Consensus and synchronisation of quantum networks
With recent development in quantum physics and information technology, quantum network systems have yielded significant potential of applications. Consensus and synchronisation in a quantum network have a close connection to distributed quantum computation, quantum communication and quantum random walks.
In this research, we proposed a master equation based approach to drive a quantum network with n qubits to a consensus state. We established a graphical method that bridges the proposed quantum consensus scheme and classical consensus dynamics. A fundamental connection was shown that quantum consensus over the quantum graph is equivalent to component wise classical consensus over the induced graph. Necessary and sufficient conditions for exponential and asymptotic quantum consensus are obtained, respectively, for switching quantum interaction graphs. As a quantum analogue of classical synchronization of coupled oscillators, quantum synchronization conditions were presented, in which the reduced states of all qubits tend to a common trajectory.