[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122741-en":3,"doc-seo-122741-105":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},122741,8796095360427,"Lucas Martin","https://ap-avatar.wpscdn.com/davatar_994ba38a5ba835b3df7d355c54d3ed8d",8,"Research & Report","Resource frugal optimizer for quantum machine learning - Research approach","Resource frugal optimizer for quantum machine learning addresses the high cost of training variational quantum machine learning models on near-term quantum hardware. It proposes simultaneous random sampling over both the dataset and measurement operators that define the loss, for a broad class of loss functions. The work constructs an unbiased estimator of the loss-gradient and introduces a shot-frugal gradient descent method named Refoqus. Numerical results show several orders of magnitude reductions in shot cost compared with strategies that sample measurement operators only.","Resource frugal optimizer for quantum machine learning  \nMOUSSA, C.; Gordon, M.H.; Baczyk, M.; Cerezo, M.; Cincio, L.; Coles, P.J.  \nCitation  \nMOUSSA, C., Gordon, M. H., Baczyk, M., Cerezo, M., Cincio, L., & Coles, P. J. (2023) . Resource frugal optimizer for quantum machine learning. Arxiv. Retrieved from [https://hdl.handle.net/1887/3566554](https://hdl.handle.net/1887/3566554)  \nVersion: Not Applicable (or Unknown)  \nLicense:  Leiden University Non-exclusive license  \nDownloaded from:  [https://hdl.handle.net/1887/3566554](https://hdl.handle.net/1887/3566554)  \nNote: To cite this publication please use the final published version (if applicable) .  \narXiv :2211 .04965v1 [ quant-ph] 9 Nov 2022  \nResource frugal optimizer for quantum machine learning  \nCharles Moussa, 1, 2, 􀀃 Max Hunter Gordon, 1, 3 Michal Baczyk, 1, 4 M. Cerezo,5 Lukasz Cincio, 1 and Patrick J. Coles 1  \n1 Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA  \n2 LIACS, Leiden University, Niels Bohrweg 1, 2333 CA Leiden, Netherlands  \n3 Instituto de Física Teórica, UAM/CSIC, Universidad Autónoma de Madrid, Madrid 28049, Spain  \n4 Faculty of Physics, University of Warsaw, ulica Pasteura 5, 02-093 Warsaw, Poland  \n5 Information Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA  \nQuantum-enhanced data science, also known as quantum machine learning (QML), is of growing interest as an application of near-term quantum computers. Variational QML algorithms have the potential to solve practical problems on real hardware, particularly when involving quantum data.  \nHowever, training these algorithms can be challenging and calls for tailored optimization procedures.  \nSpecifically, QML applications can require a large shot-count overhead due to the large datasets involved. In this work, we advocate for simultaneous random sampling over both the dataset as well as the measurement operators that define the loss function. We consider a highly general loss function that encompasses many QML applications, and we show how to construct an unbiased estimator of its gradient. This allows us to propose a shot-frugal gradient descent optimizer called Refoqus (REsource Frugal Optimizer for QUantum Stochastic gradient descent) . Our numerics indicate that Refoqus can save several orders of magnitude in shot cost, even relative to optimizers  \nthat sample over measurement operators alone.  \nI. INTRODUCTION  \nA new kind of data is emerging in recent times: quantum data. Tabletop quantum experiments and analog quantum simulators produce interesting sets of quantum states that must be characterized. Moreover, the rise of digital quantum computers is leading to the discovery of novel quantum circuits that can, once again, produce quantum states of interest. Quantum sensing, quantum phase diagrams, quantum error correction, and quantum dynamics are some of the areas that stand to benefit from quantum data analysis.  \nClassical machine learning was developed for the processing of classical data, but it is necessarily inefficient at processing quantum data. This issue has given rise to the field of quantum machine learning (QML) [1, 2] . QML has seen the proposal of parameterized quantum models, such as quantum neural networks [3–6], that could efficiently process quantum data. Variational QML, which involves classically training a parameterized quantum model, is indeed a leading candidate for implementing QML in the near term.  \nVariational QML, which we will henceforth refer to as QML for simplicity, has faced various sorts of trainability issues. Exponentially vanishing gradients, known as barren plateaus [7–15], as well as the prevalence of local minima [16, 17] are two issues that can impact the complexity of the training process. Quantum hardware noise also impacts trainability [18, 19] . All of these issues contribute to increasing the number of shots and iterations required to minimize the QML loss function. Indeed, a detailed shot-cos","cbCaijnTjLijABAR","https://ap.wps.com/l/cbCaijnTjLijABAR","pdf",1703649,1,21,"English","en",105,"# Introduction\n## Challenges in variational QML training\n## Shot-cost and trainability issues\n## Goal: resource frugality via new optimization\n## Proposed method: simultaneous sampling and unbiased gradient estimation\n## Applicability to multiple QML tasks","[{\"question\":\"Why is optimization resource usage a major challenge in variational quantum machine learning?\",\"answer\":\"Training can require many shots and iterations due to barren plateaus, local minima, hardware noise, and generally high shot-cost in loss minimization.\"},{\"question\":\"What key idea does the paper use to reduce shot overhead?\",\"answer\":\"It performs simultaneous random sampling over both the dataset and the measurement operators used to define the loss function, rather than sampling only measurement operators.\"},{\"question\":\"What is Refoqus and what does it optimize?\",\"answer\":\"Refoqus is a shot-frugal gradient descent optimizer that builds an unbiased estimator of the gradient for a highly general loss function, enabling efficient training.\"}]","Resource frugal optimizer for quantum machine learning - Research approach | PDF",1785812640,53,{"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},"resource-frugal-optimizer-for-quantum-machine-learning-research-approach","",{"@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/resource-frugal-optimizer-for-quantum-machine-learning-research-approach/122741/",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","2026-08-04",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},"Why is optimization resource usage a major challenge in variational quantum machine learning?","Question",{"text":75,"@type":76},"Training can require many shots and iterations due to barren plateaus, local minima, hardware noise, and generally high shot-cost in loss minimization.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What key idea does the paper use to reduce shot overhead?",{"text":80,"@type":76},"It performs simultaneous random sampling over both the dataset and the measurement operators used to define the loss function, rather than sampling only measurement operators.",{"name":82,"@type":73,"acceptedAnswer":83},"What is Refoqus and what does it optimize?",{"text":84,"@type":76},"Refoqus is a shot-frugal gradient descent optimizer that builds an unbiased estimator of the gradient for a highly general loss function, enabling efficient training.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]