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arXiv:2205.10000 · IEEE International Conference on Quantum Computing and Engineering (QCE)

A Linear Algebraic Framework for Quantum Internet Dynamic Scheduling

Paolo Fittipaldi, Anastasios Giovanidis, Frédéric Grosshans

Published Sep 1, 2022• 6 citations
arXivHTMLPDF

Abstract

Future quantum internet aims to enable quantum communication between arbitrary pairs of distant nodes through the sharing of end-to-end entanglement, a universal resource for many quantum applications. As in classical networks, quantum networks also have to resolve problems related to routing and satisfaction of service at a sufficient rate. We deal here with the problem of scheduling when multiple commodities must be served through a quantum network based on first generation quantum repeaters, or quantum switches. To this end, we introduce a novel discrete-time algebraic model for arbitrary network topology, including transmission and memory losses, and adapted to dynamic scheduling decisions.Our algebraic model allows the scheduler to use the storage of temporary intermediate links to optimize the performance, depending on the information availability, ranging from full global information for a centralized scheduler to partial local information for a distributed one. As an illustrative example, we compare a simple greedy scheduling policy with several Max-Weight inspired scheduling policies and illustrate the resulting achievable rate regions for two competing pairs of clients through a network.

DOI
10.1109/qce53715.2022.00066

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Future quantum internet aims to enable quantum communication between arbitrary pairs of distant nodes through the sharing of end-to-end entanglement, a universal resource for many quantum applications. As in classical networks, quantum networks also have to resolve problems related to routing and satisfaction of service at a sufficient rate. We deal here with the problem of scheduling when multiple commodities must be served through a quantum network based on first generation quantum repeaters, or quantum switches. To this end, we introduce a novel discrete-time algebraic model for arbitrary network topology, including transmission and memory losses, and adapted to dynamic scheduling decisions.Our algebraic model allows the scheduler to use the storage of temporary intermediate links to optimize the performance, depending on the information availability, ranging from full global information for a centralized scheduler to partial local information for a distributed one. As an illustrative example, we compare a simple greedy scheduling policy with several Max-Weight inspired scheduling policies and illustrate the resulting achievable rate regions for two competing pairs of clients through a network.
Quantum Internetworking is a recent field that promises numerous interesting applications, many of which require the distribution of entanglement between arbitrary pairs of users. This work deals with the problem of scheduling in an arbitrary entanglement swapping quantum network — often called first generation quantum network — in its general topology, multicommodity, loss-aware formulation. We introduce a linear algebraic framework that exploits quantum memory through the creation of intermediate entangled links. The framework is then employed to apply Lyapunov Drift Minimization (a standard technique in classical network science) to mathematically derive a natural class of scheduling policies for quantum networks minimizing the square norm of the user demand backlog. Moreover, an additional class of Max-Weight inspired policies is proposed and benchmarked, reducing significantly the computation cost at the price of a slight performance degradation. The policies are compared in terms of information availability, localization and overall network performance through an ad-hoc simulator that admits user-provided network topologies and scheduling policies in order to showcase the potential application of the provided tools to quantum network design.
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]
In this work, we describe a routing algebra corresponding to the problem of establishing end-to-end quantum entanglements between nodes connected through a network of first generation quantum repeaters. Our goal is to design an algorithm which can determine all the routes and swapping schedules to achieve maximal rates of end-to-end entanglement. We aim to provide an improvement in terms of complexity over an existing solution while increasing the number of routes and schedules available to offer more alternatives for the entanglement generation layer of a quantum protocol stack.
With a growing number of quantum networks in operation, there is a pressing need for performance analysis of quantum switching technologies. A quantum switch establishes, distributes, and maintains entanglements across a network. In contrast to a classical switching fabric, a quantum switch is a two-sided queueing network. The switch generates Link-Level Entanglements (LLEs) across links that connect users to the switch, which are then fused to process the network's entanglement requests. First, we characterize the capacity region that is defined as the set of entanglement request rates for which there exists a scheduling policy stabilizing the system. We then show that a sequence of Max-Weight policies that we propose achieve throughput optimality in the asymptotic sense. Our proof techniques analyse a two-time scale separation phenomenon at the fluid scale for a general switch topology. This allows us to demonstrate that the optimal fluid dynamics are given by a scheduling algorithm that solves a certain average reward Markov Decision Process.
With a growing number of quantum networks in operation, there is a pressing need for performance analysis of quantum switching technologies. A quantum switch establishes, distributes, and maintains entanglements across a network. In contrast to a classical switching fabric, a quantum switch is a two-sided queueing network. The switch generates Link-Level Entanglements (LLEs) across links that connect users to the switch, which are then fused to process the network's entanglement requests. First, we characterize the capacity region that is defined as the set of entanglement request rates for which there exists a scheduling policy stabilizing the system. We then show that a sequence of Max-Weight policies that we propose achieve throughput optimality in the asymptotic sense. Our proof techniques analyse a two-time scale separation phenomenon at the fluid scale for a general switch topology. This allows us to demonstrate that the optimal fluid dynamics are given by a scheduling algorithm that solves a certain average reward Markov Decision Process.
Quantum satellite networks offer a promising solution for achieving long-distance quantum communication by enabling entanglement distribution across global scales. This work formulates and solves the quantum satellite network scheduling problem by optimizing satellite-to-ground station pair assignments under realistic system and environmental constraints. Our framework accounts for limited satellite and ground station resources, fairness, entanglement fidelity thresholds, and real world non-idealities including atmospheric losses, weather and background noise. In addition, we incorporate the complexities of multi-satellite relays enabled via inter-satellite links. We propose an integer linear programming (ILP) based optimization framework that supports multiple scheduling objectives, allowing us to analyze tradeoffs between maximizing total entanglement distribution rate and ensuring fairness across ground station pairs. Our framework can also be used as a benchmark tool to measure the performance of other potential transmission scheduling policies.