Consensus for Quantum Networks: From Symmetry to Gossip Iterations

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 probabilistic generalizations of classical consensus states. We then extend the gossip consensus algorithm to the quantum setting and prove its convergence properties, showing how it converges to symmetric states while preserving the expectation of permutation-invariant global observables.

14 pages, 2 figures

References in corpus (3)

• An Open-System Quantum Simulator with Trapped Ions
• Modeling and Control of Quantum Systems: An Introduction
• Stabilizing Entangled States with Quasi-Local Quantum Dynamical Semigroups

Cited by in corpus (7)

• Learning-based Quantum Robust Control: Algorithm, Applications and Experiments
• Reaching a Quantum Consensus: Master Equations that Generate Symmetrization and Synchronization
• Finite-time Convergent Gossiping
• Symmetrizing quantum dynamics beyond gossip-type algorithms
• Distributed Partial Quantum Consensus of Qubit Networks with Connected Topologies
• Quantum coherent and measurement feedback control based on atoms coupled with a semi-infinite waveguide
• Topology identification of autonomous quantum dynamical networks