This article proposes a model of a quantum neural network based on a multilevel activation function, which has high performance. This performance is achieved by combining such unique components as: the quantum weight vector, quantum activity values and the dot product operator. In addition, algorithms for learning weight parameters and quantum intervals are presented, in particular, the Levenberg-Marquardt algorithm is improved to improve the quality of the error back propagation method in the process of learning weight parameters, which will also reduce the likelihood of quantum errors.