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
104 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.