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.
@article{arxiv.2012.15304,
title = {Quantum-controlled cluster states},
author = {R. F. Barros and G. B. Alves and O. Pfister and A. Z. Khoury},
journal= {arXiv preprint arXiv:2012.15304},
year = {2021}
}