Artificial Neural Networks (ANNs) are universal models of computation that have many applications in machine learning and AI. In the past decades, quantum computing offers fruitful approachs to process information efficiently. As an integration of ANNs and quantum computing, Quantum Neural Networks (QNNs) can provide us more powerful computing devices. The study of QNN was started since 1995. However, a precise definition of a QNN is a non-trivial open problem,

due to the incompatibility between the nonlinear dynamics of ANNs and the unitary dynamics of quantum computing. In this talk, we first give a review of earlier developments of different QNN models, then introduce our recent work in the construction of QNN.