[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-124606-en":3,"doc-seo-124606-105":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":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},124606,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1785132997149421697",8,"Research & Report","Transition role of entangled data in quantum machine learning","Entanglement is treated as a key resource for quantum computing, yet its precise influence on learning performance in quantum machine learning remains unclear. This work establishes a quantum no-free-lunch (NFL) theorem for learning quantum dynamics using entangled data. The theory reveals a dual effect on prediction error controlled by the number of allowed measurements. With sufficient measurements, higher entanglement reduces prediction error or the required training-data size; with few measurements, highly entangled data can increase prediction error, guiding early-stage QML protocol design.","arXiv :2306 .03481v1 [ quant-ph] 6 Jun 2023  \nTransition role of entangled data in quantum machine learning  \nXinbiao Wang, 1, 2, ∗ Yuxuan Du,2,† Zhuozhuo Tu,3 Yong Luo, 1 Xiao Yuan,4 and Dacheng Tao3 1 Institute of Artificial Intelligence, School of Computer Science, Wuhan University, Hubei 430070, China  \n2 JD Explore Academy, Beijing 101111, China  \n3 School of Computer Science, Faculty of Engineering, University of Sydney, NSW 2008, Australia  \n4 Center on Frontiers of Computing Studies, Peking University, Beijing 100871, China (Dated: June 7, 2023)  \nEntanglement serves as the resource to empower quantum computing. Recent progress has highlighted its positive impact on learning quantum dynamics, wherein the integration of entanglement into quantum operations or measurements of quantum machine learning (QML) models leads to substantial reductions in training data size, surpassing a specified prediction error threshold. However, an analytical understanding of how the entanglement degree in data affects model performance remains elusive. In this study, we address this knowledge gap by establishing a quantum no-free-lunch (NFL) theorem for learning quantum dynamics using entangled data. Contrary to previous findings, we prove that the impact of entangled data on prediction error exhibits a dual effect, depending on the number of permitted measurements. With a sufficient number of measurements, increasing the entanglement of training data consistently reduces the prediction error or decreases the required size of the training data to achieve the same prediction error. Conversely, when few measurements are allowed, employing highly entangled data could lead to an increased prediction error. The achieved results provide critical guidance for designing advanced QML protocols, especially for those tailored for execution on early-stage quantum computers with limited access to quantum resources.  \nI. Introduction  \nQuantum entanglement, an extraordinary characteristic of the quantum realm, drives the superiority of quantum computers beyond classical computers [1] . Over the past decade, diverse quantum algorithms leveraging entanglement have been designed to advance cryptography [2, 3] and optimization [4–8], delivering runtime speedups over classical approaches. Motivated by the exceptional abilities of quantum computers and the astonishing success in machine learning, a nascent frontier known as quantum machine learning (QML) has emerged [9–15], seeking to outperform classical models in specific learning tasks [16–25] . Substantial progress has been made in this field, exemplified by the introduction of QML protocols that offer provable advantages in terms of query or sample complexity for learning quantum dynamics [26–31], as a fundamental problem toward understanding the laws of nature [32] . Most of these protocols share a common strategy to gain advantages: the incorporation of entanglement into quantum operations and measurements, leading to reduced complexity. Nevertheless, an overlooked aspect in prior works is the impact of incorporating entanglement in quantum input states, or entangled data, on the advancement of QML in learning quantum dynamics. Due to the paramount role of data in learning [33–38], addressing this question will significantly enhance our comprehension of the capabilities and limitations of QML models.  \nA fundamental concept in machine learning that characterizes the capabilities of learning models in relation to datasets is the No-Free-Lunch (NFL) theorem [39–42] .  \n∗ This work was done when interned at JD Explore Academy.† [duyuxuan123@gmail.com](duyuxuan123@gmail.com)  \nThe NFL theorem yields a key insight: regardless of the optimization strategy employed, the ultimate performance of models is contingent upon the size and types of training data. This observation has spurred recent breakthroughsin large language models, as extensive and meticulously curated training data consistently yield superior r","cbCaicpwKHfzkmjX","https://ap.wps.com/l/cbCaicpwKHfzkmjX","pdf",2116863,1,30,"English","en",105,"# Introduction\n## Quantum entanglement and QML motivation\n## Quantum no-free-lunch theorem for entangled data\n## Dual effect of entanglement under measurement constraints","[{\"question\":\"What does the paper address about entangled data in quantum machine learning?\",\"answer\":\"It analyzes how the entanglement degree of training data affects model performance when learning quantum dynamics, an issue previously lacking an analytical understanding.\"},{\"question\":\"What is the main theoretical result of the study?\",\"answer\":\"The authors prove a quantum no-free-lunch (NFL) theorem showing a dual effect of entangled data on prediction error depending on the number of allowed measurements.\"},{\"question\":\"How does entangled data help or hurt depending on measurement availability?\",\"answer\":\"With sufficient measurements, increased entanglement consistently lowers prediction error (or training-data size for the same error). With only a few measurements, using highly entangled data can increase prediction error.\"}]","Transition role of entangled data in quantum machine learning | PDF",1785893281,76,{"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},"transition-role-of-entangled-data-in-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/transition-role-of-entangled-data-in-quantum-machine-learning/124606/",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","2026-08-05",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What does the paper address about entangled data in quantum machine learning?","Question",{"text":75,"@type":76},"It analyzes how the entanglement degree of training data affects model performance when learning quantum dynamics, an issue previously lacking an analytical understanding.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the main theoretical result of the study?",{"text":80,"@type":76},"The authors prove a quantum no-free-lunch (NFL) theorem showing a dual effect of entangled data on prediction error depending on the number of allowed measurements.",{"name":82,"@type":73,"acceptedAnswer":83},"How does entangled data help or hurt depending on measurement availability?",{"text":84,"@type":76},"With sufficient measurements, increased entanglement consistently lowers prediction error (or training-data size for the same error). 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