IFAC-PapersOnLine

Quantum Consensus Algorithms: A Brief Survey and Characterization

Hyungseop Yu, Hyo‐Sung Ahn, Kwang‐Kyo Oh

Published Jan 1, 2025• 0 citations

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.

DOI: 10.1016/j.ifacol.2025.11.585

Related papers

Consensus for Quantum Networks: Symmetry From Gossip Interactions

Luca Mazzarella, Alain Sarlette, Francesco Ticozzi

Abstract—This paper extends the consensus framework, widely studied in the literature on distributed computing and control algorithms, to networks of quantum systems. We define consensus situations on the basis of invariance and symmetry properties, finding four different generalizations of classical consensus states. This new viewpoint can be directly used to study consensus for probability distributions, as these can be seen as a particular case of quantum statistical states: in this light, our analysis is also relevant for classical problems. We then extend the gossip consen-sus algorithm to the quantum setting and prove it converges to symmetric states while preserving the expectation of permutation-invariant global observables. Applications of the framework and the algorithms to estimation and control problems on quantum networks are discussed. Index Terms—Consensus, distributed algorithms, Markov pro-cesses, quantum information and control. I.

Dec 3, 201558 citations

Consensus for Quantum Networks: Symmetry From Gossip Interactions

Luca Mazzarella, Alain Sarlette, Francesco Ticozzi

This paper extends the consensus framework, widely studied in the literature on distributed computing and control algorithms, to networks of quantum systems. We define consensus situations on the basis of invariance and symmetry properties, finding four different generalizations of classical consensus states. This new viewpoint can be directly used to study consensus for probability distributions, as these can be seen as a particular case of quantum statistical states: in this light, our analysis is also relevant for classical problems. We then extend the gossip consensus algorithm to the quantum setting and prove it converges to symmetric states while preserving the expectation of permutation-invariant global observables. Applications of the framework and the algorithms to estimation and control problems on quantum networks are discussed.

arXiv:1303.4077IEEE Transactions on Automatic ControlSep 25, 201454 citations

A new perspective on gossip iterations: From Symmetrization to quantum consensus

Luca Mazzarella, Alain Sarlette, Francesco Ticozzi

This paper extends the gossip algorithm, widely studied in the literature on distributed computing and control algorithms, to networks of quantum systems. In doing so, we reinterpret the classical algorithm and the average consensus task as a symmetrization problem with respect to the action of the permutation group. This allows us to extend in a natural way the gossip consensus algorithm to the quantum setting and prove its convergence properties to symmetric states while preserving the expectation of permutation-invariant global observables.

IEEE Conference on Decision and Control (CDC)Dec 1, 20136 citations

Continuous time quantum consensus & quantum synchronisation

Saber Jafarizadeh

Distributed consensus algorithm over networks of quantum systems has been the focus of recent studies in the context of quantum computing and distributed control. Most of the progress in this category have been on the convergence conditions and optimizing the convergence rate of the algorithm, for quantum networks with undirected underlying topology. This paper aims to address the extension of this problem over quantum networks with directed underlying graphs. In doing so, the convergence to two different stable states namely, consensus and synchronous states have been studied. Based on the intertwining relation between the eigenvalues, it is shown that for determining the convergence rate to the consensus state, all induced graphs should be considered while for the synchronous state only the underlying graph suffices. Furthermore, it is illustrated that for the range of weights that the Aldouss conjecture holds true, the convergence rate to both states are equal. Using the Pareto region for convergence rates of the algorithm, the global and Pareto optimal points for several topologies have been provided.

arXiv:1605.06976Australian Control ConferenceNov 1, 20163 citations

Distributed Partial Quantum Consensus of Qubit Networks With Connected Topologies

Xin Jin, Zhu Cao, Yang Shan Tang +1 more

In this article, we consider the partial quantum consensus problem of a qubit network in a distributed view. The local quantum operation is designed based on the Hamiltonian by using the local information of each quantum system in a network of qubits. We construct the unitary transformation for each quantum system to achieve the partial quantum consensus, that is, the directions of the quantum states in the Bloch ball will reach an agreement. A simple case of two-qubit quantum systems is considered first, and a minimum completing time of reaching partial consensus is obtained based on the geometric configuration of each qubit. Furthermore, we extend the approaches to deal with the more general N -qubit networks. Two partial quantum consensus protocols, based on the Lyapunov method for chain graphs and the geometry method for connected graphs, are proposed. The geometry method can be utilized to deal with more general connected graphs, while for the Lyapunov method, the global consensus can be obtained. The numerical simulation over a qubit network is demonstrated to verify the validity and the effectiveness of the theoretical results.

arXiv:2402.14256IEEE Transactions on CyberneticsFeb 19, 20247 citations

Distributed Consensus with Quantum-Inspired Measurement

Jincheng Zhang

This paper investigates the application of quantum-inspired measurement techniques to enhance distributed consensus algorithms. Traditional distributed consensus protocols often suffer from slow convergence rates and vulnerability to network disruptions. We propose a novel approach that leverages principles of quantum measurement—specifically, the concept of superposition and selective observation—to improve consensus performance. Our method involves a probabilistic sampling strategy where nodes selectively measure the state of their neighbors, guided by a carefully designed measurement operator. This reduces redundant communication, accelerates convergence, and increases robustness against malicious or faulty nodes. We formally define the consensus protocol, provide a mathematical analysis of its convergence properties, and demonstrate, through theoretical arguments, the potential for significant improvements in key metrics such as convergence time and fault tolerance. The core contribution lies in translating quantum-inspired ideas into a practical distributed consensus framework, offering a path toward more efficient and reliable distributed systems.

Sep 6, 20260 citations