Supplementary Video 1: The four animated sequences depict the four different sets of two-qubit gates that are generated by the specified pulse sequences, 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 the gate is active, Stark shifting the affected qubits so that they are off resonance, thereby disabling the hopping Hamiltonian.