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A modular functor which is universal for quantum computation

Michael Freedman·Michael Larsen·Zhenghan Wang
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Abstract

We show that the topological modular functor from Witten-Chern-Simons theory is universal for quantum computation in the sense 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, have topological implications which will be considered elsewhere.

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Michael Freedman, Michael Larsen, Zhenghan Wang. 2000-02-01. A modular functor which is universal for quantum computation. https://arxiv.org/abs/quant-ph/0001108

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