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The subject of the paper is Quantum Neural Network. On one hand, introducing quantum theory into the structure or training process of Classical Neural Network with regard to improving structure and capacity of Classical Neural Network, enhancing learning and generalization ability of it. On the other hand, establishing a new topological structure and training algorithm of Quantum Neural Network by the means of quoting the thought, concept and principles of quantum theory directly. In the paper, we summarize the basic model and learning algorithm of quantum neuron, propose the model and learning algorithm of Quantum Adaptive Resonance Theory Neural Network through introducing quantum computing into adaptive resonance theory, apply which in pattern recognition as well. In summary, Quantum Adaptive Resonance Theory Neural Network have an advantage over Classical Adaptive Resonance Theory Neural Network in the positive rate of clustering.