Quantum-controlled cluster states

Quantum optical cluster states have been increasingly explored, in the light of their importance for measurement-based quantum computing. Here we set forth a new method for generating quantum controlled cluster states: pumping an optical parametric oscillator with spatially structured light. We show that state-of-the-art techniques for producing clusters in the spectral and temporal domains are improved by a structured light pump, which manipulates the spatial mode couplings in the parametric interaction. We illustrate the method considering a second-order pump structure, and show that a simple mode rotation yields different cluster states, including, but not limited to the two-dimensional square and hexagonal lattices. We also introduce a novel technique for generating non-uniform cluster states, and propose a simple setup for its implementation.