[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-82006-en":3,"doc-seo-82006-105":29,"detail-sidebar-cat-0-en-105":83},{"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":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":13,"seo_description":14,"update_tm":27,"read_time":28},82006,687197207639,"Asher","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","QCNN with Rough Path Signature Kernels","Time series analysis supports many scientific and engineering tasks but is hindered by time reparameterization invariance, which makes extraction of reliable temporal features difficult for standard models. This work tackles time series classification using quantum computation ideas by combining quantum neural networks with rough path theory. It proposes a hybrid quantum–classical architecture where signature kernel feature layers compare input paths via classical or quantum VQLS solvers, followed by QCNN layers. Experiments on handwritten digit stroke sequences show benefits and analyze VQLS computational limits.","arXiv :2607 .07634v1 [ quant-ph] 8 Jul 2026  \nQCNN with Rough Path Signature Kernels  \nLeonardo Nogueira Falabella⋆1 and Vasily Sazonov♯1  \n1 Universit´e Paris-Saclay, CEA, List, F-91120, Palaiseau, France  \nJuly 9, 2026  \nAbstract  \nTime series analysis plays a vital role across a wide range of scientific and engineering domains but poses substantial computational challenges. A major difficulty arises from the time reparameterization invariance of time series data, which complicates the extraction of meaningful temporal features. In this work, we address the problem of time series classification by exploring the application of quantum computation techniques. We propose a hybrid quantum–classical architecture that integrates recent advances in quantum neural networks with the mathematical framework of path signatures, mitigating the impact of time reparametrization invariance. The architecture employs feature layers that compute a signature kernel between pairs of input paths—consisting of a reference path and a target path for classification—using either classical or quantum variational linear solvers (VQLS) . These feature layers are followed by a Quantum Convolutional Neural Network (QCNN) to perform downstream learning tasks. We evaluate several realizations of the proposed architecture, differing in QCNN configurations, on a binary classification task involving time series representations of handwritten digits. Our experiments demonstrate the potential advantages of implementing path signature kernel layers within quantum circuits and provide an analysis of the computational limitations associated with the VQLS component.  \nKeywords: Rough path signatures; Signature kernels; Quantum computing; Variational Quantum Linear Solver (VQLS); Quantum machine learning; Quantum convolutional neural networks (QCNN) .  \n⋆ [leonardo.falabella@ensta.fr](leonardo.falabella@ensta.fr)[ ](leonardo.falabella@ensta.fr)♯[vasily.sazonov@cea.fr](vasily.sazonov@cea.fr)  \n1 Introduction  \nTime series data, representing sequential measurements over time, play a pivotal role across scientific and industrial domains: from financial market fluctuations and physiological signals such as heart rate or EEG/MEG brain recordings to meteorological patterns. The ability to analyze temporal sequences is essential for modern data-driven decision-making [16, 8, 12] . Machine learning provides powerful tools for such analyses; however, these methods often face fundamental challenges arising from inherent symmetries in the data [18] .  \nA key difficulty lies in the invariance of sequential data to time reparametrization—its essential characteristics remain unchanged under arbitrary accelerations, decelerations, or nonlinear warpings of the time axis [20] . Standard models, which depend on the explicit parametrization of time, struggle to account for this invariance. Rough path theory offers an elegant mathematical framework to address this issue through the notion of the signature [3, 23] . The signature transform converts a path into an infinite-dimensional feature vector of its iterated integrals, capturing its geometric and algebraic structure in a way that is inherently invariant to time reparametrization. Despite its advantages, computing truncated signature features remains computationally intensive, as the number of terms grows exponentially with the dimension of the path and the truncation order [3, 23] . Consequently, efficient computation of path signature features represents a significant bottleneck for large-scale applications.  \nImportant steps towards efficient computations of signature features were taken by introducing the signature kernels defined as the inner product of the truncated [14] and infinite signatures [21] . As shown in [21], this kernel for infinite signatures is the unique solution to a well-defined secondorder hyperbolic linear partial differential equation (PDE) - a Goursat problem. This enables practical computation of the kerne","cbCaibxbF5WfnGxk","https://ap.wps.com/l/cbCaibxbF5WfnGxk","pdf",1277171,1,15,"English","en",105,"# Abstract\n# Introduction\n## Time reparameterization invariance\n## Rough path signatures and signature kernels\n## Hybrid quantum–classical QCNN architecture\n## Computational analysis and MNIST stroke classification\n# Paper organization","[{\"question\":\"What dataset and task are used to evaluate the framework?\",\"answer\":\"A binary classification task on handwritten digit recognition using the MNIST digits stroke sequence dataset, where standard image data are converted into time-ordered stroke sequences to form the input time series representations.\"}]",1784177536,38,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":33,"description":14,"schema_data":34,"social_meta":78,"head_meta":80,"extra_data":82,"updated_unix":27},"qcnn-with-rough-path-signature-kernels","",{"@graph":35,"@context":77},[36,53,68],{"@type":37,"itemListElement":38},"BreadcrumbList",[39,43,47,50],{"item":40,"name":41,"@type":42,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":44,"name":45,"@type":42,"position":46},"https://docshare.wps.com/document/","Document",2,{"item":48,"name":12,"@type":42,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":42,"position":52},"https://docshare.wps.com/document/qcnn-with-rough-path-signature-kernels/82006/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":23,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":40,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-17","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71],{"name":72,"@type":73,"acceptedAnswer":74},"What dataset and task are used to evaluate the framework?","Question",{"text":75,"@type":76},"A binary classification task on handwritten digit recognition using the MNIST digits stroke sequence dataset, where standard image data are converted into time-ordered stroke sequences to form the input time series representations.","Answer","https://schema.org",{"og:url":51,"og:type":79,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":81,"canonical":51},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":84},[85,89,93,97,102,107,112,115,120,123,127],{"id":20,"doc_module":4,"doc_module_name":45,"category_name":86,"show_sort_weight":87,"slug":88},"Story & Novel",90,"story-novel",{"id":46,"doc_module":4,"doc_module_name":45,"category_name":90,"show_sort_weight":91,"slug":92},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":45,"category_name":94,"show_sort_weight":95,"slug":96},"Exam",70,"exam",{"id":98,"doc_module":4,"doc_module_name":45,"category_name":99,"show_sort_weight":100,"slug":101},5,"Comic",60,"comic",{"id":103,"doc_module":4,"doc_module_name":45,"category_name":104,"show_sort_weight":105,"slug":106},6,"Technology",50,"technology",{"id":108,"doc_module":4,"doc_module_name":45,"category_name":109,"show_sort_weight":110,"slug":111},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":45,"category_name":12,"show_sort_weight":113,"slug":114},30,"research-report",{"id":116,"doc_module":4,"doc_module_name":45,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":45,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":45,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":45,"category_name":129,"show_sort_weight":98,"slug":130},19,"General","general"]