Hopf Algebras in Kitaev's Quantum Double Models: Mathematical Connections from Gauge Theory to Topological Quantum Computing and Categorical Quantum Mechanics

Conference Date: 
Monday, July 31, 2017 (All day) to Friday, August 4, 2017 (All day)
Scientific Areas: 
Condensed Matter
Mathematical Physics
Quantum Foundations
Quantum Gravity
Quantum Information

 

The Kitaev quantum double models are a family of topologically ordered spin models originally proposed to exploit the novel condensed matter phenomenology of topological phases for fault-tolerant quantum computation. Their physics is inherited from topological quantum field theories, while their underlying mathematical structure is based on a class of Hopf algebras. This structure is also seen across diverse fields of physics, and so allows connections to be made between the Kitaev models and topics as varied as quantum gauge theory and modified strong complementarity. This workshop will explore this shared mathematical structure and in so doing develop the connections between the fields of mathematical physics, quantum gravity, quantum information, condensed matter and quantum foundations.

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  • Liang Chang, Chern Institute of Mathematics
  • Bianca Dittrich, Perimeter Institute
  • Ross Duncan, University of Strathclyde
  • Tobias Fritz, Max Planck Institute for Mathematics in the Sciences
  • Jurgen Fuchs, Karlstad University
  • Robert Koenig, Technical University of Munich
  • Catherine Meusburger, Friedrich-Alexander Universitaet
  • Burak Sahinoglu, California Institute of Technology
  • Joost Slingerland, National University of Ireland
  • Pawel Sobocinski, University of Southampton
  • Jamie Vicary, University of Oxford
  • Derek Wise, University of Erlangen-Nuremberg

Scientific Organizers:

  • Courtney Brell, Perimeter Institute
  • Ross Duncan, University of Strathclyde
  • Daniel Gottesman, Perimeter Institute
  • Prince Osei, Perimeter Institute
  • Lucy Zhang, University of Toronto