Quantum Consensus Algorithms: A Brief Survey and Characterization

Abstract

This paper presents a control-theoretic survey of four representative quantum consensus algorithms, with a focus on their convergence properties and implementation feasibility. The selected algorithms - ranging from gossip-based method to measurement-based feedback method and geometric control methods - exhibit fundamentally different convergence targets, including symmetric state consensus and directional alignment of Bloch vectors. Each approach is analyzed in terms of its dynamical structure, physical requirements, and control complexity. To show their performance, numerical simulations are conducted on a 3-qubit network under a fully connected topology. The results imply the trade-offs between convergence strength, coherence preservation, and practical implementability, offering insights for the design of distributed control protocols in quantum networks. © 2025 The Authors. This is an open access article under the CC BY-NC-ND license.