Quantum Communication Advantage for Leader Election and Agreement

2025-02-11

AI Summary

This paper investigates the quantum message complexity of leader election and consensus in synchronous message-passing networks. To address the high message overhead of classical algorithms, it introduces the first analytical framework for quantum distributed algorithms, pioneering the integration of quantum walks, Grover search, and quantum counting into distributed leader election. For networks of diameter two, the proposed protocol achieves sublinear message complexity—strictly outperforming the optimal classical algorithms. Key contributions are: (1) establishing a rigorous theoretical framework for analyzing message complexity in quantum distributed algorithms; (2) the first application of quantum walks to leader election; and (3) the first formal proof that quantum communication enables a substantial improvement in message efficiency for consensus-type tasks, thereby laying foundational theoretical groundwork for quantum distributed computing.

Technology Category

• Search and Optimization: Distributed Search
• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Blockchains and distributed ledgers
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Quantum message complexity in distributed computing
• Quantum advantage in leader election and agreement
• Quantum walks enhance message-efficient algorithms

Innovation

• Quantum communication reduces message complexity
• Quantum walks enhance leader election efficiency
• Grover search optimizes distributed algorithms