# 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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