Quantum-behaved PSO-based Lyapunov control of closed quantum systems

A Lyapunov-based control scheme is presented to drive closed quantum systems into any target eigenstate with as high population as possible by the quantum-behaved particle swarm optimization (PSO) algorithm. Based on a Lyapunov function with a Hermitian operator to be constructed, a control law with the unknown parameters contained in the Hermitian operator is designed. To achieve high-population state transfer to the target state, we first initialize those unknown parameters by choosing a path to the target state in its energy-level connectivity graph and setting their values along the path. Then, a set of optimal parameters is found by the quantum-behaved PSO algorithm. Finally, numerical simulation experiments are performed on a five-level quantum system and a four-qubit system to demonstrate the effectiveness of the control scheme in this paper.