In this thesis, we analyze the problem of scheduling in the context of quantum networks. Given a quantum network, the scheduling problem amounts to choosing which entanglement swapping operations to perform to better serve user demand. The choice can be carried out following a variety of criteria (e.g., ensuring all users are served equally vs. prioritizing specific critical applications, properly managing load spikes and node failures, adopting heuristic or optimization-based algorithms...), warranting the need for a method to compare different solutions and choose the most appropriate. We present here a framework to mathematically formulate the scheduling problem over quantum networks and benchmark possible solutions in a variety of environments. Our framework enables the benchmarking of general quantum scheduling policies over arbitrary lossy multicommodity quantum networks. By leveraging the framework, we apply Lyapunov drift minimization (a standard technique in classical network science) to derive a novel class of quadratic optimization based scheduling policies, which we then analyze and compare with a simpler, Max Weight inspired linear class to quantify the performance loss due to the simplification.
We start our second chapter with an overview of the pre-existing fiber quantum simulation tools. The rest of the chapter is devoted to the development of numerous extensions to QuISP, an established quantum network simulator focused on scalability and accuracy in modeling the classical communication infrastructure underlying every quantum network. We document the development of our extensions allowing simulating satellite links and multiple connections in QuISP, with an account of the currently functional extensions (free-space links and connection tear down) and of the ones still under active development (network multiplexing). Since it is likely that a future global-scale quantum network will incorporate satellite interconnections, we devote a chapter to the study of quantum satellite links. We derive an analytical model for the entanglement distribution rates for satellite-to-ground and ground-satellite-ground links and discuss different quantum memory allocation policies for the dual-link case. Our findings show that classical communication latency is a major limiting factor for satellite communication, and the effects of physical upper bounds such as the speed of light must be taken into account when designing quantum links, limiting the attainable rates to tens of kHz. We also investigate the issue of differential latency, a Doppler-like effect caused by the displacement of satellite nodes that changes in the timing of incoming photons and adds another upper bound to the generation rate.
We conclude the thesis by summarizing our findings and highlighting the challenges that still need to be overcome in order to study the quantum scheduling problem over fiber and satellite large-scale quantum networks.