Optimal resource requirements for connected quantum sub-networks

The realization of a global quantum network capable of supporting secure communication and other quantum information processing (QIP) tasks hinges on the ability to distribute high-fidelity entanglement across long distances while optimizing resource usage. This work describes a scalable approach for building large quantum networks by connecting quantum sub-networks using entanglement backbones as interconnections and a swapping based entanglement distribution protocol. Using a statistical model for parametrized quantum sub-networks we derive a set of equations whose solutions give the optimal values of average network parameters that meet threshold requirements for QIP tasks while minimizing resource cost functions. Our analysis extends to the scenario where multiple sub-networks must be interconnected simultaneously based on the formulation of a global resource cost function. The probability of successfully satisfying the parameter thresholds of a QIP task as a function of average parameters of the sub-networks for random network demands reveals a transition from zero to full satisfiability above critical network parameter values. Moreover, we find that the satisfiability transition can be smooth or discontinuous depending on the topology of the sub-networks. Our results present a pathway for calculating optimal resource requirements in quantum sub-networks interconnected to form the global quantum internet.