Dynamic Scheduling in Fiber and Spaceborne Quantum Repeater Networks

TL;DR

This work develops a general, quantitative framework for dynamic scheduling in quantum networks that span both fiber and satellite links. It introduces a linear algebraic model of quantum network queues (ebit queues and demand queues) and a matrix representation of entanglement-swapping transitions, enabling principled policy design. Using Lyapunov drift minimization, the authors derive a family of quadratic scheduling policies and compare them to Max-Weight variants, showing near-parity performance with lower complexity in many scenarios. The thesis extends the QuISP simulator with satellite-capable channels, free-space links, and network multiplexing, and validates the framework through simple and complex topologies, culminating in a satellite-ground-satellite case study that highlights latency as a fundamental bottleneck. The results chart the practical challenges and opportunities for scheduling in large-scale fiber-satellite quantum networks and outline future directions toward multipartite entanglement and more sophisticated multiplexing schemes.

Abstract

The problem of scheduling in quantum networks 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, adopting heuristic or optimization-based algorithms...), requiring a method to compare different solutions and choose the most appropriate. We present a framework to mathematically formulate the scheduling problem over quantum networks and benchmark general quantum scheduling policies over arbitrary lossy quantum networks. By leveraging the framework, we apply Lyapunov drift minimization to derive a novel class of quadratic optimization based scheduling policies, which we then analyze and compare with a Max Weight inspired linear class. We then give an overview of the pre-existing fiber quantum simulation tools and report on the development of numerous extensions to QuISP, an established quantum network simulator focused on scalability and accuracy in modeling the underlying classical network infrastructure. To integrate satellite links in the discussion, 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 conclude 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 quantum networks. [Abridged abstract, see PDF for full version]

Figures (28)

• Figure 1: Example of entanglement swapping: a local measurement at the middle node splices states $\ket{\Phi^+}_{12}$ and $\ket{\Phi^+}_{34}$ into $\ket{\Phi^+}_{14}$. $\ket{\Phi^+}_{23}$ is created as a side effect and is not relevant to the procedure.
• Figure 2: Comparison of different quantum memory implementations in terms of their multiplexing capabilities and storage lifetime. In this picture, the tradeoff between multimodality and quality storage is made apparent. Horizontal lines represent one round-trip time across the corresponding length of fiber and/or free-space. Red points represent solid-state memories, while blue ones correspond to gaseous systems. References cited in the picture: PuMemoryWangMemoryOrtuMemoryAOrtuMemoryBBradleyMemoryChrapkiewiczMemory
• Figure 3: The Internet protocol stack, as defined in KuroseRossBook. For each layer, we provide an elementary description of its tasks and, where applicable, some examples of protocols employed in the current Internet stack.
• Figure 4: Example of simple dumbbell network topology with two communication flows $(A\rightarrow B)$ and $(C\rightarrow D)$. In the ideal case, the limiting factor is the capacity of the $EF$ bottleneck link, leading to the maximal stability region shown in the right figure. However, other nonidealities could limit communication (e.g. high losses, traffic from other users…). In that case, the shape of the stability region is usually more similar to the purple nonmaximal one.
• Figure 5: Creation of an end-to-end entangled pair in multiple steps (dashed lines represent one entangled pair of qubits shared between two nodes): quantum memories allow storage of intermediate ebits until all sublinks are ready.