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Logic, Language, Information and Computation

Volume 4576 of the series Lecture Notes in Computer Science pp 248-263

Spin Networks, Quantum Topology and Quantum Computation

  • Louis H. KauffmanAffiliated withDepartment of Mathematics, Statistics and Computer Science (m/c 249), 851 South Morgan Street, University of Illinois at Chicago, Chicago, Illinois 60607-7045
  • , Samuel J. LomonacoJr.Affiliated withDepartment of Computer Science and Electrical Engineering, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, MD 21250

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Abstract

We review the q-deformed spin network approach to Topological Quantum Field Theory and apply these methods to produce unitary representations of the braid groups that are dense in the unitary groups. The results are applied to the quantum computation of colored Jones polynomials.

Keywords

braiding knotting linking spin network Temperley – Lieb algebra unitary representation