[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-123052-en":3,"doc-seo-123052-105":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},123052,8796095461610,"Oliver","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Permutation Invariant Encodings for Quantum Machine Learning with Point Cloud Data","Quantum computing offers a powerful approach to machine learning, yet many quantum machine learning methods generalize poorly as the number of qubits grows. This work introduces a permutation-invariant quantum encoding tailored to point cloud data, where point ordering is arbitrary. The encoding forms an equal superposition over all point permutations, making it invariant to reordering. Simulations using a Quantum Support Vector Machine classify point clouds from spherical and toroidal geometries, showing higher accuracy with more points, while non-invariant encodings lose accuracy.","arXiv :2304 .03601v1 [ quant-ph] 7 Apr 2023  \nPermutation Invariant Encodings for Quantum Machine Learning with Point Cloud Data  \nJamie Heredge 1*, Charles Hill 1,2 , Lloyd Hollenberg 1 and Martin Sevior 1  \n1* School of Physics, University of Melbourne, Parkville, VIC 3010, Australia.  \n2 School of Mathematics and Statistic, University of Melbourne, Parkville, VIC 3010, Australia.  \n*Corresponding author. E-mail: [heredgej@student.unimelb.edu.au](heredgej@student.unimelb.edu.au) ; Contributing authors: [cdhill@unimelb.edu.au](cdhill@unimelb.edu.au) ; [lloydch@unimelb.edu.au](lloydch@unimelb.edu.au) ;  \n[martines@unimelb.edu.au](martines@unimelb.edu.au) ;  \nAbstract  \nQuantum Computing o􀀋ers a potentially powerful new method for performing Machine Learning. However, several Quantum Machine Learning techniques have been shown to exhibit poor generalisation as the number of qubits increases [1] . We address this issue by demonstrating a permutation invariant quantum encoding method, which exhibits superior generalisation performance, and apply it to point cloud data (three-dimensional images composed of points) . Point clouds naturally contain permutation symmetry with respect to the ordering of their points, making them a natural candidate for this technique. Our method captures this symmetry in a quantum encoding that contains an equal quantum superposition of all permutations and is therefore invariant under point order permutation. We test this encoding method in numerical simulations using a Quantum Support Vector Machine to classify point clouds drawn from either spherical or toroidal geometries. We show that a permutation invariant encoding improves in accuracy as the number of points contained in the point cloud increases, while non-invariant quantum encodings decrease in accuracy. This demonstrates that by implementing permutation invariance into the encoding, the model exhibits improved generalisation.  \nKeywords: Quantum Machine Learning, Quantum Computing, Geometric Quantum Machine Learning, Quantum Encoding Methods, 3D Computer Vision, Point Cloud Data  \n1 Introduction  \nQuantum Machine Learning (QML) is a promising candidate for real-world applications of quantum technology [2] . In recent years, a multitude of di􀀋erent techniques have been developed with the aim of using quantum computers to perform machine learning tasks [3, 4] and QML techniques have been applied to a wide range of 􀀌elds, including particle physics [5, 6], medical data [7, 8],  \naerodynamics [9] and natural language processing [10] . In many QML techniques, classical data is encoded into an exponentially larger quantum space where there is the possibility that the data may be separated more easily [11] . This is a proposed source of quantum advantage over classical routines in the case that the quantum circuit performing the encoding cannot be e􀀎ciently simulated classically [12] . When trying to 􀀌nd suitable  \nQML techniques for real-world data, it is important to use an advantageous encoding method for that data. A current active area of research is the search for methods to encode or represent di􀀋erent types of data in quantum devices, for example,􀀌nding techniques to represent two-dimensional images [13{15] .  \nMany QML techniques, such as the Quantum Support Vector Machine (QSVM) [11], are motivated by the idea that encoding classical data into a higher dimensional quantum Hilbert space can simplify data classi􀀌cation. The circuit architecture used to encode classical data into a quantum state in􀀍uences the class of functions that a QML algorithm can learn [16] . Therefore, it is critical to 􀀌nd an optimal quantum encoding for the data in any QML method. However, some QML techniques do not generalise well as the number of qubits, and hence, the dimensionality of the Hilbert space increases [1] . To improve generalisation, attempts have been made to reduce the expressivity of QML methods by introducing some form of inductive bias into the m","cbCaitonOhwp7Ogg","https://ap.wps.com/l/cbCaitonOhwp7Ogg","pdf",3699683,1,15,"English","en",105,"# Abstract\n# 1 Introduction","[{\"question\":\"What problem do the authors address in quantum machine learning?\",\"answer\":\"They address poor generalization that appears in several QML techniques as the number of qubits increases.\"},{\"question\":\"How does the proposed encoding handle point cloud ordering?\",\"answer\":\"It uses a permutation-invariant quantum encoding that is an equal superposition of all permutations, making the representation unchanged under any point reorder.\"},{\"question\":\"What results are observed in simulations using a QSVM?\",\"answer\":\"Permutation-invariant encoding improves classification accuracy as the number of points increases, while non-invariant encodings show decreasing accuracy.\"}]","Permutation Invariant Encodings for Quantum Machine Learning with Point Cloud Data | PDF",1785814412,38,{"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},"permutation-invariant-encodings-for-quantum-machine-learning-with-point-cloud-data","",{"@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/permutation-invariant-encodings-for-quantum-machine-learning-with-point-cloud-data/123052/",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","2026-08-04",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 do the authors address in quantum machine learning?","Question",{"text":75,"@type":76},"They address poor generalization that appears in several QML techniques as the number of qubits increases.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed encoding handle point cloud ordering?",{"text":80,"@type":76},"It uses a permutation-invariant quantum encoding that is an equal superposition of all permutations, making the representation unchanged under any point reorder.",{"name":82,"@type":73,"acceptedAnswer":83},"What results are observed in simulations using a QSVM?",{"text":84,"@type":76},"Permutation-invariant encoding improves classification accuracy as the number of points increases, while non-invariant encodings show decreasing accuracy.","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"]