Abstract: Aiming at the problems that there are many parameters in the process neural networks based on orthogonal basis expansion, it is difficult to determine the basis function expansion items and network structure, and the traditional BP algorithm is difficult to converge. A quantum shuffled frog leaping algorithm is presented based on the quantum theory and is applied to train the process neural network.The network structure, network parameters and expand the number of items are unified encoded with Bloch spherical coordinates of qubits. The three optimal solution is updated by this method which the rotation is realized through along the spherical surface after minor path between two points. The mutation of individuals is completed with Hadamard gates, and then the search range of solution space is effectively extended. The effectiveness of the algorithm was proved by pumping unit fault diagnosis and network traffic prediction.