Article(id=1242140670022983873, tenantId=1146029695717560320, journalId=1146031591421210625, issueId=1242140662385156262, articleNumber=null, orderNo=7, doi=10.3981/j.issn.1000-7857.2023.19.005, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1646236800000, receivedDateStr=2022-03-03, revisedDate=1653580800000, revisedDateStr=2022-05-27, acceptedDate=null, acceptedDateStr=null, onlineDate=1698393547290, onlineDateStr=2023-10-27, pubDate=1697126400000, pubDateStr=2023-10-13, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1698393547290, onlineIssueDateStr=2023-10-27, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774079013588, creator=sys-migrate, updateTime=1774079013588, updator=sys-migrate, issue=Issue{id=1242140662385156262, tenantId=1146029695717560320, journalId=1146031591421210625, year='2023', volume='41', issue='19', pageStart='1', pageEnd='188', issueExtLink='null', onlineDate='null', pubDate='1697126400000', pubDateStr='2023-10-13', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=3, issueType=-1, specialIssue=null, createTime=1774079011768, creator='sys-migrate', updateTime=1774079011768, updator='sys-migrate', preIssue=null, nextIssue=null, articleTotal=null, ext=null, issueFiles=null, downloadFileDto=null}, startPage=48, endPage=58, ext={EN=ArticleExt(id=1242140673420370135, articleId=1242140670022983873, tenantId=1146029695717560320, journalId=1146031591421210625, language=EN, title=Mathematical and neural networks representations of quantum states, columnId=1242140672887698205, journalTitle=Science & Technology Review, columnName=Innovation leads selfreliance and selfimprovement—creating a source of high-quality technological, runingTitle=null, highlight=null, articleAbstract=With wide application of deep learning, applications of data self-generation and probability simulation of neural network models in quantum state reconstruction and estimation have attracted people's attention. In this paper, from various mathematical representations of quantum states, we derive different representations of quantum states in neural networks. Nonlinear mapping relationships between input/output on corresponding neural network structures are deduced from the relationship between different physical variables of quantum state. This work provides a theoretical design basis of network function relationship and data generation for using different types of neural network models to realize quantum state estimation by means of their own data self-generation and probability simulation function., authors=CONG Shuang, authorsList=CONG Shuang, authorCompany=Department of Automation, University of Science and Technology of China, Hefei 230027, China, correspAuthors=null, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=q6mLjkfmPSpzbWCcU7czdQ==, pdfFileSize=1138600, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1242140672115946260, articleId=1242140670022983873, tenantId=1146029695717560320, journalId=1146031591421210625, language=CN, title=量子态的数学与神经网络表示, columnId=1242140671348388621, journalTitle=科技导报, columnName=专题：创新引领 自立自强——打造高质量科技创新策源地, runingTitle=null, highlight=null, articleAbstract=随着深度学习的广泛应用，神经网络模型的数据自生成以及概率模拟等功能在量子态重构与估计方面的应用得到人们关注。通过对量子态的各种不同的数学表示，引导到神经网络量子态的不同表示；从量子态不同物理变量之间的关系，推导出相应神经网络结构上的输入/输出之间的非线性映射关系，为采用不同类型的神经网络模型根据自身数据自生成以及概率模拟功能，实现量子态估计应用，提供网络函数关系及其数据生成的理论设计基础。, authors=丛爽, authorsList=丛爽, authorCompany=中国科学技术大学自动化系，合肥 230027, correspAuthors=null, authorNote=丛爽，教授，研究方向为先进控制策略、人工神经网络、智能控制及量子系统控制，电子信箱：scong@ustc.edu.cn, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=Lr/eBX7505llpANF8AOH2w==, pdfFileSize=1138600, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, 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