Photonic realization of a subgraph extraction in a quantum random network

Understanding how complex connectivity emerges in networks is a fundamental challenge in classical and quantum science. In classical random networks, complex subgraphs typically require relatively high connection probabilities, whereas quantum random network theory predicts that such structures can arise at a single, lower threshold through entanglement and local operations. Here, using an integrated silicon photonic chip, we experimentally realize a quantum subgraph predicted by quantum random network theory in a four-node quantum random network. Our integrated platform exploits probabilistic photon-pair sources and coherent control of path modes to prepare a structured quantum subgraph through local transformations and postselection, operating in a threshold regime that differs from classical random networks. We verify that the subgraph state exhibits genuine high-dimensional multipartite entanglement across the nodes, providing experimental evidence that quantum entanglement enables connectivity structures beyond classical accessibility.