  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.
