We consider a basic quantum hybrid network model consisting of a number ofnodes each holding a qubit, for which the aim is to drive the network to aconsensus in the sense that all qubits reach a common state. Projectivemeasurements are applied serving as control means, and the measurement resultsare exchanged among the nodes via classical communication channels. We show howto carry out centralized optimal path planning for this network with all-to-allclassical communications, in which case the problem becomes a stochasticoptimal control problem with a continuous action space. To overcome thecomputation and communication obstacles facing the centralized solutions, wealso develop a distributed Pairwise Qubit Projection (PQP) algorithm, wherepairs of nodes meet at a given time and respectively perform measurements attheir geometric average. We show that the qubit states are driven to aconsensus almost surely along the proposed PQP algorithm, and that the expectedqubit density operators converge to the average of the network's initialvalues.
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