Hypercubic cluster states in the phase modulated quantum optical frequency comb

We propose and fully analyze the simplest technique to date to generate light-based universal quantum computing resources, namely 2D, 3D and, in general, n-hypercubic cluster states. The technique uses two standard optical components: first, a single optical parametric oscillator pumped below threshold by a monochromatic field, which generates Einstein-Podolsky-Rosen entangled states, a.k.a. two-mode-squeezed states, over the quantum optical frequency comb; second, phase modulation at frequencies multiple of the comb spacing (via RF or optical means). The unprecedented compactness of this technique paves the way to implementing quantum computing on chip using quantum nanophotonics.