With wide application of deep learning, applications of data self-generation and probability simulation of neural network models in quantum state reconstruction and estimation have attracted people's attention. In this paper, from various mathematical representations of quantum states, we derive different representations of quantum states in neural networks. Nonlinear mapping relationships between input/output on corresponding neural network structures are deduced from the relationship between different physical variables of quantum state. This work provides a theoretical design basis of network function relationship and data generation for using different types of neural network models to realize quantum state estimation by means of their own data self-generation and probability simulation function.

quantum state  /  neural network representation  /  probabilistic simulation  /  density matrix reconstruction