Quantum Communication Advantage for Leader Election and Agreement

Dufoulon, Fabien and Magniez, Frédéric and Pandurangan, Gopal (2025) Quantum Communication Advantage for Leader Election and Agreement. In: Proceedings of the ACM Symposium on Principles of Distributed Computing (PODC) :. ACM, New York, 230–240. ISBN 9798400718854

Abstract

This work focuses on understanding the quantum message complexity of two central problems in distributed computing, namely, leader election and agreement in synchronous message-passing communication networks. We show that quantum communication gives an advantage for both problems by presenting quantum distributed algorithms that significantly outperform their respective classical counterparts under various network topologies. While prior works have studied and analyzed quantum distributed algorithms in the context of (improving) round complexity, a key conceptual contribution of our work is positing a framework to design and analyze the message complexity of quantum distributed algorithms. We present and demonstrate how quantum algorithmic techniques, such as Grover search, quantum counting, and quantum walks, can significantly enhance the message efficiency of distributed algorithms. In particular, our leader election protocol for diameter-2 networks uses quantum walks to achieve the improved message complexity. To the best of our knowledge, this is the first such application of quantum walks in distributed computing.