[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125991-en":3,"doc-seo-125991-105":31,"detail-sidebar-cat-0-en-105":92},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},125991,687207024643,"Oliver","https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2",8,"Research & Report","Variational quantum state discriminator for supervised machine learning","Quantum state discrimination (QSD) is a core task in quantum information processing, enabling minimum-error identification of quantum states for multiple applications. This paper introduces a variational quantum algorithm, the variational quantum state discriminator (VQSD), which trains a parameterized quantum circuit by minimizing a QSD-derived cost function to obtain the optimal POVM. The method can discriminate even unknown states and avoids costly state tomography. Numerical simulations and comparisons with semidefinite programming validate effectiveness for both pure and mixed states, and it also supports supervised multi-class classification. Using the Iris flower dataset, the receiver operating characteristic curve area under the curve averages around 0.985, indicating strong performance.","arXiv :2303 .03588v1 [ quant-ph] 7 Mar 2023  \nVariational quantum state discriminator for supervised machine learning  \nDongkeun Lee, 1 Kyunghyun Baek,2 Joonsuk Huh, 1, 3, 4, 􀀃 and Daniel K. Park5, 6, y  \n1 Department of Chemistry, Sungkyunkwan University, Suwon, 16419, Republic of Korea  \n2 Electronics and Telecommunications Research Institute, Daejeon, 34129, Republic of Korea  \n3 Sungkyunkwan University Advanced Institute of Nanotechnology, Suwon, 16419, Republic of Korea  \n4 Institute of Quantum Biophysics, Sungkyunkwan University, Suwon, 16419, Republic of Korea  \n5 Department of Applied Statistics, Yonsei University, Seoul, 03722, Republic of Korea  \n6 Department of Statistics and Data Science, Yonsei University, Seoul, 03722, Republic of Korea  \nQuantum state discrimination (QSD) is a fundamental task in quantum information processing with numerous applications. We present a variational quantum algorithm that performs the minimum-error QSD, called the variational quantum state discriminator (VQSD) . The VQSD uses a parameterized quantum circuit that is trained by minimizing a cost function derived from the QSD, and 􀀌nds the optimal positive-operator valued measure (POVM) for distinguishing target quantum states. The VQSD is capable of discriminating even unknown states, eliminating the need for expensive quantum state tomography. Our numerical simulations and comparisons with semide􀀌nite programming demonstrate the e􀀋ectiveness of the VQSD in 􀀌nding optimal POVMs for minimum-error QSD of both pure and mixed states. In addition, the VQSD can be utilized asa supervised machine learning algorithm for multi-class classi􀀌cation. The area under the receiver operating characteristic curve obtained in numerical simulations with the Iris 􀀍ower dataset ranges from 0.97 to 1 with an average of 0.985, demonstrating excellent performance of the VQSD classi􀀌er.  \nI. INTRODUCTION  \nQuantum measurement theory plays a crucial role in quantum information processing (QIP), driving advancements in communication, computation, and sensing [1{4] . The theory states that non-orthogonal quantum states can be distinguished with non-zero probability through quantum measurement, which can generally be described by Positive Operator-Valued Measures (POVMs) [5, 6] . This arises from the geometric structure of quantum states de􀀌ned on a Hilbert space and the measurement postulate of quantum mechanics. Quantum state discrimination (QSD) is a well-established 􀀌eld that provides a theoretical ground for the distinguishability of quantum states and the retrieval of classical information. Notably, the optimal strategy for distinguishing two quantum states was proposed even prior to the advent of quantum computing [7] .  \nThe ability to distinguish non-orthogonal states o􀀋ers exciting prospects for data science and machine learning as an arbitrary number of data can be encoded in a single qubit. There is no classical analog to this since a classical bit can only represent two orthogonal states. As a result, the concept of QSD has emerged in various contexts within machine learning. One area of research focuses on utilizing QSD for classical-quantum hybrid machine learning. For instance, the optimal measurement theory for two-element POVMs has been applied to determine the best quantum feature map for binary classi􀀌 -cation tasks [8] and to learn a quantum circuit for quantum data classi􀀌cation with a limited set of two-qubit states [9, 10] . Several quantum-inspired algorithms [11]  \n􀀃 [joonsukhuh@gmail.com](joonsukhuh@gmail.com)[y](y dkd.park@yonsei.ac.kr)[ dkd.park@yonsei.ac.kr](y dkd.park@yonsei.ac.kr)  \nbased on the theory of QSD for constructing classi􀀌ers have also been reported [12{14] . However, 􀀌nding the optimal measurement for QSD using a classical computer becomes computationally intractable for a large number of qubits, as it necessitates complete information about the states, often obtained through quantum state tomography. In addition, the t","cbCaiapXFzljAgAF","https://ap.wps.com/l/cbCaiapXFzljAgAF","pdf",1148071,3,1,12,"English","en",105,"# Introduction\n## Background and problem motivation\n## Proposed variational quantum state discriminator (VQSD)\n## Paper organization","[{\"question\":\"What problem does the variational quantum state discriminator (VQSD) address?\",\"answer\":\"VQSD addresses minimum-error quantum state discrimination by learning an optimal measurement (POVM) for distinguishing target quantum states.\"},{\"question\":\"How does VQSD find the optimal POVM?\",\"answer\":\"It trains a parameterized quantum circuit by minimizing a cost function derived from the QSD framework, yielding the optimal POVM for minimum-error discrimination.\"},{\"question\":\"How is VQSD used for supervised machine learning?\",\"answer\":\"VQSD can act as a supervised multi-class classifier, leveraging learned measurement outcomes to build decision structure within the Hilbert space.\"}]","Variational quantum state discriminator for supervised machine learning | PDF",1785902437,30,{"code":4,"msg":32,"data":33},"ok",{"site_id":25,"language":24,"slug":34,"title":13,"keywords":35,"description":14,"schema_data":36,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":29},"variational-quantum-state-discriminator-for-supervised-machine-learning","",{"@graph":37,"@context":86},[38,54,69],{"@type":39,"itemListElement":40},"BreadcrumbList",[41,45,49,51],{"item":42,"name":43,"@type":44,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":46,"name":47,"@type":44,"position":48},"https://docshare.wps.com/document/","Document",2,{"item":50,"name":12,"@type":44,"position":20},"https://docshare.wps.com/document/research-report/",{"item":52,"name":13,"@type":44,"position":53},"https://docshare.wps.com/document/variational-quantum-state-discriminator-for-supervised-machine-learning/125991/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":24,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":42,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-23","2026-08-05",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What problem does the variational quantum state discriminator (VQSD) address?","Question",{"text":76,"@type":77},"VQSD addresses minimum-error quantum state discrimination by learning an optimal measurement (POVM) for distinguishing target quantum states.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does VQSD find the optimal POVM?",{"text":81,"@type":77},"It trains a parameterized quantum circuit by minimizing a cost function derived from the QSD framework, yielding the optimal POVM for minimum-error discrimination.",{"name":83,"@type":74,"acceptedAnswer":84},"How is VQSD used for supervised machine learning?",{"text":85,"@type":77},"VQSD can act as a supervised multi-class classifier, leveraging learned measurement outcomes to build decision structure within the Hilbert space.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,121,123,128,131,135],{"id":21,"doc_module":4,"doc_module_name":47,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":48,"doc_module":4,"doc_module_name":47,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":47,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":47,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":47,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":47,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":47,"category_name":12,"show_sort_weight":30,"slug":122},"research-report",{"id":124,"doc_module":4,"doc_module_name":47,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":47,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":47,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":47,"category_name":137,"show_sort_weight":107,"slug":138},19,"General","general"]