdavi, Deborah Koslover, and Leonard L. Brown III, University of Texas at Tyler, TX

• Cartan Decomposition and Entangling Power of Braiding Quantum Gates
  A.D. Ballard and Y.-S. Wu
• A Uni?ed Approach to Universality for Three Distinct Types of 2-qubit Quantum Computing Devices
  G. Chen, V. Ramakrishna and Z. Zhang
• Efficient Algorithm for a Quantum Analogue of 2-SAT
  S. Bravyi
• Quantum Computational Curvature and Jacobi Fields
  H. E. Brandt
• A Quantum Model for the Jones Polynomial, Khovanov Homology and Generalized Simplicial Homology
  L. H. Kauffman
• Oriented Quantum Algebras and Coalgebras, Invariants of Oriented 1-1 Tangles, Knots and Links
  L. H. Kauffman and D. E. Radford
• Space and Time Lattices in Frame Fields of Quantum Representations of Real and Complex Numbers
  P. Benioff