A Linear Algebraic Framework for Dynamic Scheduling Over Memory-Equipped Quantum Networks

TL;DR

This paper introduces a linear algebraic framework for scheduling in quantum networks that leverages quantum memory and applies Lyapunov drift minimization to optimize entanglement distribution, offering scalable policies with reduced computation costs.

Contribution

It presents a novel linear algebraic approach to quantum network scheduling, integrating quantum memory and classical control techniques for efficient entanglement management.

Findings

Proposes a new scheduling framework exploiting quantum memory.

Derives policies minimizing user demand backlog.

Benchmarks show reduced computation with slight performance trade-offs.

Abstract

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.