Representations of hypergraph states with neural networks* *Supported by the National Natural Science Foundation of China (Nos. 12001480, 11871318), the Applied Basic Research Program of Shanxi Province (No. 201901D211461), the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (No. 2020L0554), the Excellent Doctoral Research Project of Shanxi Province (No. QZX-2020001), and the PhD Start-up Project of Yuncheng

Abstract

The quantum many-body problem (QMBP) has become a hot topic in high-energy physics and condensed-matter physics. With an exponential increase in the dimensions of Hilbert space, it becomes very challenging to solve the QMBP, even with the most powerful computers. With the rapid development of machine learning, artificial neural networks provide a powerful tool that can represent or approximate quantum many-body states. In this paper, we aim to explicitly construct the neural network representations of hypergraph states. We construct the neural network representations for any k-uniform hypergraph state and any hypergraph state, respectively, without stochastic optimization of the network parameters. Our method constructively shows that all hypergraph states can be represented precisely by the appropriate neural networks introduced in [Science 355 (2017) 602] and formulated in [Sci. China-Phys. Mech. Astron. 63 (2020) 210312].