[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-127265-en":3,"doc-seo-127265-105":30,"detail-sidebar-cat-0-en-105":83},{"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},127265,2336475104362,"Eden","https://ap-avatar.wpscdn.com/avatar/22000c4c46a41b752dd?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786595829695023868",8,"Research & Report","State preparation for quantum machine learning - Bachelor’s thesis","Quantum state preparation is essential for many gate-based quantum algorithms, yet there is no universally established framework for encoding classical data onto quantum devices. This bachelor’s thesis researches and compares leading quantum state preparation approaches tailored to quantum machine learning, where encoded data often requires very high dimensions. It covers both exact methods and approximate variational quantum circuit techniques, followed by implementations and experimental evaluation across selected algorithms.","Assignment of bachelor’s thesis  \nTitle: State preparation for quantum machine learning  \nStudent: Martin Vidmar  \nSupervisor: Ing. Daniel Vašata, Ph. D.  \nStudy program: Informatics  \nBranch / specialization: Artificial Intelligence 2021  \nDepartment: Department of Applied Mathematics  \nValidity: until the end of summer semester 2024/2025  \nInstructions  \nQuantum state preparation is a vital routine in many quantum algorithms, including a solution of linear systems of equations, Monte Carlo simulations, quantum sampling, and machine learning. However, to date, there is no established framework for encoding classical data into gate-based quantum devices.  \nThe aim of the thesis is to research and compare various state-of-the-art approaches of quantum state preparation suitable for quantum machine learning where the need for very high dimension of encoded data is significant.  \nThe thesis should focus on both exact algorithms and approximative methods based on variational quantum circuits that produce approximate states that are, however, sufficient in machine learning applications.  \nDetailed assignment points:  \n1) Research state-of-the-art algorithms for quantum state preparation. Focus both on exact and approximate methods.  \n2) Select at least two methods suitable for quantum machine learning.  \n3) Implement and experimentally compare selected algorithms. Discuss their benefits  \nand drawbacks.  \nElectronically approved by Ing. Magda Friedjungová, Ph.D. on 14 February 2024 in Prague.  \nBachelor’s thesis  \nSTATE PREPARATION FOR QUANTUM MACHINE LEARNING  \nMartin Vidmar  \nFaculty of Information Technology Katedra aplikovan´e matematiky Supervisor: Ing. Danial Vaˇsata, Ph.D.  \nMay 13, 2025  \nCzech Technical University in Prague Faculty of Information Technology © 2024 Martin Vidmar. All rights reserved.  \nThis thesis is school work as defined by Copyright Act of the Czech Republic. It has been submitted at Czech Technical University in Prague, Faculty of Information Technology. The thesis is protected by the  \nCopyright Act and its usage without author’s permission is prohibited (with exceptions defined by the Copyright Act) .  \nCitation of this thesis: Vidmar Martin. State preparation for quantum machine learning. Bachelor’s thesis. Czech Technical University in Prague, Faculty of Information Technology, 2024 .  \nContents  \nAcknowledgments vii  \nDeclaration viii  \nAbstract ix  \n1 Theory of quantum computation 3  \n1. 1 A note on notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3  \n1.2 Introduction to quantum information   5  \n1.2.1 Single systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5  \n1.2.2 Multiple systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6  \n1.2.3 Measuring quantum states . . . . . . . . . . . . . . . . . . . . . . . . . . . 7  \n1.2.4 Evolution of quantum systems . . . . . . . . . . . . . . . . . . . . . . . . 9  \n1.2.5 The density operator and mixed states . . . . . . . . . . . . . . . . . . . . 9  \n1.2.6 Fidelity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12  \n1.2.7 The Schmidt decomposition   12  \n1.3 An overview of quantum computing . . . . . . . . . . . . . . . . . . . . . . . . . 14  \n1.3. 1 Qubits   15  \n1.3.2 Single qubit operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16  \n1.3.3 Multiple qubits and measurements . . . . . . . . . . . . . . . . . . . . . . 18  \n1.3.4 Controlled (conditional) operations ...................... 18  \n1.3.5 Uniformly controlled (multiplexed) operations ................ 21  \n1.3.6 Isometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24  \n1.3.7 Universality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25  \n2 Applications thereof 27  \n2. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27  \n2.2 Quantum machine learning . . . . . . . . . . . . . . . . . . . . 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