Freedman, Michael H.; Larsen, Michael; Wang, Zhenghan A modular functor which is universal for quantum computation. (English) Zbl 1012.81007 Commun. Math. Phys. 227, No. 3, 605-622 (2002). 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. Cited in 2 ReviewsCited in 74 Documents MSC: 81P68 Quantum computation 57R56 Topological quantum field theories (aspects of differential topology) 81T45 Topological field theories in quantum mechanics Keywords:Witten-Chern-Simons theory; quantum circuit computation; intertwining action of a braid; Jones representation PDFBibTeX XMLCite \textit{M. H. Freedman} et al., Commun. Math. Phys. 227, No. 3, 605--622 (2002; Zbl 1012.81007) Full Text: DOI arXiv