[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-120732-en":3,"doc-seo-120732-105":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},120732,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","The Quantum Path Kernel - a Generalized Neural Tangent Kernel for Deep Quantum Machine Learning","Building a quantum analog of classical deep neural networks addresses a core challenge in quantum computing: reconciling deep-learning non-linearity with inherently linear quantum dynamics, where sequences of quantum gates form unitary transformations. Prior work introduces measurements between unitary layers to enable hierarchical representations. This paper proposes the Quantum Path Kernel, a quantum machine-learning formulation that replicates key deep-learning traits linked to superior classical generalization, especially hierarchical feature learning, by leveraging parameter trajectories in gradient space. Evaluations use Gaussian XOR mixtures to test multilevel learning.","This article has been accepted for publication in IEEE Transactions on Quantum Engineering. This is the author's version which has not been fully edited and  \ncontent may change prior to final publication. Citation information: DOI 10. 1109/TQE.2023.3287736  \nDate of publication xxxx 00, 0000, date of current version xxxx 00, 0000 .  \nDigital Object Identifier 10.1109/TQE.2022.DOI  \nThe Quantum Path Kernel: a Generalized Neural Tangent Kernel for Deep Quantum Machine Learning  \nMASSIMILIANO INCUDINI1 , MICHELE GROSSI2 , ANTONIO MANDARINO3 , SOFIA VALLECORSA2 , ALESSANDRA DI PIERRO1 , and DAVID WINDRIDGE 4  \n.  \n1Department of Computer Science, University of Verona, Verona 37134, Italy 2European Organization for Nuclear Research (CERN), Geneva 1211, Switzerland  \n3International Centre for Theory of Quantum Technologies (ICTQT), University of Gdansk, 80-309 Gda´nsk, Poland 4Department of Computer Science, Middlesex University, The Burroughs, London, NW4 4BT, UK Corresponding author: Massimiliano Incudini ([email: massimiliano.incudini@univr.it](email: massimiliano.incudini@univr.it)).  \nAntonio Mandarino is supported by Foundation for Polish Science (FNP), IRAP project ICTQT, contract no. 2018/MAB/5, co-financed by EU Smart Growth Operational Programme and the University of Verona throughout Mobility Grant No. PIA2022_CATB_DIPIERRO.  \n ABSTRACT Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. A key issue is how to address the inherent non-linearity of classical deep learning, a problem in the quantum domain due to the fact that the composition of an arbitrary number of quantum gates, consisting of a series of sequential unitary transformations, is intrinsically linear. This problem has been variously approached in the literature, principally via the introduction of measurements between layers of unitary transformations. In this paper, we introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning typically associated with superior generalization performance in the classical domain, specifically, hierarchical feature learning. Our approach generalizes the notion of Quantum Neural Tangent Kernel, which has been used to study the dynamics of classical and quantum machine learning models. The Quantum Path Kernel exploits the parameter trajectory, i.e. the curve delineated by model parameters as they evolve during training, enabling the representation of differential layer-wise convergence behaviors, orthe formation of hierarchical parametric dependencies, in terms of their manifestation in the gradient space of the predictor function. We evaluate our approach with respect to variants of the classification of Gaussian XOR mixtures-an artificial but emblematic problem that intrinsically requires multilevel learning in order to achieve optimal class separation.  \n INDEX TERMS Machine Learning, Neural Tangent Kernel, Quantum Kernel, Quantum Machine Learning, Quantum Neural Networks, Support Vector Machine (SVM) .  \nI. INTRODUCTION  \nBridging classical deep neural networks and quantum computing represents a key research challenge in the field of quantum machine learning [1], [2] . The potential for improvement offered by quantum computing in the machine learning domain may be characterized in terms of its impact on algorithmic efficiency, generalization error, or else its capacity for treating quantum data [3] .  \nA notable recent result in the field has been the introduction of the concept of variational quantum algorithms and the related neural network analog referred to as the quantum neural network (QNN) [4] . This, in essence, consists of a feature map encoding data into a quantum Hilbert space upon  \nwhich certain parameterized unitary rotations are applied prior to final measurement in order to obtain a classification or regression output. The system as a whole is then optimized by clas","cbCaitn9bXq8rM0O","https://ap.wps.com/l/cbCaitn9bXq8rM0O","pdf",2079739,1,17,"English","en",105,"# ABSTRACT\n# INTRODUCTION\n## Bridging classical deep neural networks and quantum computing\n## Quantum neural networks and their limitations\n## Linearity and the need for hierarchical feature learning","[{\"question\":\"What is the main challenge in creating a quantum analog of classical deep neural networks?\",\"answer\":\"Classical deep learning relies on non-linearity, but quantum systems evolve through inherently linear unitary gate compositions. This makes it difficult to realize hierarchical feature learning in the quantum setting.\"},{\"question\":\"How does the Quantum Path Kernel address the linearity issue?\",\"answer\":\"It generalizes the Quantum Neural Tangent Kernel by using the parameter trajectory during training. This enables modeling differential layer-wise convergence and hierarchical parametric dependencies through behavior in the gradient space.\"},{\"question\":\"How is the proposed method evaluated in the paper?\",\"answer\":\"The approach is evaluated against variants of classifying Gaussian XOR mixtures, an artificial but representative task that requires multilevel learning to achieve optimal class separation.\"}]","The Quantum Path Kernel - a Generalized Neural Tangent Kernel for Deep Quantum Machine Learning | PDF",1785731750,43,{"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},"the-quantum-path-kernel-a-generalized-neural-tangent-kernel-for-deep-quantum-machine-learning","",{"@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/the-quantum-path-kernel-a-generalized-neural-tangent-kernel-for-deep-quantum-machine-learning/120732/",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","2026-08-03",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 challenge in creating a quantum analog of classical deep neural networks?","Question",{"text":75,"@type":76},"Classical deep learning relies on non-linearity, but quantum systems evolve through inherently linear unitary gate compositions. This makes it difficult to realize hierarchical feature learning in the quantum setting.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the Quantum Path Kernel address the linearity issue?",{"text":80,"@type":76},"It generalizes the Quantum Neural Tangent Kernel by using the parameter trajectory during training. This enables modeling differential layer-wise convergence and hierarchical parametric dependencies through behavior in the gradient space.",{"name":82,"@type":73,"acceptedAnswer":83},"How is the proposed method evaluated in the paper?",{"text":84,"@type":76},"The approach is evaluated against variants of classifying Gaussian XOR mixtures, an artificial but representative task that requires multilevel learning to achieve optimal class separation.","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"]