In this study, we develop a resource management framework for a quantum virtual private network (qVPN), which involves the sharing of an underlying public quantum network by multiple organizations for quantum entanglement distribution. Our approach involves resolving the issue of link entanglement resource allocation in a qVPN by utilizing a centralized optimization framework. We provide insights into the potential of genetic and learning-based algorithms for optimizing qVPNs, and emphasize the significance of path selection and distillation in enabling efficient and reliable quantum communication in multi-organizational settings. Our findings demonstrate that compared to traditional greedy based heuristics, genetic and learning-based algorithms can identify better paths. Furthermore, these algorithms can effectively identify good distillation strategies to mitigate potential noises in gates and quantum channels, while ensuring the necessary quality of service for end users.
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