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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.

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