  We propose a method to generate a two-dimensional cluster state of
polarization encoded photonic qubits from two coupled quantum dot emitters. We
combine the recent proposal [N. H. Lindner and T. Rudolph, Phys. Rev. Lett.
103, 113602 (2009)] for generating 1-dimensional cluster state strings from a
single dot, with a new proposal for an optically induced conditional phase (CZ)
gate between the two quantum dots. The entanglement between the two quantum
dots translates to entanglement between the two photonic cluster state strings.
Further inter-pair coupling of the quantum dots using cavities and waveguides
can lead to a 2-dimensional cluster sheet. Detailed analysis of errors
indicates that our proposal is feasible with current tech- nology. Crucially,
the emitted photons need not have identical frequencies, and so there are no
constraints on the resonance energies for the quantum dots, a standard problem
for such sources.
