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Digraph states and their neural network representations |
| Ying Yang(杨莹)1 and Huaixin Cao(曹怀信)2,† |
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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Received: 11 August 2021
Revised: 01 December 2021
Accepted manuscript online: 05 December 2021
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PACS:
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03.67.-a
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(Quantum information)
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03.65.-w
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(Quantum mechanics)
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03.65.Aa
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(Quantum systems with finite Hilbert space)
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03.65.Wj
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(State reconstruction, quantum tomography)
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| Fund: This work was supported by the National Natural Science Foundation of China (Grant Nos. 12001480 and 11871318), the Applied Basic Research Program of Shanxi Province (Grant Nos. 201901D211461 and 201901D211462), the Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi (Grant No. 2020L0554), the Excellent Doctoral Research Project of Shanxi Province (Grant No. QZX-2020001), and the PhD Start-up Project of Yuncheng University (Grant No. YQ-2019021). |
Corresponding Authors:
Huaixin Cao
E-mail: caohx@snnu.edu.cn
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Cite this article:
Ying Yang(杨莹) and Huaixin Cao(曹怀信) Digraph states and their neural network representations 2022 Chin. Phys. B 31 060303
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