[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-116894-en":3,"doc-seo-116894-105":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},116894,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1785132997149421697",8,"Research & Report","Tensor Networks for Quantum Machine Learning","Tensor networks, originally developed for quantum theory, have become an effective machine learning paradigm and are now extended back into the quantum realm through quantum machine learning. Their physics–ML interface enables natural deployment on quantum computers for tasks that classical computers struggle with efficiently. This review focuses on a key architecture for variational quantum machine learning, explaining mappings of MPS, PEPS, TTNs and MERA to quantum hardware, their roles in learning and data encoding, and implementation techniques that improve performance.","arXiv :2303 . 11735v1 [ quant-ph] 21 Mar 2023  \nTensor Networks for Quantum Machine Learning  \nHans-Martin Rieser 1,* , Frank K¨oster 1 , and Arne Peter Raulf 1,+  \n1 Deutsches Zentrum f¨ur Luft-und Raumfahrt, Institute for AI safety and security, Ulm / St. Augustin, Germany  \n* e-mail: [hans-martin.rieser@dlr.de](hans-martin.rieser@dlr.de), [https://orcid.org/0000-0002-1921-1436](https://orcid.org/0000-0002-1921-1436)[ ](https://orcid.org/0000-0002-1921-1436)+ [https://orcid.org/0009-0003-8672-3014](https://orcid.org/0009-0003-8672-3014)  \nABSTRACT  \nOnce developed for quantum theory, tensor networks have been established as a successful machine learning paradigm. Now, they have been ported back to the quantum realm in the emerging 􀀂eld of quantum machine learning to assess problems that classical computers are unable to solve ef􀀂ciently. Their nature at the interface between physics and machine learning makes tensor networks easily deployable on quantum computers. In this review article, we shed light on one of the major architectures considered to be predestined for variational quantum machine learning. In particular, we discuss how layouts like MPS, PEPS, TTNs and MERA can be mapped to a quantum computer, how they can be used for machine learning and data encoding and which implementation techniques improve their performance.  \n1 Introduction  \nQuantum computation is widely believed to set a new paradigm in computation. Utilizing quantum phenomena allows to solve certain problems 1 far more ef􀀂cient than classical binary algorithms. This raises hope that quantum implementations of other tasks also may provide quantum advantages.  \nOne of the applications that could bene􀀂t from the access to the high dimensional Hilbert spaces of quantum computers is machine learning (ML) . ML is a data driven approach for solving complex problems. An ML algorithm generates a model from training data that can be used to make predictions against previously unseen data. Quantum machine learning (QML) could advance learning by improved generalization to unknown data2 , higher noise robustness and the need for less training data3 , and provide a more natural approach to quantum data analysis circumventing intermediate measurements4 or generally a better computational complexity scaling5.  \nPromising candidates for QML architectures are tensor networks (TN) . They provide a structured approach for handling large objects with tensor structure which carry high amounts of correlated information like quantum states. Initially developed to store and process physical states of many-body quantum systems in numerical simulations6, 7 , TNs also turned out to be useful for ML applications. Their approach to realize learning architectures is complementary to neural networks. As the TN description uses a (quantum) state and operator formulation, the transfer to a quantum computer can be done naturally.  \nIn this review, we focus on the application of TNs for QML. We will begin with a short introduction to the classical TN theory including optimization and ML approaches in Section 2. Then, we will discuss how to apply these concepts to a quantum computer in Section 3 and the encoding of data to quantum states for ML applications in Section 4 .  \nWe will not cover many aspects of classical TNs in detail. For a deeper technical dive into TNs, the reader may refer to a general introduction8 and the reviews on speci􀀂c layouts9, 10 or decomposition and optimization techniques 11–13. Applications are many-body quantum systems 14 , nonlinear system identi􀀂cation 15 and classical ML 16, 17.  \nThe 􀀂eld of TN-QML is just developing, and notations and terminology vary throughout the community. Due to their origin in quantum theory, some authors call even ML with classical TNs \"quantum machine learning\"18. In our opinion, amore suitable term would be quantum-inspired here. Furthermore, one can argue that variational quantum circuits (VQC)19 require classical optimizatio","cbCaicfT8DoJ2d5t","https://ap.wps.com/l/cbCaicfT8DoJ2d5t","pdf",324254,1,20,"English","en",105,"# Introduction\n## Quantum machine learning and potential advantages\n## Tensor networks as QML architectures\n# Classical Tensor Networks\n## Introduction on tensors and tensor networks\n## Common tensor network layouts","[{\"question\":\"What problem does quantum machine learning aim to solve compared with classical machine learning?\",\"answer\":\"Quantum machine learning targets advantages such as improved generalization, higher noise robustness, less training data, and better scaling for certain tasks. It also enables quantum data analysis with fewer intermediate measurements or improved computational complexity.\"},{\"question\":\"Why are tensor networks considered promising architectures for QML?\",\"answer\":\"Tensor networks provide a structured way to represent large correlated objects such as quantum states using low-rank tensor decompositions. Their state/operator formulation transfers naturally to quantum computers, complementing neural-network-style learning.\"},{\"question\":\"Which variational quantum machine learning architectures are discussed in the review?\",\"answer\":\"The review discusses layouts including MPS, PEPS, TTNs and MERA, explaining how they can be mapped to quantum computers, used for machine learning, and applied for data encoding.\"}]","Tensor Networks for Quantum Machine Learning | PDF",1785672297,50,{"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},"tensor-networks-for-quantum-machine-learning","",{"@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/tensor-networks-for-quantum-machine-learning/116894/",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 quantum machine learning aim to solve compared with classical machine learning?","Question",{"text":75,"@type":76},"Quantum machine learning targets advantages such as improved generalization, higher noise robustness, less training data, and better scaling for certain tasks. It also enables quantum data analysis with fewer intermediate measurements or improved computational complexity.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"Why are tensor networks considered promising architectures for QML?",{"text":80,"@type":76},"Tensor networks provide a structured way to represent large correlated objects such as quantum states using low-rank tensor decompositions. Their state/operator formulation transfers naturally to quantum computers, complementing neural-network-style learning.",{"name":82,"@type":73,"acceptedAnswer":83},"Which variational quantum machine learning architectures are discussed in the review?",{"text":84,"@type":76},"The review discusses layouts including MPS, PEPS, TTNs and MERA, explaining how they can be mapped to quantum computers, used for machine learning, and applied for data encoding.","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},[93,97,101,105,110,114,119,122,126,129,133],{"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":29,"slug":113},6,"Technology","technology",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":120,"slug":121},30,"research-report",{"id":123,"doc_module":4,"doc_module_name":46,"category_name":124,"show_sort_weight":21,"slug":125},9,"Religion & Spirituality","religion-spirituality",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":127,"show_sort_weight":21,"slug":128},"World Cup","world-cup",{"id":130,"doc_module":4,"doc_module_name":46,"category_name":131,"show_sort_weight":130,"slug":132},10,"Lifestyle","lifestyle",{"id":134,"doc_module":4,"doc_module_name":46,"category_name":135,"show_sort_weight":106,"slug":136},19,"General","general"]