A modular functor which is universal for quantum computation
Quantum Physics
2007-05-23 v2 Geometric Topology
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.
Cite
@article{arxiv.quant-ph/0001108,
title = {A modular functor which is universal for quantum computation},
author = {Michael Freedman and Michael Larsen and Zhenghan Wang},
journal= {arXiv preprint arXiv:quant-ph/0001108},
year = {2007}
}