Peer-to-Peer Distribution of Graph States Across Spacetime Quantum Networks of Arbitrary Topology

Graph states are a class of important multiparty entangled quantum states, of which Bell pairs are the special case. Realizing a robust and fast distribution of arbitrary graph states in the downstream layer of the quantum network is essential for enabling large-scale quantum networks. To address this, we propose a novel quantum network protocol, called P2PGSD, inspired by the classical Peer-to-Peer network. This protocol efficiently implements general graph state distribution in the network layer, demonstrating significant advantages in resource efficiency and scalability, particularly for sparse graph states. An explicit mathematical model for the general graph state distribution problem has also been constructed, above which the intractability for a wide class of resource minimization problems is proved and the optimality of the existing algorithms is discussed. Moreover, we leverage the space-time quantum network for memory management in network challenges, drawing inspiration from special relativity. We suggest a universal quantum distributed computation framework to exploit the strengths of our protocols, as confirmed by numerical simulations that reveal up to a 50% enhancement for general sparse graph states. This work marks a significant step toward resource-efficient multiparty entanglement distribution for diverse network topologies.