Cluster states with higher-dimensional lattices that cannot be physically embedded in three-dimensional space have important theoretical interest in quantum computation and quantum simulation of topologically ordered condensed-matter systems. We present a simple, scalable, top-down method of entangling the quantum optical frequency comb into hypercubic-lattice continuous-variable cluster states of a size of about 10^4 quantum field modes, using existing technology. A hypercubic lattice of dimension D (linear, square, cubic, hypercubic, etc.) requires but D optical parametric oscillators with bichromatic pumps whose frequency splittings alone determine the lattice dimensionality and the number of copies of the state.
@article{arxiv.1309.4105,
title = {Weaving quantum optical frequency combs into continuous-variable hypercubic cluster states},
author = {Pei Wang and Moran Chen and Nicolas C. Menicucci and Olivier Pfister},
journal= {arXiv preprint arXiv:1309.4105},
year = {2014}
}