Consensus for Quantum Networks: From Symmetry to Gossip Iterations

TL;DR

This paper extends classical consensus algorithms to quantum networks, defining new probabilistic consensus states and proving convergence of a quantum gossip algorithm that maintains permutation-invariant observables.

Contribution

It introduces a quantum consensus framework based on symmetry, defining probabilistic states and extending gossip algorithms with proven convergence properties.

Findings

Four probabilistic generalizations of classical consensus states

Quantum gossip algorithm converges to symmetric states

Preserves expectation of permutation-invariant observables

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.