Neural network representations of quantum many-body states

作     者：Ying Yang HuaiXin Cao ZhanJun Zhang Ying Yang;HuaiXin Cao;ZhanJun Zhang

作者机构：School of Mathematics and Information ScienceShaanxi Normal UniversityXi'an 710119China School of Mathematics and Information TechnologyYuncheng UniversityYuncheng 044000China School of Physics and Materials ScienceAnhui UniversityHefei 230039China 

出 版 物：《Science China(Physics,Mechanics & Astronomy)》 (中国科学：物理学、力学、天文学（英文版）)

年 卷 期：2020年第63卷第1期

页      面：55-69页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 081104[工学-模式识别与智能系统] 08[工学] 070201[理学-理论物理] 0835[工学-软件工程] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 0702[理学-物理学] 

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.11871318,11771009,11571213,and 11601300) the Fundamental Research Funds for the Central Universities(Grant Nos.GK201703093,and GK201801011) the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2018JM1020) the Shaanxi Province Innovation Ability Support Program(Grant No.2018KJXX-054) the Subject Research Project of Yuncheng University(Grant No.XK-2018032) 

主　　题：representation neural network quantum state graph state 

摘      要：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.