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In the quest to build general-purpose photonic quantum computers,fusion-based quantum computation has risen to prominence as a promisingstrategy. This model allows a ballistic construction of large cluster stateswhich are universal for quantum computation, in a scalable and loss-tolerantway without feed-forward, by fusing many small n-photon entangled resourcestates. However, a key obstacle to this architecture lies in efficientlygenerating the required essential resource states on photonic chips. One suchcritical seed state that has not yet been achieved is the heralded three-photonGreenberger-Horne-Zeilinger (3-GHZ) state. Here, we address this elementaryresource gap, by reporting the first experimental realization of a heraldeddual-rail encoded 3-GHZ state. Our implementation employs a low-loss and fullyprogrammable photonic chip that manipulates six indistinguishable singlephotons of wavelengths in the telecommunication regime. Conditional on theheralding detection, we obtain the desired 3-GHZ state with a fidelity0.573+-0.024. Our work marks an important step for the future fault-tolerantphotonic quantum computing, leading to the acceleration of building alarge-scale optical quantum computer.

Heralded three-photon entanglement from a single-photon source on a photonic chip