Digraph states and their neural network representations |
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Institution: | 1.School of Mathematics and Information Technology, Yuncheng University, Yuncheng 044000, China;2.School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, China |
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Abstract: | With the rapid development of machine learning, artificial neural networks provide a powerful tool to represent or approximate many-body quantum states. It was proved that every graph state can be generated by a neural network. Here, we introduce digraph states and explore their neural network representations (NNRs). Based on some discussions about digraph states and neural network quantum states (NNQSs), we construct explicitly an NNR for any digraph state, implying every digraph state is an NNQS. The obtained results will provide a theoretical foundation for solving the quantum many-body problem with machine learning method whenever the wave-function is known as an unknown digraph state or it can be approximated by digraph states. |
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Keywords: | digraph state neural network quantum state representation |
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