Spin Networks and Anyonic Topological Computing II

TL;DR

This paper reviews q-deformed spin networks in topological quantum field theory, demonstrating their application in creating dense unitary braid group representations, including the universal Fibonacci model for quantum computation.

Contribution

It formulates braid group representations derived from spin networks in a computationally and algebraically accessible form, highlighting their universality.

Findings

Constructed dense unitary representations of braid groups

Applied these methods to the Fibonacci model for quantum computing

Provided a formulation suitable for computational and algebraic analysis

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 simplest case of these models is the Fibonacci model, itself universal for quantum computation. We here formulate these braid group representations in a shape suitable for computation and algebraic work.