[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117013-en":3,"doc-seo-117013-105":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},117013,16904993612988,"Olivia Brown","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Expressive Quantum Supervised Machine Learning using Kerr-nonlinear Parametric Oscillators - Resource-Efficient Approach for NISQ","Quantum machine learning with variational quantum algorithms (VQA) is actively explored for the NISQ era, yet expressive models in standard circuit architectures often require data reuploading and substantial quantum resources. To address this bottleneck, the work introduces supervised quantum machine learning using Kerr-nonlinear parametric oscillators (KPOs) as an alternative device platform. By leveraging ground, first excited, and higher excited states, the approach achieves access to a large Hilbert space with a single KPO mode. Numerical simulations show substantially higher expressibility than a conventional six-qubit method, supporting resource-efficient quantum machine learning for practical NISQ applications.","arXiv :2305 .00688v2 [ quant-ph] 13 Nov 2023  \nExpressive Quantum Supervised Machine Learning using Kerr-nonlinear Parametric  \nOscillators  \nYuichiro Mori, 1, ∗ Kouhei Nakaji,2, 1, 3,† Yuichiro Matsuzaki, 1, 4,‡ and Shiro Kawabata 1, 4, §  \n1 Global Research and Development Center for Business by Quantum-AI Technology (G-QuAT), National Institute of Advanced Industrial Science and Technology (AIST),  \n1-1-1, Umezono, Tsukuba, Ibaraki 305-8568, Japan  \n2 Chemical Physics Theory Group, Department of Chemistry,  \nUniversity of Toronto, Toronto, Ontario, Canada  \n3 Quantum Computing Center, Keio University, 3-14-1 Hiyoshi,  \nKohoku-ku, Yokohama, Kanagawa, 223-8522, Japan  \n4 NEC-AIST Quantum Technology Cooperative Research Laboratory,  \nNational Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki 305-8568, Japan  \n(Dated: November 14, 2023)  \nQuantum machine learning with variational quantum algorithms (VQA) has been actively investigated as a practical algorithm in the noisy intermediate-scale quantum (NISQ) era. Recent researches reveal that the data reuploading, which repeatedly encode classical data into quantum circuit, is necessary for obtaining the expressive quantum machine learning model in the conventional quantum computing architecture. However, the data reuploding tends to require large amount of quantum resources, which motivates us to find an alternative strategy for realizing the expressive quantum machine learning efficiently. In this paper, we propose quantum machine learning with Kerr-nonlinear Parametric Oscillators (KPOs), as another promising quantum computing device. We use not only the ground state and first excited state but also use higher excited states, which allows us to use a large Hilbert space even if we have a single KPO. Our numerical simulations show that the expressibility of our method with only one mode of the KPO is much higher than that of the conventional method with six qubits. Our results pave the way towards resource efficient quantum machine learning, which is essential for the practical applications in the NISQ era.  \nI. INTRODUCTION  \nThe quantum computers have attracted much attention due to its potential impact on quantum chemistry [1– 4], machine learning [5–7], cryptography [8–10], search problems [11] and so on. With advancements in quantum technology, commercially available quantum computers have become a reality. In principle, we could realize a fault-tolerant quantum computer, if the number of qubits is more than 10 millions with a fidelity around 0.999 [12– 14] . However, in the current device, the available number of qubits is an order of 500 or less, which is much smaller than that required for the fault-tolerant quantum computation. A more feasible scenario to be realized in the near future is the so-called NISQ regime [15, 16] .  \nNumerous quantum algorithms have been designed for execution on NISQ devices. Among these, VQAs are considered some of the most promising applications for NISQ devices [16, 17] . Specifically, quantum machine learning has emerged as an appealing use case for VQAs. As a NISQ algorithm, quantum machine learning has been predominantly investigated in the context of qubitbased systems. Recent studies have shown that data reuploading, the process of repeatedly encoding classical  \n∗ [mori-yuichiro.9302@aist.go.jp](mori-yuichiro.9302@aist.go.jp)[ ](mori-yuichiro.9302@aist.go.jp)† [kohei.nakaji@utoronto.ca](kohei.nakaji@utoronto.ca)  \n‡ Present E-mail address: [ymatsuzaki872@g.chuo-u.ac.jp](ymatsuzaki872@g.chuo-u.ac.jp)  \n§ [s-kawabata@aist.go.jp](s-kawabata@aist.go.jp)  \ndata into quantum circuits, is essential for achieving expressive quantum machine learning models within traditional quantum computing frameworks [18–20] . However, data reuploading often demands much quantum resources. This encourages us to seek alternative approaches to achieve expressive quantum machine learning. We could adopt a photonic device where f","cbCaisvRg9o2pTky","https://ap.wps.com/l/cbCaisvRg9o2pTky","pdf",1894462,1,13,"English","en",105,"# Introduction\n## Background: NISQ and VQAs\n## Challenge: Resource cost of data reuploading\n## Proposed platform: Kerr-nonlinear parametric oscillators (KPOs)\n## Method overview and expressibility study","[{\"question\":\"Why is data reuploading important for expressive quantum machine learning in conventional architectures?\",\"answer\":\"Data reuploading repeatedly encodes classical data into a quantum circuit and is essential for obtaining expressive quantum machine learning models within traditional quantum computing frameworks. However, it often demands large quantum resources.\"},{\"question\":\"How does the proposed method use Kerr-nonlinear parametric oscillators (KPOs) differently?\",\"answer\":\"The method employs KPOs and uses not only the ground and first excited states but also higher excited states. This enables a large effective Hilbert space even with a single KPO mode.\"},{\"question\":\"What do numerical simulations show about expressibility compared with a qubit-based approach?\",\"answer\":\"With only one mode of the KPO, the expressibility is much higher than that of the conventional method using six qubits. The simulations also indicate a trade-off with overfitting that can be tuned by adjusting the coherent-state amplitude.\"}]","Expressive Quantum Supervised Machine Learning using Kerr-nonlinear Parametric Oscillators - Resource-Efficient Approach for NISQ | PDF",1785673084,33,{"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},"expressive-quantum-supervised-machine-learning-using-kerr-nonlinear-parametric-oscillators-resource-efficient-approach-for-nisq","",{"@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/expressive-quantum-supervised-machine-learning-using-kerr-nonlinear-parametric-oscillators-resource-efficient-approach-for-nisq/117013/",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 is data reuploading important for expressive quantum machine learning in conventional architectures?","Question",{"text":75,"@type":76},"Data reuploading repeatedly encodes classical data into a quantum circuit and is essential for obtaining expressive quantum machine learning models within traditional quantum computing frameworks. However, it often demands large quantum resources.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed method use Kerr-nonlinear parametric oscillators (KPOs) differently?",{"text":80,"@type":76},"The method employs KPOs and uses not only the ground and first excited states but also higher excited states. This enables a large effective Hilbert space even with a single KPO mode.",{"name":82,"@type":73,"acceptedAnswer":83},"What do numerical simulations show about expressibility compared with a qubit-based approach?",{"text":84,"@type":76},"With only one mode of the KPO, the expressibility is much higher than that of the conventional method using six qubits. The simulations also indicate a trade-off with overfitting that can be tuned by adjusting the coherent-state amplitude.","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"]