Quantum Computation and the localization of Modular Functors
Quantum Physics
2007-05-23 v5
Abstract
The mathematical problem of localizing modular functors to neighborhoods of points is shown to be closely related to the physical problem of engineering a local Hamiltonian for a computationally universal quantum medium. For genus surfaces, such a local Hamiltonian is mathematically defined. Braiding defects of this medium implements a representation associated to the Jones polynomial and this representation is known to be universal for quantum computation.
Cite
@article{arxiv.quant-ph/0003128,
title = {Quantum Computation and the localization of Modular Functors},
author = {Michael H. Freedman},
journal= {arXiv preprint arXiv:quant-ph/0003128},
year = {2007}
}