Topological Quantum Computation

@inproceedings{Freedman2001TopologicalQC,
  title={Topological Quantum Computation},
  author={Michael H. Freedman and Alexei Y. Kitaev and Michael Larsen and Zhenghan Wang},
  year={2001}
}
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones poly- nomial and arise in Witten-Chern-Simons theory. The braiding and fusion of anyonic excitations in quantum Hall electron liquids and 2D-magnets are modeled by modular functors, opening a new possi- bility for the realization of quantum computers. The chief advantage of anyonic computation would be… 

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