This paper presents the servo controller design of using a quantum neural network and investigates its characteristics for control systems. A multi-layer quantum neural network that uses qubit neurons as an information processing unit is used to design three types of neural network-based servo controller: the direct controller, the parallel controller and the self-tuning controller. Computational experiments to control the nonlinear discrete-time plant are conducted in order to evaluate the learning performance and the capability of the quantum neural controller. The results of the computational experiments confirm both the feasibility and effectiveness of the quantum neural controllers.