[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118754-en":3,"doc-seo-118754-105":30,"detail-sidebar-cat-0-en-105":84},{"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},118754,1099513958762,"Logic","https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253",8,"Research & Report","Towards provably efficient quantum algorithms for large-scale machine-learning models","The work investigates how fault-tolerant quantum computing can yield provably efficient solutions for generic (stochastic) gradient descent, scaling as O(T^2 · polylog(n)) where n denotes model size and T denotes training iterations. The proposed efficiency relies on sufficiently dissipative, sparse models and small learning rates, building on earlier quantum algorithms for dissipative differential equations and adapting them to (stochastic) gradient descent via linearization. Benchmarks on sparse training instances from 7M to 10^3M parameters indicate a quantum enhancement early after pruning, motivating a sparse parameter download and re-upload scheme.","Towards provably efficient quantum algorithms for large-scale machine-learning models  \narXiv :2303 .03428v2 [ quant-ph] 26 Apr 2023  \nJunyu Liu, 1, 2, 3, 4, 5, 6 Minzhao Liu,7, 8 Jin-Peng Liu,9, 10, 11 Ziyu Ye,2 Yuri Alexeev,8, 2, 3 Jens Eisert, 12 and Liang Jiang 1, 3  \n1 Pritzker School of Molecular Engineering, The University of Chicago, Chicago, IL 60637, USA 2 Department of Computer Science, The University of Chicago, Chicago, IL 60637, USA 3 Chicago Quantum Exchange, Chicago, IL 60637, USA  \n4 Kadanoff Center for Theoretical Physics, The University of Chicago, Chicago, IL 60637, USA  \n5qBraid Co., Chicago, IL 60615, USA  \n6 SeQure, Chicago, IL 60615, USA  \n7 Department of Physics, The University of Chicago, Chicago, IL 60637, USA 8 Computational Science Division, Argonne National Laboratory, Lemont, IL 60439, USA 9 Simons Institute for the Theory of Computing, University of California, Berkeley, CA 94720, USA 10 Department of Mathematics, University of California, Berkeley, CA 94720, USA 11 Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA 12 Dahlem Center for Complex Quantum Systems, Free University Berlin, Berlin, 14195, Germany  \nLarge machine learning models are revolutionary technologies ofartificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efficient resolutions for generic (stochastic) gradient descent algorithms, scaling as O (T2 􀀂 polylog (n)), where n is the size of the models and T is the number of iterations in the training, as long as the models are both sufficiently dissipative and sparse, with small learning rates. Based on earlier efficient quantum algorithms for dissipative differential equations, we find and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We find that, in the context of sparse training, a quantum enhancement is possible at the early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that fault-tolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machinelearning problems.  \nIt is widely believed that large-scale machine learning might be one of the most revolutionary technologies benefiting society [1], including already important breakthroughs in digital arts [2], conversation like GPT-3 [3, 4], and mathematical problem solving [5] . However, training such models with considerable parameters is costly and has high carbon emissions. For instance, twelve million dollars and over five-hundred tons of CO2 equivalent emissions have been produced to train GPT-3 [6] . Thus, on the one hand, it is important to make large-scale machine-learning models (like large language models, LLM) sustainable and efficient.  \nOn the other hand, machine learning might possibly be oneof the flag applications of quantum technology. Running machine learning algorithms on quantum devices, implementing readings of so-called quantum machine learning, is widely seen as a potentially very fruitful application of quantum algorithms [7] . Despite rapid development and significant progress, current quantum machine learning algorithms feature substantial limitations both in theory and practice. First, practical applica-  \ntions of quantum machine learning algorithms for near-term devices are often lacking theoretical grounds that guarantee or at least plausibly suggest to outperform their classical counterparts. Second, for fault-tolerant settings of quantum machine learning problems [8–16], rigorous super-polynomial quantum speedups can actually be proven [17–19] for highly structured problems. That said, these pres","cbCaipMpynF41fLY","https://ap.wps.com/l/cbCaipMpynF41fLY","pdf",1871823,1,35,"English","en",105,"# Overview and motivation\n## Quantum advantages for gradient-based learning\n# Proposed quantum framework\n## Fault-tolerant efficiency and complexity scaling\n## Conditions: dissipativity, sparsity, small learning rates\n# Algorithmic construction\n## Mapping differential-equation techniques to gradient descent\n## Use of HHL-style sparse matrix inversion\n# Experimental benchmarking\n## Benchmarks across sparse training parameter scales\n## Sparse parameter download and re-upload scheme","[{\"question\":\"How do the benchmarks motivate a concrete training strategy?\",\"answer\":\"For sparse training, the paper finds a potential quantum enhancement early in learning after model pruning, motivating a sparse parameter download and re-upload scheme before further training proceeds.\"}]","Towards provably efficient quantum algorithms for large-scale machine-learning models | PDF",1785720065,88,{"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":79,"head_meta":81,"extra_data":83,"updated_unix":28},"towards-provably-efficient-quantum-algorithms-for-large-scale-machine-learning-models","",{"@graph":36,"@context":78},[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/towards-provably-efficient-quantum-algorithms-for-large-scale-machine-learning-models/118754/",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],{"name":73,"@type":74,"acceptedAnswer":75},"How do the benchmarks motivate a concrete training strategy?","Question",{"text":76,"@type":77},"For sparse training, the paper finds a potential quantum enhancement early in learning after model pruning, motivating a sparse parameter download and re-upload scheme before further training proceeds.","Answer","https://schema.org",{"og:url":52,"og:type":80,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":82,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":85},[86,90,94,98,103,108,113,116,121,124,128],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":87,"show_sort_weight":88,"slug":89},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":91,"show_sort_weight":92,"slug":93},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Exam",70,"exam",{"id":99,"doc_module":4,"doc_module_name":46,"category_name":100,"show_sort_weight":101,"slug":102},5,"Comic",60,"comic",{"id":104,"doc_module":4,"doc_module_name":46,"category_name":105,"show_sort_weight":106,"slug":107},6,"Technology",50,"technology",{"id":109,"doc_module":4,"doc_module_name":46,"category_name":110,"show_sort_weight":111,"slug":112},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":114,"slug":115},30,"research-report",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":118,"show_sort_weight":119,"slug":120},9,"Religion & Spirituality",20,"religion-spirituality",{"id":119,"doc_module":4,"doc_module_name":46,"category_name":122,"show_sort_weight":119,"slug":123},"World Cup","world-cup",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":126,"show_sort_weight":125,"slug":127},10,"Lifestyle","lifestyle",{"id":129,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":99,"slug":131},19,"General","general"]