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neural network representations of quantum many-body states

Science China(Physics,Mechanics & Astronomy) 2020年第1期63卷 55-69页

作者： Ying Yang HuaiXin Cao ZhanJun Zhang School of Mathematics and Information Science Shaanxi Normal UniversityXi'an 710119China School of Mathematics and Information Technology Yuncheng UniversityYuncheng 044000China School of Physics and Materials Science Anhui UniversityHefei 230039China

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 operation. 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.

关键词： representation neural network quantum state graph state

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Representations of hypergraph states with neural networks

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Communications in Theoretical Physics 2021年第10期73卷 97-106页

作者： Ying Yang Huaixin Cao School of Mathematics and Information Technology Yuncheng UniversityYuncheng 044000China School of Mathematics and Statistics Shaanxi Normal UniversityXi'an 710119China

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. ***. Astron. 63(2020) 210312].

关键词： hypergraph state neural network quantum state representation

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Representations of Graph states with neural networks

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Acta Mathematica Sinica,English Series 2023年第4期39卷 685-694页

作者： Ying YANG School of Mathematics and Information Technology Yuncheng UniversityYuncheng 044000P.R.China

quantum many-body problem(QMBP)has become a hot topic in high energy physics and condensed matter *** the exponential increasing of the dimension of the Hilbert space,it becomes a big challenge to solve the QMBP even with the most powerful *** the rapid development of machine learning,artificial neural networks provide a powerful tool to represent or approximate quantum many-body *** this paper,we aim to construct explicitly the neural network representations of graph states,without stochastic optimization of the network *** method shows constructively that all graph states can be represented precisely by proper neural networks originated from[Science,355,602(2017)]and formulated in[***.,63,210312(2020)].

关键词： Graph state neural network quantum state representation

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