[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122018-en":3,"doc-seo-122018-105":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},122018,2336464648322,"Aria","https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488",8,"Research & Report","Quantum Machine Learning - Quantum Kernel Methods","Quantum Kernel Methods explores how quantum kernel approaches can potentially deliver computational advantage over classical machine learning. It introduces quantum variants of feature spaces and connects them to a Quantum version of Support Vector Machines (SVM), including projected, data-dependent quantum kernels. The discussion evaluates whether quantum kernels can be validated using data from the venture capital investment process and outlines extending quantum kernels as a feature-extraction layer in convolutional neural networks (CNNs).","Quantum Machine Learning: Quantum Kernel Methods  \nSanjeev Naguleswaran, QSPectral Systems  \nIntroduction  \nQuantum algorithms based on quantum kernel methods have been investigated previously [1] . A quantum advantage is derived from the fact that it is possible to construct a family of datasets for which, only quantum processing can recognise the intrinsic labelling patterns, while for classical computers the dataset looks like noise. This is due to the algorithm leveraging inherent efficiencies in the computation of logarithms in a cyclic group. The discrete log problem.is a well-known advantage of quantum vs classical computation: where it is possible to generate all the members of the group using a single mathematical operation.  \nKernel methods are a powerful and popular technique in classical Machine Learning. The use of a quantum feature space that can only be calculated efficiently on a quantum computer potentially allows for deriving a quantum advantage [1] . In this paper, we first describe the application of such a kernel method to a Quantum version of the classical Support Vector Machine (SVM) algorithm to identify conditions under which, a quantum advantage is realised. A data-dependent projected quantum kernel was shown to provide a significant advantage over classical kernels [2] .  \nIn this paper, we use data from the Venture Capital (VC) investment process to determine the validity of using quantum kernel methods. Thus far, other than for a few notable exceptions, deciding on companies that are likely to succeed is undertaken through labour-intensive screening processes and the intuition of the investor [3][4] .  \nWe present the results of investigations and ideas pertaining to extending the use of quantum kernels as a feature extraction layer in a Convolutional Neural Network (CNN), which is a widely used architecture in deep-learning applications. In particular, we discuss,  \n• The investigation and development of quantum kernel functions that leverage quantum-enhanced feature spaces for favourable representations of real-world data; and  \n• Investigation of properties and structure of real-world data that could be leveraged to provide a quantum advantage.  \nMethod  \nMachine Learning (ML) is a component Artificial Intelligence (AI) that focuses on learning from data. It primarily addresses the interface between learning, complexity, and computation. Research in this area spans many theoretical topics as well as practical applications. ML concerns the extraction of insights from data, developing predictions to permit data-driven decision-making. Algorithms that constitute ML fall into two broad categories: Supervised and Unsupervised learning. Supervised learning is applicable when training data is available and typically most classification and regression algorithms fall within this category. Decision Trees, Neural Networks Support Vector Machines (SVM) and Bayesian networks can also be used under supervised learning. In the case of unsupervised learning clustering algorithms, such as k-means, clustering can be used to derive insights into  \nthe nature of the data. In practice, other categories such as semi-supervised learning are encountered where the boundary between algorithm types is blurred, resulting in hybrid fitfor-purpose algorithms using any of the available approaches in an appropriate manner. Machine Learning theory is also closely connected to statistical inference where a basis function is applied to combine the features of a problem to infer the response for the subset of data used for training. Further details on Machine Learning can be found in [5], [6] .  \nThe start-up picking (or identification) problem can be considered as classifying or clustering the start-ups into predefined categories. Machine Learning provides several methods with varying degrees of sophistication and complexity to achieve this classification and/or clustering objectives.  \nDecision trees are decision support tools ","cbCaivRy9sWf3aN4","https://ap.wps.com/l/cbCaivRy9sWf3aN4","pdf",306276,1,10,"English","en",105,"# Introduction\n## Quantum kernel methods and quantum advantage\n## Quantum SVM and projected quantum kernels\n## Venture capital data validation\n## Quantum kernels with CNN feature extraction\n# Method\n## Supervised vs unsupervised learning\n## Decision trees and ensemble methods\n## Support vector machines and the kernel trick\n## Extending kernels with quantum computing","[{\"question\":\"What is the main idea behind quantum kernel methods in this document?\",\"answer\":\"Quantum kernel methods use a quantum-computable feature space to capture intrinsic patterns in data efficiently on a quantum computer, potentially enabling quantum advantage over classical processing.\"},{\"question\":\"How does the paper relate quantum kernels to Support Vector Machines (SVM)?\",\"answer\":\"It describes applying quantum kernel methods to a quantum version of the classical SVM and highlights conditions under which quantum advantage is realized, including a data-dependent projected quantum kernel.\"},{\"question\":\"Why does the document use venture capital (VC) investment data?\",\"answer\":\"It uses VC data as an application setting to test the validity of quantum kernel methods for deciding which companies are likely to succeed, contrasting against labor-intensive classical screening and investor intuition.\"}]","Quantum Machine Learning - Quantum Kernel Methods | PDF",1785808317,25,{"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-quantum-kernel-methods","",{"@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-quantum-kernel-methods/122018/",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","2026-08-04",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},"What is the main idea behind quantum kernel methods in this document?","Question",{"text":75,"@type":76},"Quantum kernel methods use a quantum-computable feature space to capture intrinsic patterns in data efficiently on a quantum computer, potentially enabling quantum advantage over classical processing.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the paper relate quantum kernels to Support Vector Machines (SVM)?",{"text":80,"@type":76},"It describes applying quantum kernel methods to a quantum version of the classical SVM and highlights conditions under which quantum advantage is realized, including a data-dependent projected quantum kernel.",{"name":82,"@type":73,"acceptedAnswer":83},"Why does the document use venture capital (VC) investment data?",{"text":84,"@type":76},"It uses VC data as an application setting to test the validity of quantum kernel methods for deciding which companies are likely to succeed, contrasting against labor-intensive classical screening and investor intuition.","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},[93,97,101,105,110,115,120,123,128,131,134],{"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":21,"doc_module":4,"doc_module_name":46,"category_name":132,"show_sort_weight":21,"slug":133},"Lifestyle","lifestyle",{"id":135,"doc_module":4,"doc_module_name":46,"category_name":136,"show_sort_weight":106,"slug":137},19,"General","general"]