[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118388-en":3,"doc-seo-118388-105":30,"detail-sidebar-cat-0-en-105":91},{"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":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},118388,1099514067415,"Rowan","https://ap-avatar.wpscdn.com/avatar/100002539d78ffe74a7?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779092875211072502",8,"Research & Report","Quantum machine learning - Bachelor thesis","Quantum computing remains largely unused in real-world applications, yet studying it is essential for understanding core quantum concepts and expanding knowledge of what quantum systems can enable. This bachelor thesis compares quantum machine learning approaches with classical kernel methods, focusing on how to design quantum kernels that are difficult to simulate on classical computers. Proposed methodologies are evaluated on real datasets, producing only limited and somewhat disappointing outcomes.","Czech Technical University in Prague  \nF3  \nFaculty of Electrical Engineering Department of Control Engineering  \nQuantum machine learning  \nBc. Jan Svoboda  \nSupervisor: Mgr. Jakub Mareček Ph.D.  \nSupervisor–specialist: Ing. Aleš Wodecki Ph.D. Field of study: Cybernetics and robotics May 2024  \nctuthesis t1606152353 ii  \nAcknowledgements  \nI would like to thank everyone who stood by my side throughout this amazing part of my life, the last chapter of which is this thesis.  \nDeclaration  \nI declare that the presented work is solely mine and that I cited all the literature used.  \nIn Prague, 24 . May 2024  \niii ctuthesis t1606152353  \nAbstract  \nAlthough quantum computing is still not yet used in the real world, it is important to study it in order to understand the concepts of quantum computing and to expand our knowledge of the possibilities of quantum computing. This paper compares quantum machine learning methods with kernel methods, as the two have much in common. It is our intention to devise a methodology for the generation of quantum kernels in such a way that they may be challenging to simulate using classical computer systems. The aforementioned methodologies are subsequently tested on real data sets, with somewhat disappointing results.  \nKeywords: quantum computing, quantum kernels, kernel target alignment, kernel methods  \nSupervisor: Mgr. Jakub Mareček Ph.D.Ústav X,  \nUliční 5, Praha 99  \nAbstrakt  \nKlíčová slova: slovo, klíč  \nPřeklad názvu: Moje bakalářka se strašně, ale hrozně dlouhým předlouhýmnázvem—Cesta do tajů kdovíčeho  \nctuthesis t1606152353 iv  \nContents  \n1 Introduction 1  \n2 Quantum kernels 3  \n2.1 Reproducing kernel Hilbert spaces 5  \n2.2 Spectral decomposition ......... 5  \n2.2.1 Kernel classifier ............. 6  \n3 Quantum kernel methods  \nproperties 7  \n3.1 Kernel target alignment ........ 8  \n3.2 Asymmetric geometric difference . 8  \n3.3 Speed-up using quantum kernels . 9  \n4 Hardness of random circuits 11  \n4.1 Circuit architecture ........... 11  \n4.2 Worst case and average case circuits ........................ 12  \n4.3 Haar random circuit distribution 12  \n4.3.1 Cayley transformation and Cayley path .................. 13  \n4.3.2 Theorems ................. 14  \n5 Main concept 15  \n6 Embeddings 17  \n6.1 Basis embedding .............. 17  \n6.2 Amplitude embedding ......... 18  \n6.3 Rotation embedding .......... 18  \n6.4 Pauli feature map ............. 19  \n6.5 ZZ-feature map ............... 19  \n6.6 Repeated embedding .......... 20  \n7 Experiments 21  \n7.1 Random unitaries ............. 21  \n7.2 Algorithm ................... 22  \n7.3 Ad hoc data experiment ....... 23  \n7.3.1 ZZ feature mapping ........ 24  \n7.3.2 XY feature mapping ........ 24  \n7.3.3 Rotational embedding ...... 25  \n7.3.4 Amplitude embedding ...... 25  \n7.4 MNIST data experiment ....... 26  \nv ctuthesis t1606152353  \n8 Discussion 29  \n9 Conclusion 31  \nA Bibliography 33  \nB Project Specification 35  \nctuthesis t1606152353 vi  \nFigures  \n4.1 Circut architecture A blueprint . 12  \n4.2 Cayley path .................. 13  \n6.1 Pauli Y feature map .......... 19  \n6.2 Pauli Z feature map ........... 20  \n6.3 ZZ-feature map ............... 20  \n7.1 Example of data from ad hoc dataset ........................ 24  \nTables  \nvii ctuthesis t1606152353  \nctuthesis t1606152353  \nChapter 1  \nIntroduction  \nIn recent years, quantum computing has gained more and more scientific focus, lending itself to being the revolutionizer across various artificial intelligence fields, including machine learning. While machine learning is obviously one of the growing fields of artificial intelligence, it is not disregarded by quantum computing with much-desired properties, with exponential speedup being oneof them. Exponential speedup using quantum computation is the result of quantum phenomena called entanglement and superposition. These enable us to perform computations exponentially faster than classical computers. This may accelerate not only the train","cbCaimZmEX7tTVCF","https://ap.wps.com/l/cbCaimZmEX7tTVCF","pdf",881207,1,44,"English","en",105,"# Introduction\n# Quantum kernels\n## Reproducing kernel Hilbert spaces\n## Spectral decomposition\n## Kernel classifier\n# Quantum kernel methods\n## Kernel target alignment\n## Asymmetric geometric difference\n## Speed-up using quantum kernels\n# Hardness of random circuits\n## Circuit architecture\n## Worst case and average case circuits\n## Haar random circuit distribution","[{\"question\":\"Why study quantum computing if it is not widely used in practice yet?\",\"answer\":\"It helps develop understanding of quantum computing concepts and expands knowledge of the potential capabilities of quantum computing systems.\"},{\"question\":\"What is the main goal of the methodology in this thesis?\",\"answer\":\"To devise a way to generate quantum kernels that are challenging to simulate using classical computer systems.\"},{\"question\":\"How were the proposed quantum-kernel methodologies evaluated?\",\"answer\":\"They were tested on real data sets through experiments, which resulted in somewhat disappointing findings.\"}]","Quantum machine learning - Bachelor thesis | PDF",1785683395,111,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"quantum-machine-learning-bachelor-thesis","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/quantum-machine-learning-bachelor-thesis/118388/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-02",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why study quantum computing if it is not widely used in practice yet?","Question",{"text":75,"@type":76},"It helps develop understanding of quantum computing concepts and expands knowledge of the potential capabilities of quantum computing systems.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the main goal of the methodology in this thesis?",{"text":80,"@type":76},"To devise a way to generate quantum kernels that are challenging to simulate using classical computer systems.",{"name":82,"@type":73,"acceptedAnswer":83},"How were the proposed quantum-kernel methodologies evaluated?",{"text":84,"@type":76},"They were tested on real data sets through experiments, which resulted in somewhat disappointing findings.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]