[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119180-en":3,"doc-seo-119180-105":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},119180,8796095461610,"Oliver","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Quantum Machine Learning With Canonical Variables - paper","Quantum Machine Learning With Canonical Variables presents a learning platform where dynamic electromagnetic-field control acts on observables rather than directly on quantum states. The field profile provides the ansatz within the learning algorithm and can be physically implemented using ion traps or particle confinement devices. The resulting quantum models are exactly solvable, enabling regression and classification to emerge from solvable precursor dynamics, with attention focused on canonical variables under semiclassical behavior, excluding relativistic degrees of freedom.","Quantum Machine Learning With Canonical Variables  \nJ. Fuentes∗  \nLCSB, University of Luxembourg  \n6, Avenue Du Swing,  \nL-4364 Belval, Luxembourg  \narXiv :2406 .06666v1 [ quant-ph] 10 Jun 2024  \nUtilising dynamic electromagnetic field control over charged particles serves as the basis for a quantum machine learning platform that operates on observables rather than directly on states. Such a platform can be physically realised in ion traps or particle confinement devices that utilise electromagnetic fields as the source of control. The electromagnetic field acts as the ansatz within the learning algorithm. The models discussed are exactly solvable, with exact solutions serving as precursors for learning tasks to emerge, including regression and classification algorithms as particular cases. This approach is considered in terms of canonical variables with semi-classical behaviour, disregarding relativistic degrees of freedom.  \nINTRODUCTION  \nA machine learning algorithm consists of fitting the parameters of a sufficiently smooth ansatz through an optimisation process to approximate the pattern in the data, if any, identifying how x maps to y. Therefore, if the algorithm has accurately learned (or fitted) the map f (x) = y, then any unseen data of the same kind could be predicted.  \nAny learning method comprises three fundamental components: the data, the ansatz or model, and the optimisation scheme. The type of data determines whether the learning algorithm should be modelled by a classical or quantum ansatz, while the optimisation can be either classical or quantum, irrespective of the data’s nature. In principle, classical data can be mapped to a quantum ansatz, but not all quantum data can be mapped to a classical ansatz.  \nFor classical learning algorithms, the ansatz is intangible, being it modelled as a smooth function, such asa polynomial or a neural network. The entire algorithm is instantiated as code, and then is transformed into a low-level language via a compiler or interpreter. At that level, the instructions are executed by the central processing unit, where the arithmetic operations and logic decisions required by the optimisation protocol are processed as 1s and 0s by arrays of transistors.  \nIn contrast, the ansatz in quantum learning algorithms is inherently physical, modelled through quantum circuits. Initially instantiated as classical digital code, the algorithm is transformed into quantum instructions via a quantum compiler, enabling qubit-level processing. Classical data is encoded into quantum states for this process and then decoded back to classical form for interpretation. In cases where the data is quantum, it remains in quantum states, allowing direct manipulation by quantum algorithms. Regardless the type of data—quantum or classical—decoding qubits into the digital domain is necessary for interpreting the results in the classical landscape.  \nOptimisation in this context can be carried out using  \neither quantum or classical algorithms. Quantum optimisation is usually performed using techniques like the quantum approximate optimisation algorithm [1] or the variational quantum eigensolver [2] to find optimal parameters. Classical optimisation schemes, such as gradient descent or Bayesian optimisation [3], can also be used, and often a hybrid approach is employed [4, 5] where classical and quantum computations complement each other.  \nThe field of quantum machine learning has seen rapid advancements [6–8] . The implementation of quantum algorithms for supervised learning tasks has demonstrated the potential for significant improvements over classical methods [9] . Research also indicates that quantumenhanced clustering and quantum neural networks can achieve more accurate data segmentation and faster learning rates compared to their classical counterparts [10] . Furthermore, experimental demonstrations, such as the implementation of quantum neural networks on actual quantum processors, reflect the ","cbCaivML4eorBcXU","https://ap.wps.com/l/cbCaivML4eorBcXU","pdf",388461,1,7,"English","en",105,"# Introduction\n## Learning algorithms: data, ansatz, and optimisation\n## Classical vs quantum ansatz and implementation\n## Optimisation: quantum, classical, and hybrid\n## Quantum machine learning with continuous variables and motivation\n## Canonical-variable platform and exactly solvable models\n## Dimensionless variables and formulation","[{\"question\":\"What distinguishes this quantum machine learning approach from state-based methods?\",\"answer\":\"It uses observables rather than directly manipulating quantum states. The electromagnetic field functions as the ansatz inside the learning algorithm.\"},{\"question\":\"How can the proposed learning algorithm be physically implemented?\",\"answer\":\"It can be embedded in devices that confine ions, such as ion traps or particle confinement systems that use time-dependent electromagnetic or elastic potentials for control.\"},{\"question\":\"What learning tasks are investigated in the work?\",\"answer\":\"Two supervised learning tasks are studied: regression and classification, enabled by a quantum model that is exactly solvable and supports the required operations.\"}]","Quantum Machine Learning With Canonical Variables - paper | PDF",1785722954,18,{"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":87,"head_meta":89,"extra_data":91,"updated_unix":28},"quantum-machine-learning-with-canonical-variables-paper","",{"@graph":36,"@context":86},[37,54,69],{"@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/quantum-machine-learning-with-canonical-variables-paper/119180/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04","2026-08-03",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"What distinguishes this quantum machine learning approach from state-based methods?","Question",{"text":76,"@type":77},"It uses observables rather than directly manipulating quantum states. The electromagnetic field functions as the ansatz inside the learning algorithm.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How can the proposed learning algorithm be physically implemented?",{"text":81,"@type":77},"It can be embedded in devices that confine ions, such as ion traps or particle confinement systems that use time-dependent electromagnetic or elastic potentials for control.",{"name":83,"@type":74,"acceptedAnswer":84},"What learning tasks are investigated in the work?",{"text":85,"@type":77},"Two supervised learning tasks are studied: regression and classification, enabled by a quantum model that is exactly solvable and supports the required operations.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":46,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":21,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},"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":107,"slug":138},19,"General","general"]