QUANTUM QUEUEING THEORY: MODELING AND ANALYSIS OF QUANTUM COMPUTING-BASED SERVICE SYSTEMS: A RESEARCH ROADMAP

Abstract

The convergence of quantum computing and classical service system modeling presents a transformative opportunity. This paper proposes the formalization of Quantum Queueing Theory (QQT), a novel framework for modeling, analyzing, and optimizing service systems where quantum processors act as servers, quantum algorithms constitute service tasks, and quantum communication channels facilitate arrivals and departures. We outline the fundamental challenges posed by quantum mechanics (superposition, entanglement, measurement, decoherence) to classical queueing paradigms. Key research directions include defining quantum analogues of arrival processes, service disciplines, and performance metrics (quantum fidelity, task success probability, decoherence-limited waiting time). We explore modeling approaches leveraging quantum stochastic processes, quantum walks, and modified Lindblad master equations. The paper details critical areas for future research: hybrid quantum-classical queueing networks, resource allocation under decoherence, stability analysis in the quantum regime, and the development of quantum-aware scheduling policies. QQT is poised to become essential for designing efficient and scalable quantum computing data centers, quantum cloud services, and integrated quantum-classical computing infrastructures.