[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-290155-105":59,"doc-detail-290155-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","quantum-machine-learning-of-large-datasets-using-randomized-measurements-abstract","Quantum machine learning of large datasets using randomized measurements - Abstract","","Quantum machine learning can accelerate practical machine-learning tasks, but real-world applications require handling extensive high-dimensional datasets. Conventional quantum-kernel measurements become impractical because their cost scales as the square of the dataset size. This work measures quantum kernels through randomized measurements, achieving linear quantum computation time with dataset size and quadratic classical post-processing time. It uses a linear-in-circuit-depth feature scaling for encoding, links the encoding to the quantum Fisher information metric and the radial basis function kernel, and applies a cost-free error-mitigation strategy. Experiments on an IBM quantum computer classify images and enable benchmarking on current devices by distributing quantum tasks.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/quantum-machine-learning-of-large-datasets-using-randomized-measurements-abstract/290155/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/quantum-machine-learning-of-large-datasets-using-randomized-measurements-abstract/290155.png","ImageObject",300,407,{"name":92,"@type":93},"Jiven","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-02","2026-09-17",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",12,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"Why are conventional quantum-kernel measurements impractical for large datasets?","Question",{"text":113,"@type":114},"Their measurement cost scales quadratically with the training dataset size, which becomes a severe limitation for data-hungry machine-learning workflows.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How do randomized measurements change the runtime scaling?",{"text":118,"@type":114},"The quantum computation time scales linearly with dataset size, while the classical post-processing time scales quadratically.",{"name":120,"@type":111,"acceptedAnswer":121},"What encoding and noise-mitigation methods does the approach use?",{"text":122,"@type":114},"High-dimensional data is encoded with features that scale linearly with circuit depth, characterized using the quantum Fisher information metric and related to the radial basis function kernel. Noise is addressed with a cost-free error-mitigation scheme that enables robust benchmarking on noisy intermediate-scale quantum computers.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},290155,1789640810,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145,"preview_page_count":4},1099513958607,"https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399","BENCHMARK • OPEN ACCESS  \nQuantum machine learning of large datasets using randomized measurements  \nTo cite this article: Tobias Haug et al 2023 Mach. Learn. : Sci. Technol. 4 015005  \nView the article online for updates and enhancements.  \nYou may also like  \n-Hardening quantum machine learning against adversaries  \nNathan Wiebe and Ram Shankar Siva Kumar  \n-Compact quantum kernel-based binary classifier  \nCarsten Blank, Adenilton J da Silva, Lucas P de Albuquerque et al.  \n-Quantum machine learning and quantum biomimetics: A perspective  \nLucas Lamata  \nThis content was downloaded from IP address [86.175.40.123](86.175.40.123) on 02/05/2023 at 15:59  \n Mach. Learn.: Sci. Technol. 4 (2023) 015005 [https://doi.org/10.1088/2632-2153/acb0b4](https://doi.org/10.1088/2632-2153/acb0b4)  \nBENCHMARK  \nQuantum machine learning of large datasets using randomized OPEN ACCESS measurements  \nRECEIVED  \n12 December 2022 Tobias Haug∗􀁂, Chris N Self and M S Kim  \nACCEPTED FOR PUBLICATION QOLS, Blackett Laboratory, Imperial College, London SW7 2AZ, United Kingdom  \n5 January 2023 ∗ Author to whom any correspondence should be addressed.  \nPUBLISHED  \n20 January 2023 E-mail: [thaug@ic.ac.uk](thaug@ic.ac.uk)  \n   Keywords: quantum machine learning, quantum algorithm, quantum kernel, quantum computing, supervised learning  \nOriginal Content from this work may be used under the terms of the  \nCreative Commons Attribution 4 .0 licence.  \nAny further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.  \nAbstract  \nQuantum computers promise to enhance machine learning for practical applications. Quantum machine learning for real-world data has to handle extensive amounts of high-dimensional data. However, conventional methods for measuring quantum kernels are impractical for large datasets as they scale with the square of the dataset size. Here, we measure quantum kernels using randomized measurements. The quantum computation time scales linearly with dataset size and quadratic for classical post-processing. While our method scales in general exponentially in qubit number, we gain a substantial speed-up when running on intermediate-sized quantum computers. Further, we efficiently encode high-dimensional data into quantum computers with the number of features scaling linearly with the circuit depth. The encoding is characterized by the quantum Fisher information metric and is related to the radial basis function kernel. Our approach is robust to noise via a cost-free error mitigation scheme. We demonstrate the advantages of our methods for noisy quantum computers by classifying images with the IBM quantum computer. To achieve further speedups we distribute the quantum computational tasks between different quantum computers. Our method enables benchmarking of quantum machine learning algorithms with large datasets on currently available quantum computers.  \n1. Introduction  \nQuantum machine learning aims to use quantum computers to enhance the power of machine learning [1, 2]. One possible route to quantum advantage in machine learning is the use of quantum embedding kernels [3–6], where quantum computers are used to encode data in ways that are difficult for classical machine learning methods [7–9]. Noisy intermediate scale quantum computers [10, 11] may be capable of solving tasks difficult for classical computers [12, 13] and have shown promise in running proof-of-principle quantum machine learning applications [14–25] . However, currently available quantum computers are at least 6 orders of magnitude orders slower than classical computers. Furthermore, running quantum computers is comparatively expensive, necessitating methods to reduce quantum resources above all else. Thus, it is important to develop better methods to run and benchmark noisy quantum computers. Here, several bottlenecks limit quantum hardware for machine learning in practice. First, the quantum cost of measurin","cbCaibqaJvA6LGb7","https://ap.wps.com/l/cbCaibqaJvA6LGb7","pdf",1744539,18,"English","# Abstract\n# 1. Introduction\n# Quantum kernels via randomized measurements\n## Runtime scaling and measurement requirements\n## Noise mitigation and data encoding\n## Experimental validation on IBM quantum computer","[{\"question\":\"Why are conventional quantum-kernel measurements impractical for large datasets?\",\"answer\":\"Their measurement cost scales quadratically with the training dataset size, which becomes a severe limitation for data-hungry machine-learning workflows.\"},{\"question\":\"How do randomized measurements change the runtime scaling?\",\"answer\":\"The quantum computation time scales linearly with dataset size, while the classical post-processing time scales quadratically.\"},{\"question\":\"What encoding and noise-mitigation methods does the approach use?\",\"answer\":\"High-dimensional data is encoded with features that scale linearly with circuit depth, characterized using the quantum Fisher information metric and related to the radial basis function kernel. Noise is addressed with a cost-free error-mitigation scheme that enables robust benchmarking on noisy intermediate-scale quantum computers.\"}]","Quantum machine learning of large datasets using randomized measurements - Abstract | PDF",45]