[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117132-en":3,"doc-seo-117132-105":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},117132,549758252649,"Ivy","https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819",8,"Research & Report","Fourier series weight in quantum machine learning","The work investigates how Fourier series weighting influences quantum machine learning models. It builds a quantum machine learning approach based on Hamiltonian encoding and introduces trigonometric interpolation, binary and multiclass quantum classifiers, and a quantum signal processing application. It further presents a block-diagram approach to approximately determine Fourier coefficients using quantum machine learning. All proposed models are implemented and tested with the PennyLane framework to evaluate their behavior and effectiveness for Fourier-related quantum tasks.","arXiv :2302 .00105v2 [ quant-ph] 26 Feb 2024  \nFourier series weight in quantum machine learning  \nParfait Atchade-Adelomou 1, 2, 3 and Kent Larson 1  \n1 MIT Media Lab - City Science Group, Cambridge, USA ∗  \n2 Smart Society Research Group - La Salle - Universitat Ramon Llull  \nCarrer de Sant Joan de La Salle, 42 08022 Barcelona (Spain) †  \n3 Lighthouse Disruptive Innovation Group, LLC 7 Broadway Terrace, Apt 1 Cambridge MA 02139 Middlesex County, Massachusetts (USA) ‡  \n(Dated: Feb 2023)  \nIn this work, we aim to confirm the impact of the Fourier series on the quantum machine learning model. We will propose models, tests, and demonstrations to achieve this objective. We designed a quantum machine learning leveraged on the Hamiltonian encoding. With a subtle change, we performed the trigonometric interpolation, binary and multiclass classifier, and a quantum signal processing application. We also proposed a block diagram of determining approximately the Fourier coefficient based on quantum machine learning. We performed and tested all the proposed models using the Pennylane framework.  \nKeyWords: Quantum Computing, Quantum Machine Learning, Fourier Series, QML, QSP, Interpolation, Regression model, quantum classifiers  \nI. INTRODUCTION  \nThe Fourier series, adept at decomposing complex functions into simpler trigonometric components, aligns seamlessly with quantum computing’s intrinsic properties, such as superposition and interference. This synergy results in a more effective and precise representation of quantum information, significantly enhancing data processing, analysis, and exploring periodic patterns within quantum data. This work delves into the profound advantages of Fourier series applications in Quantum Machine Learning (QML), contrasting their unique alignment with quantum computing against conventional methodologies.  \nThe Fourier series is a mathematical tool that allows us to model any arbitrary periodic signal with a combination of sines and cosines. Its main advantage is that more signal information is needed during the transformation from one domain to another. Indeed, this series does not exist for all signals (Dirichlet conditions[1]); however, in various fields and sectors, the Fourier series is the tool used to transform a signal from the time domain to the frequency domain, breaking it down into harmonically related sinusoidal functions. In quantum computing and specifically in the branch of quantum machine learning (QML), a quantum model is described by a parametric function f (x,θ) subject to some independent variables x that could be our input data and some parameters θ that help our function to attempt to generalize itself across the input data. Taking this into account and knowing the tremendous impact that the Fourier series has on signal processing, it is therefore of great interest to analyze and experiment to see how the Fourier series impacts the quantum models thus, if it could help us in  \n∗ [parfait@mit.edu](parfait@mit.edu)  \n† [parfait.atchade@salle.url.edu](parfait.atchade@salle.url.edu)[ ](parfait.atchade@salle.url.edu)‡ [parfait.atchade@lighthouse-dig.com](parfait.atchade@lighthouse-dig.com)  \nquantum trigonometric interpolation techniques, regression models, etc. In this article, we will highlight the importance of the Fourier series in solving real problems with quantum machine learning. We will also propose a generic quantum circuit that, with little change, can help us solve classification problems, interpolation for banking problems, and signal processing, among others. Complementing this, our method incorporates classical preprocessing techniques to optimize the interplay between data and quantum algorithms. By normalizing and adapting data, we ensure coherent and quantum-compatible inputs, thereby maximizing the efficiency of information encoding within quantum circuits. This holistic approach not only elevates the performance of quantum algorithms but also fosters innovation in","cbCaisSYrlucpYzg","https://ap.wps.com/l/cbCaisSYrlucpYzg","pdf",1993848,1,13,"English","en",105,"# Introduction\n# Motivation\n# Related Work\n# Quantum machine learning framework and Hamiltonian connection\n# Fourier series scenarios and proposed models\n# Model analysis and universality steps\n# Results\n# Discussion and implications\n# Conclusion and future directions","[{\"question\":\"What is the main goal of the document?\",\"answer\":\"To confirm the impact of the Fourier series on quantum machine learning models by proposing models, tests, and demonstrations tied to Fourier-series structure.\"},{\"question\":\"How do the authors construct their quantum machine learning approach?\",\"answer\":\"They design a quantum machine learning model leveraging Hamiltonian encoding, and then apply trigonometric interpolation, quantum classifiers, and quantum signal processing.\"},{\"question\":\"Which tools are used to implement and evaluate the proposed models?\",\"answer\":\"The models are implemented and tested using the PennyLane framework.\"}]","Fourier series weight in quantum machine learning | 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is the main goal of the document?","Question",{"text":76,"@type":77},"To confirm the impact of the Fourier series on quantum machine learning models by proposing models, tests, and demonstrations tied to Fourier-series structure.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How do the authors construct their quantum machine learning approach?",{"text":81,"@type":77},"They design a quantum machine learning model leveraging Hamiltonian encoding, and then apply trigonometric interpolation, quantum classifiers, and quantum signal processing.",{"name":83,"@type":74,"acceptedAnswer":84},"Which tools are used to implement and evaluate the proposed models?",{"text":85,"@type":77},"The models are implemented and tested using the PennyLane 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