Automated discovery of high-probability heralded schemes for path-entangled states

Entangled states of light lie at the heart of photonic quantum technologies, from distributed quantum communication to quantum-enhanced measurement and information processing. Their practical generation, however, remains constrained by the weak interactions between photons, which make the deterministic assembly of large multiphoton entangled states a central challenge in quantum optics. In this work, we use AI techniques to discover heralded linear-optical schemes for path-entangled states and show that the resulting solutions can be elevated from individual circuits to a new scalable family. This family contains previously known constructions as special cases while generally providing exponential and super-exponential improvements over those, and its extension to broader classes of target states shows how automated discovery can reveal transferable physical understanding. By presenting compact experimental proposals for large path-entangled states, our results provide both a theoretical advance in photonic heralding and a route towards a substantial leap in experimentally accessible multiphoton entanglement.