[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119269-en":3,"doc-seo-119269-105":30,"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":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},119269,7971461740909,"Levi","https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d",8,"Research & Report","Quantum Resonant Dimensionality Reduction and Its Application in Quantum Machine Learning","Quantum computing offers strong potential for accelerating machine learning tasks, yet current hardware limits control accuracy and increases the consumption of quantum resources. This work proposes a quantum resonant dimension reduction (QRDR) algorithm using quantum resonant transitions to shrink input data from dimension N to R while preserving effective information. QRDR achieves polylogarithmic time complexity, improves error scaling from O(1/ε^3) to O(1/ε), and reduces computational complexity and quantum storage requirements. Experiments with quantum support vector machines and quantum convolutional neural networks demonstrate improved efficiency and accuracy.","arXiv :2405 . 12625v1 [ quant-ph] 21 May 2024  \nQuantum Resonant Dimensionality Reduction and Its Application in Quantum  \nMachine Learning  \nFan Yang, 1, 2, ∗ Furong Wang,3, ∗ Xusheng Xu,2 Pao Gao, 1 Tao Xin,4 ShiJie Wei, 1,† and Guilu Long2, 5, 6,‡  \n1 Beijing Academy of Quantum Information Sciences, Beijing 100193, China  \n2 State Key Laboratory of Low-Dimensional Quantum Physics and  \nDepartment of Physics, Tsinghua University, Beijing 100084, China  \n3 China North Vehcle Research Institute, Beijing 100072, China  \n4 Shenzhen Institute for Quantum Science and Engineering,  \nSouthern University of Science and Technology, Shenzhen 518055, China  \n5 Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, People’s Republic of China  \n6 Collaborative Innovation Center of Quantum Matter, Beijing 100084, China  \nQuantum computing is a promising candidate for accelerating machine learning tasks. Limited by the control accuracy of current quantum hardware, reducing the consumption of quantum resources is the key to achieving quantum advantage. Here, we propose a quantum resonant dimension reduction (QRDR) algorithm based on the quantum resonant transition to reduce the dimension of input data and accelerate the quantum machine learning algorithms. After QRDR, the dimension of input data N can be reduced into desired scale R, and the effective information of the original data will be preserved correspondingly, which will reduce the computational complexity of subsequent quantum machine learning algorithms or quantum storage. QRDR operates with polylogarithmic time complexity and reduces the error dependency from the order of 1/ϵ3 to the order of 1/ϵ, compared to existing algorithms. We demonstrate the performance of our algorithm combining with two types of quantum classifiers, quantum support vector machines and quantum convolutional neural networks, for classifying underwater detection targets and quantum many-body phase respectively. The simulation results indicate that reduced data improved the processing efficiency and accuracy following the application of QRDR. As quantum machine learning continues to advance, our algorithm has the potential to be utilized in a variety of computing fields.  \nI. INTRODUCTION  \nMachine learning has proven to be a remarkably powerful tool with broad practical applications across various fields of science and engineering, including finance [1, 2], medical science [3, 4], and the simulation of classical and complex quantum systems. It has shown notable success in compressing high-dimensional data, where near-term quantum devices may offer significant speed enhancements [5] . Given the potential quantum advantage of quantum computing, numerous quantum machine learning (QML) algorithms have been proposed [6], such as quantum recommendation systems (QRS) [7], quantum support vector machines (QSVM) [8], quantum principal component analysis (QPCA) [9], and quantum neural networks [10, 11], among others.  \nIn machine learning, dimensionality reduction (DR) is a valuable technique for refining information and significantly decreasing data processing time. DR involves compressing high-dimensional datasets into lowerdimensional representations while preserving key information from the original dataset. Principle component analysis (PCA) DR is the most representative example of linear DR. It works by projecting the original data onto the subspace of the covariance matrix with larger singular  \n∗  \n†  \n‡  \nThese authors contributed equally to this work.  \n[weisj@baqis.ac.cn](weisj@baqis.ac.cn)  \n[gllong@tsinghua.edu.cn](gllong@tsinghua.edu.cn)  \nvalues while disregarding components with smaller values. These smaller principal components often represent noise, so dimensionality reduction can enhance the accuracy of subsequent data processing. By applying kernel methods, kernel principal component analysis (KPCA) extends the concept of PCA to enable nonlinear dimensionality reductio","cbCaijDFjTbLHIpH","https://ap.wps.com/l/cbCaijDFjTbLHIpH","pdf",699814,1,11,"English","en",105,"# Introduction\n## Dimensionality reduction in classical and quantum machine learning\n## PCA-based quantum dimensionality reduction and QPCA\n## QRDR motivation and approach","[{\"question\":\"What problem does QRDR aim to solve in quantum machine learning?\",\"answer\":\"QRDR targets the high consumption of quantum resources caused by current hardware control limits by reducing the dimension of input data while preserving effective information.\"},{\"question\":\"How does QRDR improve error dependence compared with existing dimensionality-reduction algorithms?\",\"answer\":\"QRDR reduces the error dependency from the order of 1/ε^3 to the order of 1/ε, while operating with polylogarithmic time complexity.\"},{\"question\":\"Which quantum learning models are used to evaluate QRDR’s performance?\",\"answer\":\"The algorithm is demonstrated with two types of quantum classifiers: quantum support vector machines and quantum convolutional neural networks.\"}]","Quantum Resonant Dimensionality Reduction and Its Application in Quantum Machine Learning | PDF",1785723424,28,{"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":87,"head_meta":89,"extra_data":91,"updated_unix":28},"quantum-resonant-dimensionality-reduction-and-its-application-in-quantum-machine-learning","",{"@graph":36,"@context":86},[37,54,69],{"@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-resonant-dimensionality-reduction-and-its-application-in-quantum-machine-learning/119269/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04","2026-08-03",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 QRDR aim to solve in quantum machine learning?","Question",{"text":76,"@type":77},"QRDR targets the high consumption of quantum resources caused by current hardware control limits by reducing the dimension of input data while preserving effective information.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does QRDR improve error dependence compared with existing dimensionality-reduction algorithms?",{"text":81,"@type":77},"QRDR reduces the error dependency from the order of 1/ε^3 to the order of 1/ε, while operating with polylogarithmic time complexity.",{"name":83,"@type":74,"acceptedAnswer":84},"Which quantum learning models are used to evaluate QRDR’s performance?",{"text":85,"@type":77},"The algorithm is demonstrated with two types of quantum classifiers: quantum support vector machines and quantum convolutional neural networks.","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":24},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,121,124,129,132,136],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":46,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":46,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":46,"category_name":138,"show_sort_weight":107,"slug":139},19,"General","general"]