Representations of Graph States with Neural Networks

Quantum many-body problem(QMBP)has become a hot topic in high energy physics and condensed matter physics.With the exponential increasing of the dimension of the Hilbert space,it becomes a big challenge to solve the QMBP even with the most powerful computers.With the rapid development of machine learning,artificial neural networks provide a powerful tool to represent or approximate quantum many-body states.In this paper,we aim to construct explicitly the neural network representations of graph states,without stochastic optimization of the network parameters.Our method shows constructively that all graph states can be represented precisely by proper neu-ral networks originated from[Science,355,602(2017)]and formulated in[Sci.China-Phys.Mech.Astron.,63,210312(2020)].