Simulations of quantum double models
Abstract
We demonstrate how to build a simulation of two dimensional physical theories describing topologically ordered systems whose excitations are in one to one correspondence with irreducible representations of a Hopf algebra, D(G), the quantum double of a finite group G. Our simulation uses a digital sequence of operations on a spin lattice to prepare a ground "vacuum" state and to create, braid and fuse anyonic excitations. The simulation works with or without the presence of a background Hamiltonian though only in the latter case is the system topologically protected. We describe a physical realization of a simulation of the simplest non-Abelian model, D(S_3), using trapped neutral atoms in a two dimensional optical lattice and provide a sequence of steps to perform universal quantum computation with anyons. The use of ancillary spin degrees of freedom figures prominently in our construction and provides a novel technique to prepare and probe these systems.
Cite
@article{arxiv.0901.1345,
title = {Simulations of quantum double models},
author = {G. K. Brennen and M. Aguado and J. I. Cirac},
journal= {arXiv preprint arXiv:0901.1345},
year = {2009}
}
Comments
24 pages, 2 figures