Abstract: The approximation ability of neural networks plays an important role to the result when one uses neural networks to resolve problems. Unfortunately there is no ideal way to construct proper networks with strong approximation ability. A novel construction approach based on the multi-qubits controller-not gates is proposed for neural networks model in this paper. The proposed model consists of three layers where the hidden nodes are the quantum neurons and the output nodes are the common neurons. The quantum neuron consists of the quantum rotation gates and the multi-qubits controlled-not gates. The overall memory of input sequences is captured from information feedback of target qubit from output to input in the multi-qubits controlled-not gate. The output of quantum neuron is obtained from the controlled relationship of the multi-qubits controlled-not gate. The L-M learning algorithms are designed in detail based on the basic principles of quantum computation. The features of input sequences can be effectively obtained in two ways of breadth and depth. The experimental results of solitaire forecast show that, when the number of input nodes is close to the length of sequences, the training set recognition rate of the proposed model increases about 8% than the common neural networks, which reveals the effectiveness of the quantum computation for enhancing the approximation capability of the common neural networks.