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We introduce a repeater scheme to efficiently distribute multipartiteentangled states in a quantum network with optimal scaling. The scheme allowsto generate graph states such as 2D and 3D cluster states of growing size orGHZ states over arbitrary distances, with a constant overhead per node/channelthat is independent of the distance. The approach is genuine multipartite, andis based on the measurement-based implementation of multipartite hashing, anentanglement purification protocol that operates on a large ensemble togetherwith local merging/connection of elementary building blocks. We analyze theperformance of the scheme in a setting where local or global storage islimited, and compare it to bipartite and hybrid approaches that are based onthe distribution of entangled pairs. We find that the multipartite approachoffers a storage advantage, which results in higher efficiency and betterperformance in certain parameter regimes. We generalize our approach toarbitrary network topologies and different target graph states.

Multipartite state generation in quantum networks with optimal scaling