Index-Based Scheduling for a Resource-Constrained Quantum Switch

TL;DR

This paper introduces index-based scheduling policies for a resource-limited quantum switch, optimizing entanglement request handling using a novel age metric and Whittle index within a restless bandit framework.

Contribution

It formulates the quantum switch scheduling as a restless bandit problem, derives a closed-form Whittle index, and proposes efficient greedy policies for resource management.

Findings

Scheduling policies improve request throughput.

Whittle index is indexable and has a closed-form expression.

Greedy policies offer low-complexity solutions.

Abstract

We consider a quantum switch with a finite number of quantum memory registers that aims to serve multipartite entanglement requests among $N$ users. We propose scheduling policies that aim to optimize the average number of requests served per unit time by efficiently utilizing the switch's available memory. To measure the performance of the scheduling policies, we employ the newly introduced metric of age of entanglement establishment (AoEE). We formulate the scheduling problem in a restless multi-armed bandit (RMAB) framework. We show that the scheduling of entanglement requests is indexable. Subsequently, we find a closed-form expression of the Whittle index for all possible request-age pairs. By modeling the Whittle index of each request as its reward and its cardinality as its cost, we formulate the memory-constrained scheduling problem as a $0$-$1$ knapsack problem and solve it via dynamic programming. Furthermore, we consider two low-complexity sequential greedy policies that leverage two different modified Whittle indices.