[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-116831-en":3,"doc-seo-116831-105":30,"detail-sidebar-cat-0-en-105":92},{"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},116831,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","Quantum Machine Learning Beyond Kernel Methods","Noisy intermediate-scale quantum computers motivate machine-learning models based on parametrized quantum circuits, yet their comparative performance versus classical methods and between quantum model types is not well understood. The work builds on kernel-method reformulations and extends this guarantee to data re-uploading circuits. Using constructions and numerical simulations, it shows that variationally trained models can achieve markedly better generalization than kernel formulations, advancing theory for quantum model performance.","View metadata, citation and similar [papers at ](papers at core.ac.uk)[core.ac.uk](papers at core.ac.uk) brought to you by CORE  \n[provided by](provided by arXiv.org)[ arXiv.org](provided by arXiv.org) e-Print Archive  \narXiv :2110 . 13162v1 [ quant-ph] 25 Oct 2021  \nQuantum Machine Learning Beyond Kernel Methods  \nSo􀀌ene Jerbi, 1 Lukas J. Fiderer, 1 Hendrik Poulsen Nautrup, 1 Jonas M. K􀁿ubler,2 Hans J. Briegel, 1 and Vedran Dunjko3  \n1 Institute for Theoretical Physics, University of Innsbruck, Technikerstr. 21a, A-6020 Innsbruck, Austria  \n2 Max Planck Institute for Intelligent Systems, T􀁿ubingen, Germany  \n3 Leiden University, Niels Bohrweg 1, 2333 CA Leiden, Netherlands (Dated: October 27, 2021)  \nWith noisy intermediate-scale quantum computers showing great promise for near-term applications, a number of machine learning algorithms based on parametrized quantum circuits have been suggested as possible means to achieve learning advantages. Yet, our understanding of how these quantum machine learning models compare, both to existing classical models and to each other, remains limited. A big step in this direction has been made by relating them to so-called kernel methods from classical machine learning. By building on this connection, previous works have shown that a systematic reformulation of many quantum machine learning models as kernel models was guaranteed to improve their training performance. In this work, we 􀀌rst extend the applicability of this result to a more general family of parametrized quantum circuit models called data re-uploading circuits. Secondly, we show, through simple constructions and numerical simulations, that models de􀀌ned and trained variationally can exhibit a critically better generalization performance than their kernel formulations, which is the true 􀀌gure of merit of machine learning tasks. Our results constitute another step towards a more comprehensive theory of quantum machine learning models next to kernel formulations.  \nIntroduction| In the current Noisy Intermediate-Scale Quantum (NISQ) era [1], a few methods have been proposed to construct useful quantum algorithms that are compatible with mild hardware restrictions [2, 3] . Most of these methods involve the speci􀀌cation of a quantum circuit Ansatz, optimized in a classical fashion to solve speci􀀌c computational tasks. Next to variational quantum eigensolvers in chemistry [4] and variants of the quantum approximate optimization algorithm [5], machine learning approaches based on such parametrized quantum circuits [6] stand as some of the most promising practical applications to yield quantum advantages.  \nIn essence, a supervised machine learning problem often reduces to the task of 􀀌tting a parametrized function { also referred to as the machine learning model { to a set of previously labeled points, called a training set. Interestingly, many problems in physics and beyond, from the classi􀀌cation of phases of matter [7] to predicting what structures proteins fold into [8], can be phrased as such machine learning tasks. In the domain of quantum machine learning [9, 10], an emerging approach for this typeof problem is to use parametrized quantum circuits to de􀀌ne a hypothesis class of functions [11{16] . The hope is for these parametrized models to o􀀋er classi􀀌cation power beyond what is possible with classical models, including the highly successful deep neural networks. And indeed, we have substantial evidence of such a quantum learning advantage for arti􀀌cial problems [16{21], but the next frontier is to show that quantum models can be advantageous in solving real-world problems as well. To achieve this, we 􀀌rst need a deeper understanding of these quantum methods and how they relate.  \nMuch progress has been made in this direction by exploiting a connection between quantum models and kernel methods from classical machine learning [22] .  \nFIG. 1. The three types of quantum machine learning models studied in this Letter. a) An exp","cbCaicXqhWZPH9cs","https://ap.wps.com/l/cbCaicXqhWZPH9cs","pdf",971399,1,13,"English","en",105,"# Introduction\n## Quantum machine learning models and parametrized circuits\n## Connection to kernel methods\n## Data encoding and classifier types","[{\"question\":\"What kernel-method connection does the work build on?\",\"answer\":\"It leverages the previously established reformulation of quantum machine-learning models as kernel models from classical machine learning, where the training performance can be systematically improved.\"},{\"question\":\"Which broader circuit family is studied beyond earlier results?\",\"answer\":\"The paper extends the applicability of the kernel-model performance results to data re-uploading circuits, a more general family of parametrized quantum circuit models.\"},{\"question\":\"How do variationally trained models compare to their kernel formulations?\",\"answer\":\"Numerical simulations show that models defined and trained variationally can exhibit critically better generalization performance than their kernel counterparts, which serves as the key figure of merit.\"}]","Quantum Machine Learning Beyond Kernel Methods | 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kernel-method connection does the work build on?","Question",{"text":76,"@type":77},"It leverages the previously established reformulation of quantum machine-learning models as kernel models from classical machine learning, where the training performance can be systematically improved.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"Which broader circuit family is studied beyond earlier results?",{"text":81,"@type":77},"The paper extends the applicability of the kernel-model performance results to data re-uploading circuits, a more general family of parametrized quantum circuit models.",{"name":83,"@type":74,"acceptedAnswer":84},"How do variationally trained models compare to their kernel formulations?",{"text":85,"@type":77},"Numerical simulations show that models defined and trained variationally can exhibit critically better generalization performance than their kernel counterparts, which serves as the key figure of 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