Quantum Communication Advantage for Leader Election and Agreement

TL;DR

This paper demonstrates that quantum communication can significantly reduce message complexity in distributed leader election and agreement problems, introducing new quantum algorithms and a framework for analyzing their efficiency.

Contribution

It introduces a framework for analyzing quantum message complexity and presents novel quantum algorithms that outperform classical ones in distributed leader election and agreement.

Findings

Quantum algorithms reduce message complexity in leader election and agreement.

Quantum walks enable efficient leader election in diameter-2 networks.

First application of quantum walks in distributed computing for message efficiency.

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 show how quantum algorithmic techniques such as Grover search, quantum counting, and quantum walks can make distributed algorithms significantly message-efficient. 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.