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A modular functor which is universal for quantum computation. (English) Zbl 1012.81007
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.

81P68 Quantum computation
57R56 Topological quantum field theories (aspects of differential topology)
81T45 Topological field theories in quantum mechanics
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