[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117751-en":3,"doc-seo-117751-105":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},117751,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","Overfitting in quantum machine learning and entangling dropout","Machine learning aims to build model functions that generalize to unseen data, yet excessive expressibility can cause overfitting to the training set and degrade out-of-sample performance. Building on classical dropout regularization, this paper introduces an analogue for quantum machine learning: entangling dropout, which randomly removes selected entangling gates in a parametrized quantum circuit during training to reduce circuit expressibility. Case studies are provided to demonstrate suppressed overfitting and improved generalization error.","Noname manuscript No.(will be inserted by the editor)  \nOver􀀂tting in quantum machine learning and entangling dropout  \nMasahiro Kobayashi 1 · Kouhei Nakaji2 ,3 · Naoki Yamamoto 1 ,2,⋆  \narXiv :2205 . 11446v2 [ quant-ph] 22 Jan 2023  \nthe date of receipt and acceptance should be inserted later  \nAbstract The ultimate goal in machine learning is to construct a model function that has a generalization capability for unseen dataset, based on given training dataset. If the model function has too much expressibility power, then it may over􀀂t to the training data and as a result lose the generalization capability. To avoid such over􀀂tting issue, several techniques have been developed in the classical machine learning regime, and the dropout is one such effective method. This paper proposes a straightforward analogue of this technique in the quantum machine learning regime, the entangling dropout, meaning that some entangling gates in a given parametrized quantum circuit are randomly removed during the training process to reduce the expressibility of the circuit. Some simple case studies are given to show that this technique actually suppresses the over􀀂tting.  \nKeywords Quantum machine learning · parametrized quantum circuit · over􀀂tting · dropout regularization  \n1 Introduction  \nQuantum computer has potential to execute machine learning tasks more ef􀀂ciently than conventional computers [1– 3] . Both in classical and quantum machine learning problems, it is important to use an approximator (a model function) that has a high expressibility power to achieve a good computational accuracy. For this purpose, recently the data re-uploading method was proposed [4–6], which encodes  \n1, Department of Applied Physics and Physico-Informatics, Keio University, Hiyoshi 3-14-1, Kohoku, Yokohama 223-8522, Japan  \n2, Quantum computing center, Keio University, Hiyoshi 3-14-1, Kohoku, Yokohama 223-8522, Japan  \n3, Present address: Research Center for Emerging Computing Technologies, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan  \n⋆ Email: [yamamoto@appi.keio.ac.jp](yamamoto@appi.keio.ac.jp)  \nthe input data into the quantum circuit multiple times in the depth direction of the circuit. On the other hand, if the expressibility is too high, then the approximator may over􀀂t to the training dataset and lose the generalization capability for unseen dataset. That is, we need to carefully design an approximator with appropriate expressibility power, such that it can achieve as small generalization (out-of-sample) error as possible. In fact, we recently 􀀂nd some theoretical analysis on the generalization error in quantum machine learning regime [7–12], although practical quantum-oriented methods for suppressing the over􀀂tting issue have not been suf􀀂 -ciently discussed.  \nIn this paper, we propose a practical method for suppressing the over􀀂tting issue in quantum machine learning problems, the entangling dropout. This is a straightforward analogue of the classical dropout [13], which randomly removes some connections between nodes of a neural network during the training process; although the mechanism for suppressing the over􀀂tting has not been fully revealed, the effectiveness of classical dropout is very well recognized, and it has been widely used. The proposed entangling dropout is a similar technique, that randomly removes some entangling gates contained in a given parametrized quantum circuit during the training process. This clearly decreases the expressibility, but its actual effectiveness is not obvious; in this paper some examples are given to show that the entangling dropout certainly works to suppress the over􀀂tting and improve the out-of-sample errors. We then discuss how to choose the dropout ratio, which determines the number of entangling gates removed in each iteration. Also, a comparison to the L 1 or L2 regularization technique is provided, showing a merit of using","cbCaiboCtXK8MG35","https://ap.wps.com/l/cbCaiboCtXK8MG35","pdf",969792,1,7,"English","en",105,"# Introduction\n## Expressibility and generalization\n## Classical dropout vs quantum dropout\n# Overfitting in quantum machine learning\n## Quantum circuit model\n## Expressibility via Fourier form","[{\"question\":\"What problem does the paper address in quantum machine learning?\",\"answer\":\"The paper addresses overfitting, where an overly expressive quantum model fits the training data but loses generalization capability on unseen datasets.\"},{\"question\":\"How does entangling dropout work during training?\",\"answer\":\"Entangling dropout randomly removes some entangling gates from a parametrized quantum circuit in each training step, reducing the circuit’s expressibility.\"},{\"question\":\"Why is limiting expressibility important in this context?\",\"answer\":\"If expressibility is too high, the model can overfit and produce larger out-of-sample generalization error; reducing it helps improve generalization.\"}]","Overfitting in quantum machine learning and entangling dropout | PDF",1785679362,18,{"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},"overfitting-in-quantum-machine-learning-and-entangling-dropout","",{"@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/overfitting-in-quantum-machine-learning-and-entangling-dropout/117751/",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},"What problem does the paper address in quantum machine learning?","Question",{"text":75,"@type":76},"The paper addresses overfitting, where an overly expressive quantum model fits the training data but loses generalization capability on unseen datasets.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does entangling dropout work during training?",{"text":80,"@type":76},"Entangling dropout randomly removes some entangling gates from a parametrized quantum circuit in each training step, reducing the circuit’s expressibility.",{"name":82,"@type":73,"acceptedAnswer":83},"Why is limiting expressibility important in this context?",{"text":84,"@type":76},"If expressibility is too high, the model can overfit and produce larger out-of-sample generalization error; 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