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Neural network representations of quantum many-body states

Authors
  • Yang, Ying1, 2
  • Cao, HuaiXin1
  • Zhang, ZhanJun3
  • 1 Shaanxi Normal University, School of Mathematics and Information Science, Xi’an, 710119, China , Xi’an (China)
  • 2 Yuncheng University, School of Mathematics and Information Technology, Yuncheng, 044000, China , Yuncheng (China)
  • 3 Anhui University, School of Physics and Materials Science, Hefei, 230039, China , Hefei (China)
Type
Published Article
Journal
Science China Physics Mechanics and Astronomy
Publisher
Springer-Verlag
Publication Date
Jun 20, 2019
Volume
63
Issue
1
Identifiers
DOI: 10.1007/s11433-018-9407-5
Source
Springer Nature
Keywords
License
Yellow

Abstract

Machine learning is currently the most active interdisciplinary field having numerous applications; additionally, machine-learning techniques are used to research quantum many-body problems. In this study, we first propose neural network quantum states (NNQSs) with general input observables and explore a few related properties, such as the tensor product and local unitary op- eration. Second, we determine the necessary and sufficient conditions for the representability of a general graph state using normalized NNQS. Finally, to quantify the approximation degree of a given pure state, we define the best approximation degree using normalized NNQSs. Furthermore, we observe that some N-qubit states can be represented by a normalized NNQS, such as separable pure states, Bell states and GHZ states.

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