A Modular Functor Which is Universal¶for Quantum Computation

@article{Freedman2000AMF,
  title={A Modular Functor Which is Universal¶for Quantum Computation},
  author={Michael H. Freedman and Michael Larsen and Zhenghan Wang},
  journal={Communications in Mathematical Physics},
  year={2000},
  volume={227},
  pages={605-622}
}
Abstract:We show that the topological modular functor from Witten–Chern–Simons theory is universal for quantum computation in the sense that a quantum circuit computation can be efficiently approximated by an intertwining action of a braid on the functor's state space. A computational model based on Chern–Simons theory at a fifth root of unity is defined and shown to be polynomially equivalent to the quantum circuit model. The chief technical advance: the density of the irreducible sectors of… 
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