[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-122667-en":3,"doc-seo-122667-105":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},122667,549758146520,"Patrick","https://ap-avatar.wpscdn.com/avatar/80002397d8c0411e94?_k=1775819394049821470",8,"Research & Report","Resource frugal optimizer for quantum machine learning - Refoqus shot-frugal gradient descent optimizer","Quantum-enhanced data science, or quantum machine learning (QML), targets practical use of near-term quantum computers, but variational training is resource intensive. Large shot counts can be required by dataset sizes and by how measurement operators define the loss. This work presents a shot-frugal optimization strategy that performs simultaneous random sampling over the dataset and measurement operators, constructs an unbiased gradient estimator for a highly general loss function, and introduces Refoqus (a resource frugal optimizer) with convergence support for stochastic gradient descent. Numerical results indicate substantial reductions in shot cost.","arXiv :2211 .04965v2 [ quant-ph] 18 Jul 2023  \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-cost analysis has painted a concerning picture [20] .  \n􀀃 [c.moussa@liacs.leidenuniv.nl](c.moussa@liacs.leidenuniv.nl)  \nIt is therefore clear that QML requires careful frugality in terms of the resources expended during the optimization process. Indeed, novel optimizers have been developed in response to these challenges. Quantum-aware optimizers aim to replace off-the-shelf classical optimizers with ones that are specifically tailored to the quantum setting [21–23] . Shot-frugal optimizers [24–27] have been proposed in the context of variational quantum eigensolver (VQE), whereby one can sample over terms in the Hamiltonian instead of measuring every term ","cbCaihKD8f1cbrc9","https://ap.wps.com/l/cbCaihKD8f1cbrc9","pdf",2285337,1,22,"English","en",105,"# Introduction\n## Quantum data and variational QML\n## Trainability challenges and shot-cost overhead\n## Shot-frugal optimizers and motivation\n# Main approach (resource frugality)\n## Simultaneous random sampling over dataset and measurements\n## Unbiased gradient estimator and convergence guarantees\n## Applications under a generic loss function","[{\"question\":\"Why is optimization for variational quantum machine learning resource intensive?\",\"answer\":\"Training can require many shots and iterations due to large shot-count overhead from dataset sizes and the loss defined by measurement operators, along with trainability issues such as barren plateaus, local minima, and hardware noise.\"},{\"question\":\"How does the proposed method reduce shot cost?\",\"answer\":\"It uses simultaneous random sampling over both the dataset and the measurement operators defining the loss, enabling an unbiased estimator of the loss gradient and allowing shot-frugal gradient descent via Refoqus.\"},{\"question\":\"What is Refoqus and what does it optimize?\",\"answer\":\"Refoqus is a shot-frugal gradient descent optimizer (standing for REsource Frugal Optimizer for QUantum stochastic gradient descent) designed for a highly general QML loss function, using estimator structure to distribute shots effectively.\"}]","Resource frugal optimizer for quantum machine learning - Refoqus shot-frugal gradient descent optimizer | PDF",1785812059,55,{"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-refoqus-shot-frugal-gradient-descent-optimizer","",{"@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-refoqus-shot-frugal-gradient-descent-optimizer/122667/",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 for variational quantum machine learning resource intensive?","Question",{"text":75,"@type":76},"Training can require many shots and iterations due to large shot-count overhead from dataset sizes and the loss defined by measurement operators, along with trainability issues such as barren plateaus, local minima, and hardware noise.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed method reduce shot cost?",{"text":80,"@type":76},"It uses simultaneous random sampling over both the dataset and the measurement operators defining the loss, enabling an unbiased estimator of the loss gradient and allowing shot-frugal gradient descent via Refoqus.",{"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 (standing for REsource Frugal Optimizer for QUantum stochastic gradient descent) designed for a highly general QML loss function, using estimator structure to distribute shots effectively.","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"]