[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118592-en":3,"doc-seo-118592-105":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},118592,1374391974585,"Genevieve","https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c",8,"Research & Report","Quantum Machine Learning and Quantum Protocols for Solving Differential Equations - Thesis Abstract","Quantum devices are developed to compute in ways that differ fundamentally from classical computers, leveraging superposition and entanglement while also facing significant noise. This thesis addresses how quantum computing may achieve practical advantage for problems that are difficult to solve with today’s methods, with emphasis on quantum machine learning and variational quantum algorithms. Differential equations are identified as a high-impact application domain. The work presents four developed algorithms, including approaches using quantum function models, the parameter shift rule, kernel methods, quantile mechanics, and a collaborative transform between computational and Chebyshev space for encoding physics-informed constraints.","Quantum Machine Learning and Quantum Protocols for Solving Differential Equations  \nSubmitted by Annie Paine to the University of Exeter as a thesis for the degree of Doctor of Philosophy in Physics, February 2024 .  \nThis thesis is available for Library use on the understanding that it is copyright material and that no quotation from the thesis may be published without proper  \nacknowledgement.  \nI certify that all material in this thesis which is not my own work has been identified and that any material that has previously been submitted and approved for the award of a  \ndegree by this or any other University has been acknowledged.  \nAbstract  \nQuantum devices are being developed to perform computation in an inherently non-classical way. These devices are fundamentally different from conventional computers and have unique properties due to effects such as superposition and entanglement. At the same time, quantum devices are prone to noise, posing limitations on the depth of calculations and scaling. It remains an important challenge for quantum computing to offer advantage in solving of currently intractable industrial problems.  \nOne rising area of quantum algorithms is quantum machine learning. Building off classical machine learning, quantum machine learning concerns the training of quantum models to learn and recognise relationships in data. Another class is variational quantum algorithms which utilise an optimisation loop to train a trial solution involving quantum evaluations to solve a given problem. These classes of algorithm have possibility of advantage for problems with large amounts of data or large search spaces due to the wide range of functions expressible and data encodable because of the exponential working space.  \nA possible area of application is differential equations. Differential equations govern many areas of industrial and research interest, from aerodynamics to finance to chemistry, yet many instances remain difficult to solve classically. Throughout my research I have considered solving differential equations with quantum machine learning and variational approaches.  \nIn my thesis I describe four algorithms that I have developed for solving differential equations, each with different strengths and weaknesses, quantum resource requirements and areas of applications. Particular techniques utilised are quantum models representing functions, the parameter shift rule, kernel methods and quantile mechanics. Additionally, I (in collaboration) develop a technique to transform between computational and Chebyshev space. This technique is utilised  \nfor developing the algorithm for efficient encoding of physics-informed constraints into quantum models. I conclude this thesis with an outlook into the nascent area of quantum scientific machine learning.  \nPublications and Manuscripts  \n1. A. E. Paine, V. E. Elfving, and O. Kyriienko, Physics-informed quantum machine learning: Solving nonlinear differential equations in latent spaces without costly grid evaluations, Aug. 2023. arXiv:2308.01827 [quant-ph]  \n2. A. E. Paine, V. E. Elfving, and O. Kyriienko, Quantum quantile mechanics: Solving stochastic differential equations for generating time-series, Advanced Quantum Technologies, p. 2 300 065, Aug. 2023  \n3. C. Umeano, A. E. Paine, V. E. Elfving, and O. Kyriienko, What can we learn from quantum convolutional neural networks?, Aug. 2023. arXiv:  \n2308.16664 [quant-ph]  \n4. C. A. Williams∗ , A. E. Paine∗ , H.-Y. Wu, V. E. Elfving, and O. Kyriienko, Quantum Chebyshev transform: Mapping, embedding, learning and sampling distributions, Jun. 2023. arXiv: 2306.17026 [quant-ph](∗ co-first authors)  \n5. A. E. Paine, V. E. Elfving, and O. Kyriienko, Quantum kernel methods for solving regression problems and differential equations, Phys. Rev. A, vol. 107, p. 032 428, 3 Mar. 2023  \n6. O. Kyriienko, A. E. Paine, and V. E. Elfving, Protocols for trainable and differentiable quantum generative modelling Feb. 2022. arXiv: 2202","cbCaimKmG9cdlNpy","https://ap.wps.com/l/cbCaimKmG9cdlNpy","pdf",7135379,1,249,"English","en",105,"# Definitions\n# Introduction\n## Aims & Objectives\n## Thesis Overview\n# Background\n## Introduction to Quantum Computing\n## Variational Quantum Algorithms Overview\n## Classical & Quantum Machine Learning Overview\n## Quantum Models of Functions\n# Publications and Manuscripts","[{\"question\":\"Why do quantum devices differ from conventional computers, and what limitation does noise introduce?\",\"answer\":\"Quantum devices use superposition and entanglement, enabling inherently non-classical computation. Noise limits circuit depth and reduces scalability for larger problems.\"},{\"question\":\"What are the main algorithm classes discussed in the thesis for quantum machine learning?\",\"answer\":\"The thesis covers quantum machine learning models trained to learn relationships in data, and variational quantum algorithms that use an optimization loop with quantum evaluations to train a trial solution.\"},{\"question\":\"How does the thesis approach solving differential equations using quantum methods?\",\"answer\":\"It develops four algorithms for differential equations, using techniques such as quantum function models, the parameter shift rule, kernel methods, quantile mechanics, and a Chebyshev-space transform to efficiently encode physics-informed constraints.\"}]","Quantum Machine Learning and Quantum Protocols for Solving Differential Equations - Thesis Abstract | PDF",1785684418,627,{"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-and-quantum-protocols-for-solving-differential-equations-thesis-abstract","",{"@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-and-quantum-protocols-for-solving-differential-equations-thesis-abstract/118592/",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","2026-08-05","2026-08-02",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},"Why do quantum devices differ from conventional computers, and what limitation does noise introduce?","Question",{"text":76,"@type":77},"Quantum devices use superposition and entanglement, enabling inherently non-classical computation. Noise limits circuit depth and reduces scalability for larger problems.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"What are the main algorithm classes discussed in the thesis for quantum machine learning?",{"text":81,"@type":77},"The thesis covers quantum machine learning models trained to learn relationships in data, and variational quantum algorithms that use an optimization loop with quantum evaluations to train a trial solution.",{"name":83,"@type":74,"acceptedAnswer":84},"How does the thesis approach solving differential equations using quantum methods?",{"text":85,"@type":77},"It develops four algorithms for differential equations, using techniques such as quantum function models, the parameter shift rule, kernel methods, quantile mechanics, and a Chebyshev-space transform to efficiently encode physics-informed constraints.","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},[94,98,102,106,111,116,121,124,129,132,136],{"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":117,"doc_module":4,"doc_module_name":46,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":46,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":46,"category_name":138,"show_sort_weight":107,"slug":139},19,"General","general"]