[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118468-en":3,"doc-seo-118468-105":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":4,"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},118468,1374391974468,"Eden","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Single-shot quantum machine learning - Erik Recio-Armengol","Single-shot quantum machine learning studies how quantum computers can enable learning models with reduced inference overhead. Because measurement outcomes of quantum classifiers are inherently probabilistic, standard prediction requires many runs and aggregation, increasing time and cost. The work develops a rigorous definition of single-shotness in quantum classifiers and shows that near-deterministic predictions are limited by the distinguishability of the embedded quantum states. It further proves that if the embedding uses quantum circuits, a minimum circuit depth is necessary, and concludes that models cannot be generically both single-shot and trainable.","Single-shot quantum machine learning  \nErik Recio-Armengol  , 1, 2 Jens Eisert  ,3, 4, 5 and Johannes Jakob Meyer 3  \n1ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain  \n2Eurecat, Centre Tecnològic de Catalunya, Multimedia Technologies, 08005 Barcelona, Spain  \n3 Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany  \n4 Fraunhofer Heinrich Hertz Institute, 10587 Berlin, Germany  \n5Helmholtz-Zentrum Berlin für Materialien und Energie, 14109 Berlin, Germany  \n (Received 26 July 2024; revised 26 November 2024; accepted 26 March 2025; published 15 April 2025)  \nQuantum machine learning aims to improve learning methods through the use of quantum computers. If it is to ever realize its potential, many obstacles need to be overcome. A particularly pressing one arises at the prediction stage because the outputs of quantum learning models are inherently random. This creates an often considerable overhead, as many executions of a quantum learning model have to be aggregated to obtain an actual prediction. In this work, we analyze when quantum learning models can evade this issue and produce predictions in a near-deterministic way—paving the way to single-shot quantum machine learning. We give a rigorous definition of single shotness in quantum classifiers and show that the degree to which a quantum learning model is near deterministic is constrained by the distinguishability of the embedded quantum states used in the model. Opening the black box of the embedding, we show that if the embedding is realized by quantum circuits, a certain depth is necessary for single shotness to be even possible. We conclude by showing that quantum learning models cannot be single shot in a generic way and trainable at the same time.  \nDOI: 10.1103/PhysRevA.111.042420  \nI. INTRODUCTION  \nMachine learning is a burgeoning field where rapid advances regularly overturn assumptions on what can and cannot be learned by classical computers. This ongoing success story spurs interest in quantum machine learning, its intersection with quantum computing, another field that has recently seen tremendous technical progress. Investigating if quantum computers can be used to construct learning models that somehow outperform their classical counterparts has become one of the principal avenues of research in quantum machine learning.  \nWhile the intrinsic quantum nature of such models gives them at least some theoretical potential to push beyond the boundary of what is classically possible [1–4], it also comes with inherent downsides. Previous research in that direction mostly focused on the training stage, where issues such as barren plateaus [5] complicate the optimization of quantum learning models. Issues do, however, also appear at the inference stage, i.e., when a prediction is to be produced by a quantum learning model. A quantum learning model that deserves that name needs to perform some sort of manipulation of a quantum system. To extract a classical label, however, a measurement needs to be performed. It is the nature of quantum mechanics that the outcomes of such measurements are inherently probabilistic. For the model to solve a learning problem, for example, to correctly classify an image, the out-  \nPublished by the American Physical Society under the terms of the Creative Commons Attribution 4 .0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.  \nput needs to be deterministic. In practice, a quantum learning model is run a large number of times to circumvent the probabilistic outcomes of measurements and to extract a prediction, e.g., in the form of an expectation value of a suitably chosen observable. This issue, an instance of what has been called the measurement problem, 1 even persists if the model is run on a fault-tolerant quantum ","cbCaikD3war4XbwE","https://ap.wps.com/l/cbCaikD3war4XbwE","pdf",483170,1,14,"English","en",105,"# Introduction\n## Measurement overhead and probabilistic inference in quantum classifiers\n## Single-shot learning as a way to avoid aggregation\n## Rigorous definition and limitations via quantum hypothesis testing\n## Circuit depth requirements for single-shotness\n## Conclusions","[{\"question\":\"Why do quantum machine learning models usually require many runs at inference time?\",\"answer\":\"Because extracting a classical label requires measuring a quantum system, and quantum measurement outcomes are inherently probabilistic. As a result, repeated executions and aggregation are needed to obtain a stable prediction.\"},{\"question\":\"How is single-shotness defined for quantum classifiers in this work?\",\"answer\":\"The study provides a rigorous definition of single-shotness in quantum classifiers and analyzes when predictions can be produced in a near-deterministic way from a single execution.\"},{\"question\":\"What ultimately limits how close to deterministic a single-shot quantum model can be?\",\"answer\":\"The degree of near determinism is constrained by the distinguishability of the embedded quantum states used inside the model.\"}]","Single-shot quantum machine learning - Erik Recio-Armengol | PDF",1785683759,35,{"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},"single-shot-quantum-machine-learning-erik-recio-armengol","",{"@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/single-shot-quantum-machine-learning-erik-recio-armengol/118468/",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","2026-08-02",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why do quantum machine learning models usually require many runs at inference time?","Question",{"text":75,"@type":76},"Because extracting a classical label requires measuring a quantum system, and quantum measurement outcomes are inherently probabilistic. As a result, repeated executions and aggregation are needed to obtain a stable prediction.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How is single-shotness defined for quantum classifiers in this work?",{"text":80,"@type":76},"The study provides a rigorous definition of single-shotness in quantum classifiers and analyzes when predictions can be produced in a near-deterministic way from a single execution.",{"name":82,"@type":73,"acceptedAnswer":83},"What ultimately limits how close to deterministic a single-shot quantum model can be?",{"text":84,"@type":76},"The degree of near determinism is constrained by the distinguishability of the embedded quantum states used inside the model.","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"]