  Building large-scale quantum computers, essential to demonstrating quantum
advantage, is a key challenge. Quantum Networks (QNs) can help address this
challenge by enabling the construction of large, robust, and more capable
quantum computing platforms by connecting smaller quantum computers. Moreover,
unlike classical systems, QNs can enable fully secured long-distance
communication. Thus, quantum networks lie at the heart of the success of future
quantum information technologies. In quantum networks, multipartite entangled
states distributed over the network help implement and support many quantum
network applications for communications, sensing, and computing. Our work
focuses on developing optimal techniques to generate and distribute
multipartite entanglement states efficiently. Prior works on generating general
multipartite entanglement states have focused on the objective of minimizing
the number of maximally entangled pairs (EPs) while ignoring the heterogeneity
of the network nodes and links as well as the stochastic nature of underlying
processes. In this work, we develop a hypergraph based linear programming
framework that delivers optimal (under certain assumptions) generation schemes
for general multipartite entanglement represented by graph states, under the
network resources, decoherence, and fidelity constraints, while considering the
stochasticity of the underlying processes. We illustrate our technique by
developing generation schemes for the special cases of path and tree graph
states, and discuss optimized generation schemes for more general classes of
graph states. Using extensive simulations over a quantum network simulator
(NetSquid), we demonstrate the effectiveness of our developed techniques and
show that they outperform prior known schemes by up to orders of magnitude.
