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.

翻译：构建展示量子优势所需的大规模量子计算机是一项关键挑战。量子网络可通过连接多个小型量子计算机，构造大型、稳健且能力更强的量子计算平台，从而帮助应对这一挑战。此外，与经典系统不同，量子网络还能实现完全安全的远距离通信。因此，量子网络是未来量子信息技术成功的关键。在量子网络中，分布在网络中的多体纠缠态有助于实现并支持众多用于通信、感知和计算的量子网络应用。我们的工作聚焦于开发高效生成和分布多体纠缠态的最优技术。以往关于生成通用多体纠缠态的研究，目标是最小化最大纠缠对的数量，却忽略了网络节点与链路的异构性以及底层过程的随机性。在本工作中，我们开发了一种基于超图的线性规划框架，能在考虑网络资源、退相干和保真度约束以及底层过程随机性的条件下，为图态表示的通用多体纠缠态提供（在特定假设下）最优的生成方案。我们通过为路径图态和树图态这两种特例开发生成方案来阐述我们的技术，并讨论了更一般图态类的最优生成方案。通过在量子网络模拟器（NetSquid）上进行大量仿真，我们证明了所开发技术的有效性，并表明其性能比先前已知方案高出数个数量级。