Figure 1: Experimental setup.

(a) Setup used to generate the graph state resource consisting of the four-qubit graph code plus ancilla qubit. Two PCF sources are pumped using a Ti:sapphire laser producing picosecond pulses at 720 nm. The first source produces a pair of photons in the state and the second produces photons in the state . The signal photons from the first pair are rotated to the state |+ using a HWP and both signal photons are then fused using a (PBS). The polarizations of the signal photons are then rotated using half-wave plates to form the three-qubit linear cluster state , where the first idler photon is used as a trigger to verify a fourfold coincidence signifying the generation of the state. The path degree of freedom of the signal photons is then used to expand the resource to a five-qubit linear cluster state using a Sagnac interferometer, as shown in the dashed boxes and explained in the main text. (b) Five-qubit linear cluster state and local complementation steps (LC₁ and LC₂) to generate the graph code plus ancilla qubit. Here, the vertices correspond to qubits initialized in the state |+› and edges correspond to controlled-phase gates, C_Z=diag(1,1,1,−1), applied to the qubits. The LC operations are performed using half-wave plates, QWPs and phase shifters in the relevant photon modes and correspond to LC₁=A₁B₂(AA)₃B₄A₅ and LC₂=A₁A₂B₃A₄A₅, where and . In the steps shown in the figure, the operation A (B) is depicted as a dashed (solid) outline around the qubit. The background shading in the final step represents the quantum resource used to perform the quantum error-correction schemes. (c) Expectation values of the operators used to verify genuine multipartite entanglement in the graph state. Here Õ corresponds to measurements in the O basis with the eigenstates swapped. The ideal values correspond to the dashed line. All error bars in the figures are calculated using a Monte Carlo method with Poissonian noise on the count statistics⁶⁵.