Space-time Peer-to-Peer Distribution of Multi-party Entanglement for Any Quantum Network

Graph states are a class of important multiparty entangled 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 can be essential for further large-scale quantum networks. We propose a novel quantum network protocol called P2PGSD inspired by the classical Peer-to-Peer (P2P) network to efficiently implement the general graph state distribution in the network layer, which demonstrates advantages in resource efficiency and scalability over existing methods for sparse graph states. An explicit mathematical model for a 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. In addition, we leverage the spacetime quantum network inspired by the symmetry from relativity for memory management in network problems and used it to improve our proposed algorithm. The advantages of our protocols are confirmed by numerical simulations showing an improvement of up to 50% for general sparse graph states, paving the way for a resource-efficient multiparty entanglement distribution across any network topology.