Index-Based Scheduling for a Resource-Constrained Quantum Switch

2026-03-24

AI Summary

This work addresses the scheduling of multi-user entanglement requests under quantum memory constraints by modeling it as a Restless Multi-Armed Bandit (RMAB) problem with resource constraints. The study establishes, for the first time, the indexability of this problem and derives a closed-form Whittle index in terms of request–age pairs. Building on this analytical result, two enhanced greedy algorithms based on the Whittle index are proposed, which efficiently reduce the scheduling decision to a 0–1 knapsack problem. To better capture service timeliness, a novel performance metric termed Age of Entanglement Experience (AoEE) is introduced, grounded in an “age entropy” formulation. Experimental evaluations demonstrate that the proposed methods significantly increase the number of served requests per unit time while maintaining low computational complexity, thereby enabling efficient and scalable quantum switch scheduling.

Technology Category

• Machine Learning: Quantum Machine Learning
• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• quantum switch
• entanglement scheduling
• resource-constrained
• age of entanglement establishment
• multipartite entanglement

Innovation

• Whittle index
• quantum switch
• entanglement scheduling
• restless multi-armed bandit
• age of entanglement establishment