A modular functor which is universal for quantum computation
| Venue: | Comm. Math. Phys |
| Citations: | 67 - 17 self |
BibTeX
@ARTICLE{Freedman_amodular,
author = {Michael H. Freedman and Michael Larsen and Zhenghan Wang},
title = {A modular functor which is universal for quantum computation},
journal = {Comm. Math. Phys},
year = {},
pages = {605--622}
}
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Abstract
Abstract: 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. 1.
