  A quantum internet aims at harnessing networked quantum technologies, namely
by distributing bipartite entanglement between distant nodes. However,
multipartite entanglement between the nodes may empower the quantum internet
for additional or better applications for communications, sensing, and
computation. In this work, we present an algorithm for generating multipartite
entanglement between different nodes of a quantum network with noisy quantum
repeaters and imperfect quantum memories, where the links are entangled pairs.
Our algorithm is optimal for GHZ states with 3 qubits, maximising
simultaneously the final state fidelity and the rate of entanglement
distribution. Furthermore, we determine the conditions yielding this
simultaneous optimality for GHZ states with a higher number of qubits, and for
other types of multipartite entanglement. Our algorithm is general also in the
sense that it can optimise simultaneously arbitrary parameters. This work opens
the way to optimally generate multipartite quantum correlations over noisy
quantum networks, an important resource for distributed quantum technologies.
