This paper investigates a quantum neural network and discusses its application to control systems. A learning-type neural control system that uses a multi-layer quantum neural network having qubit neurons as its information processing unit is proposed. A conjugate gradient algorithm is applied instead of the back-propagation algorithm for the supervised training of the multi-layer quantum neural network in order to improve learning performance. To evaluate the capability of the learning-type quantum neural control system, computational experiments are conducted for controlling a nonholonomic system - in this study a two-wheeled robot. Simulation results confirm both feasibility and robustness of the learning-type quantum neural control system.