Supplementary Video 1: The four animated sequences depict the four different parallel applications of two-qubit gates that are generated by Stark shifting sets of qubits off resonance, which finally realise a two-dimensional cluster state. For clarity, the controlled-phase gates which are generated in each step are only indicated at the end of each sequence, the dotted lines showing where they were applied. The yellow areas indicate that a gate is active, Stark shifting the affected qubits so that they are off resonance, thereby disabling the hopping Hamiltonian.