All-optical cluster-state generation using Rydberg dipole blockade

We analyze the generation of cluster-states, which are useful in one-way quantum computing architectures, in a 2D array of Rydberg atoms. Dipole blockade is used as a mechanism for controlled-Z operation between nearest neighbors. Applying an electric field gradient allows individual atomic addressing due to spatially dependent Stark-shifts. The latter combined with a train of optical pulses tailored to resonantly excite spatially selected pairs of atoms is proposed to entangle nearest neighbors. In order to efficiently generate a 2D cluster-state, we apply this protocol in parallel to non-interacting 1D chains of atoms.