Quantumnetworking is emerging as a new research area to explore the opportunities of interconnecting quantum systems through end-to-end entanglement of qubits at geographical distance via quantum repeaters. A promising architecture has been proposed in the literature that decouples entanglement between adjacent quantum nodes/repeaters from establishing end-to-end paths by adopting a time slotted approach. Within this model, we destructure further end-to-end path establishment into two subproblems: path selection and scheduling. The former is set to determine the best repeaters to connect two end nodes, provided that all their local entanglements have succeeded. On the other hand, scheduling is concerned with deciding, which pairs of end nodes are served in the current time slot, while the others remain queued for later time slots. Unlike path selection, scheduling has not been investigated so far in the literature, particularly in presence of quantum noise, which makes both problems even more challenging. In this article, we propose to address it via a general framework of heuristic algorithms, for which we propose three illustrative instances with the objective of keeping the application delay small while achieving a good system utilization, in terms of high entanglement rate and fidelity of remotely entangled qubits. The system proposed is evaluated extensively via event-driven quantum network simulations, with noisy repeaters, in different node topologies under a Poisson arrival of requests from quantum applications. The results show the existence of a fundamental tradeoff between system- and application-level metrics, such as fairness versus entanglement and fidelity, which lays the foundations for further studies in this thriving research area.
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