{"title":"Interpolation of positive matrices by quantum-inspired optimal control","authors":"Chen Jiang, Yu Pan, Yi Yang, Daoyi Dong","doi":"10.1049/cth2.12625","DOIUrl":null,"url":null,"abstract":"<p>Interpolation of probability distributions can be formulated as an optimal transport problem. Positive matrix, which can be viewed as the generalization of probability distribution to higher dimension, is used in quantum theory to describe the state of a quantum system. Here, a quantum-inspired method for the interpolation of positive matrices is proposed. Particularly, this method employs the quantum state purification of the positive matrices in an extended space. Since pure state controllability can be easily achieved using open-loop coherent control, the continuous interpolation of positive matrices is given as a completely positive map induced by simulating the optimal control for pure state transfer. The quantum-inspired interpolation is shape-preserving with applications to tensor field processing.</p>","PeriodicalId":50382,"journal":{"name":"IET Control Theory and Applications","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1049/cth2.12625","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IET Control Theory and Applications","FirstCategoryId":"94","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1049/cth2.12625","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
Interpolation of probability distributions can be formulated as an optimal transport problem. Positive matrix, which can be viewed as the generalization of probability distribution to higher dimension, is used in quantum theory to describe the state of a quantum system. Here, a quantum-inspired method for the interpolation of positive matrices is proposed. Particularly, this method employs the quantum state purification of the positive matrices in an extended space. Since pure state controllability can be easily achieved using open-loop coherent control, the continuous interpolation of positive matrices is given as a completely positive map induced by simulating the optimal control for pure state transfer. The quantum-inspired interpolation is shape-preserving with applications to tensor field processing.
期刊介绍：
IET Control Theory & Applications is devoted to control systems in the broadest sense, covering new theoretical results and the applications of new and established control methods. Among the topics of interest are system modelling, identification and simulation, the analysis and design of control systems (including computer-aided design), and practical implementation. The scope encompasses technological, economic, physiological (biomedical) and other systems, including man-machine interfaces.
Most of the papers published deal with original work from industrial and government laboratories and universities, but subject reviews and tutorial expositions of current methods are welcomed. Correspondence discussing published papers is also welcomed.
Applications papers need not necessarily involve new theory. Papers which describe new realisations of established methods, or control techniques applied in a novel situation, or practical studies which compare various designs, would be of interest. Of particular value are theoretical papers which discuss the applicability of new work or applications which engender new theoretical applications.
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