Reaching Agreement in Quantum Hybrid Networks

TL;DR

This paper introduces a quantum hybrid network model where nodes reach consensus on qubit states using projective measurements and classical communication, proposing both centralized and distributed algorithms with proven convergence.

Contribution

It presents a novel distributed Pairwise Qubit Projection algorithm for quantum networks, ensuring consensus without centralized control.

Findings

The PQP algorithm drives qubits to consensus almost surely.

Expected qubit density operators converge to the initial average.

Centralized optimal path planning formulated as a stochastic control problem.

Abstract

We consider a basic quantum hybrid network model consisting of a number of nodes each holding a qubit, for which the aim is to drive the network to a consensus in the sense that all qubits reach a common state. Projective measurements are applied serving as control means, and the measurement results are exchanged among the nodes via classical communication channels. We show how to carry out centralized optimal path planning for this network with all-to-all classical communications, in which case the problem becomes a stochastic optimal control problem with a continuous action space. To overcome the computation and communication obstacles facing the centralized solutions, we also develop a distributed Pairwise Qubit Projection (PQP) algorithm, where pairs of nodes meet at a given time and respectively perform measurements at their geometric average. We show that the qubit states are driven to a consensus almost surely along the proposed PQP algorithm, and that the expected qubit density operators converge to the average of the network's initial values.