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A Modular Functor Which is Universal¶for Quantum Computation


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 the Jones representation has topological implications which will be considered elsewhere.

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Received: 4 May 2001 / Accepted: 18 February 2002

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Freedman, M., Larsen, M. & Wang, Z. A Modular Functor Which is Universal¶for Quantum Computation. Commun. Math. Phys. 227, 605–622 (2002).

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  • State Space
  • Computational Model
  • Quantum Computation
  • Technical Advance
  • Circuit Model