Dynamic Scheduling in Fiber and Spaceborne Quantum Repeater Networks

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]

• The paper introduces a novel linear algebraic framework employing Lyapunov Drift Minimization to schedule entanglement distribution and ensure network stability.
• It extends classical scheduling policies like Max-Weight to quantum networks, optimizing memory allocation and entanglement swapping efficiency in hybrid setups.
• Simulation results validate significant throughput and reliability improvements in hybrid fiber and satellite quantum repeater networks under high-latency conditions.

Dynamic Scheduling in Fiber and Spaceborne Quantum Repeater Networks

Introduction

The paper presents a comprehensive framework for dynamic scheduling within both terrestrial fiber networks and spaceborne quantum repeater networks. With the growing interest in developing global-scale quantum networks, connecting metro-scale quantum subnetworks through satellite links becomes crucial. The study integrates the classical network scheduling concepts with quantum networks' distinctive needs—focusing on entanglement distribution and multiplexing across interconnected quantum networks.

System and Model Overview

The research utilizes a linear algebraic approach to address scheduling complexities in quantum networks, particularly through Lyapunov Drift Minimization (LDM) techniques, adapted for quantum scenarios. The system modeled consists of satellite nodes equipped with quantum memories, interlinking terrestrial quantum repeaters. Each node can perform Bell State Measurements (BSM) for entanglement swapping to increase connectivity over long distances.

Core Contributions

1. Linear Algebraic Framework: The paper proposes a mathematical formulation to handle the scheduling of entangled pairs distribution across nodes, integrating traditional drift minimization methodologies suited for quantum environments. This approach ensures network stability through proper scheduling decisions across lossy quantum channels.
2. Integration of Classical and Quantum Models: By extending classical scheduling policies like Max-Weight to quantum networks, the paper examines how classical methodologies can optimize quantum communication. Variants of quadratic optimization-based policies are discussed, highlighting their adaptability to quantum-specific constraints like memory lifetimes and photon-pair successes.
3. Hybrid Network Simulation: Utilizing QuISP, the paper presents simulation results that account for both fiber and satellite communication. It employs OMNeT++ to simulate complex network scenarios where ground stations are interconnected via spaceborne satellites—addressing latency challenges and resource bottlenecks intrinsic to quantum network design.

Key Findings

• Performance Scaling: Simulations indicate that the proposed scheduling framework enhances throughput and connection reliability in hybrid networks, especially under high-latency conditions, typical of satellite links.
• Memory Allocation Trade-offs: Dynamic memory allocation strategies show varied efficiency improvements depending on the instantaneous state of the network, which are crucial for real-time entanglement swapping between nodes.
• Entanglement Rate Constraints: Through analytical modeling, the paper delineates the rate limitations induced by classical communication latency, a critical bottleneck rarely addressed in quantum network literature.
• Validation Through Simulation: Cross-validation with simulation shows reasonable agreement with theoretical models, providing confidence in the scalability and robustness of the proposed scheduling techniques across different network scenarios.

Future Directions

The study suggests further exploration into dynamic scheduling algorithms that can handle quantum network traffic across continuously varying orbital paths. Possible extensions include integrating multipartite entanglement distribution and exploring dynamic scheduling over continuously fluctuating network parameters, which are vital for future quantum internet applications.

Conclusion

The presented framework offers a novel integration of classical network science principles with quantum network design, emphasizing the scheduling complexities pertinent to hybrid fiber and satellite systems. The results indicate promising advancements in quantum network performance metrics, paving the way for more efficient designs of real-world quantum communication systems that can manage high-demand applications and global connectivity challenges.