Digraph states and their neural network representations

doi:10.1088/1674-1056/ac401d

中国物理B ›› 2022, Vol. 31 ›› Issue (6): 60303-060303.doi: 10.1088/1674-1056/ac401d

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

收稿日期:2021-08-11 修回日期:2021-12-01 接受日期:2021-12-05 出版日期:2022-05-17 发布日期:2022-05-17
通讯作者: Huaixin Cao E-mail:caohx@snnu.edu.cn
基金资助:
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).

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

Received:2021-08-11 Revised:2021-12-01 Accepted:2021-12-05 Online:2022-05-17 Published:2022-05-17
Contact: Huaixin Cao E-mail:caohx@snnu.edu.cn
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: digraph state, neural network, quantum state, representation

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.

Key words: digraph state, neural network, quantum state, representation

中图分类号: (Quantum information)

03.67.-a

03.65.-w (Quantum mechanics) 03.65.Aa (Quantum systems with finite Hilbert space) 03.65.Wj (State reconstruction, quantum tomography)

Ying Yang(杨莹) and Huaixin Cao(曹怀信). Digraph states and their neural network representations[J]. 中国物理B, 2022, 31(6): 60303-060303.

Ying Yang(杨莹) and Huaixin Cao(曹怀信). Digraph states and their neural network representations[J]. Chin. Phys. B, 2022, 31(6): 60303-060303.

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Digraph states and their neural network representations

Digraph states and their neural network representations

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