[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-117461-en":3,"doc-seo-117461-105":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},117461,1374391975076,"Riley","https://ap-avatar.wpscdn.com/avatar/14000253ca4ec9f6853?x-image-process=image/resize,m_fixed,w_180,h_180&k=1783305029341752051",8,"Research & Report","Quantum machine learning optimization using Koopman operator technique","Quantum machine learning (QML) offers promising capabilities for tackling complex optimization tasks by leveraging qubit properties such as entanglement, interference, and superposition. This work investigates a Koopman operator–based strategy for quantum optimization within QML, focusing on data-driven discovery of Koopman models and the use of Koopman/transfer operators to capture nonlinear system behavior. The paper proposes a complete pipeline to encode classical dynamical systems into quantum-accessible representations, enabling quantum-suitable state-space modeling. A practical implementation framework is also provided for using the Koopman operator in QML workflows on IBM Qiskit.","Quantum machine learning optimization using Koopman operator  \ntechnique  \nSubodh Nath Pushpak1*, Sarika Jain2, Siddharth Kalra3  \n1 Amity University, Sector 125, Noida, India  \n2 Amity University, Sector 125, Noida, India  \n3 Capgemini, Australia  \n*Corresponding author E-mail: [subodh.pushpak@s.amity.edu](subodh.pushpak@s.amity.edu)  \n\n| ABSTRACT |\n| --- |\n| Quantum machine learning (QML) is a nascent field showing great potential in addressing complex problems. QML algorithms aim to combine the qubit’s properties, like entanglement, interference, and superposition, to perform better than any classical computation in specific tasks. This paper explores a new way of employing the Koopman operator to demonstrate its application to quantum optimization in quantum machine learning.\u003Cbr>Koopman operator-based quantum optimization has applications in various dynamical systems, where it can optimally capture the full nonlinear behavior of a system. This work investigates the Koopman operator approach for quantum optimization for quantum machine learning algorithms. To do so, we capitalize on recent breakthroughs in the field, such as data-driven methods for uncovering Koopman models and the application of the Koopman operator to investigate quantum machine learning optimal strategies. Specifically, we provide a strategy-driven approach with the full pipeline for encoding classical dynamical systems into quantum-accessible representation, thus employing beneficial properties of Koopman and transfer operators. This strategy enables us to represent the state space of classical systems in terms suitable for quantum computation. Here, we introduce a framework for using the Koopman operator to represent complex, high-dimensional classical dynamics on a quantum computer to enhance classical machine learning algorithms by transferring their capabilities onto quantum systems. Additionally, we provide aprogrammatical framework for using the Koopman operator in quantum machine learning frameworks on the IBM Qiskit framework. |\n| Keywords: Quantum machine learning, Koopman operator theory, Variational Quantum\u003Cbr>Eigensolver (VQE) |\n\n1. Introduction  \nAn entirely new research frontier of research in AI has emerged through the mix of machine learning and quantum computing. This compelling mix offers a whole new perspective on processing complex datasets and finding solutions to intricate problems, potentially providing efficient solutions to complex problems.  \nQuantum Machine Learning (QML) is a fascinating fusion of the remarkable qualities of qubits—like entanglement and superposition—with the power of classical machine learning algorithms. The domain of QML has been constrained due to the constraints of logical qubits present in quantum hardware and quantum information processing complexity [1][2] . Nonetheless, the NISQ (Near Immediate scale quantum) algorithms provide the techniques to optimize represent, and solve problems, despite the existing technological limitations [3][4] . The Koopman operator theory paves the way for quantum optimization methods and techniques. This paper presents the proposals and a framework for quantum optimization by means of the Koopman operator and discusses the pros and cons ofthe approach in practice. The central premise of this paper is to provide a practical approach to using the Koopman operator framework to represent classical dynamical systems. The results from  \nthe proposed approach that uses the Koopman Operator are then compared to the results with the approach without the Koopman operator [5] . This study introduces a novel framework for using the Koopman operator with QML techniques, offering a versatile and effective approach. It also demonstrates the effectiveness of this approach on precise quantum algorithms and datasets.  \nThe research is organized as follows: A comprehensive introduction to Quantum ML and Koopman Operator theory is provided in Section 1. Section 2 reviews existing literature","cbCaiqlBdHuJK2oh","https://ap.wps.com/l/cbCaiqlBdHuJK2oh","pdf",509158,1,10,"English","en",105,"# Introduction\n## Quantum ML and Koopman operator theory\n## Koopman operator theory","[{\"question\":\"What problem does this paper address in quantum machine learning optimization?\",\"answer\":\"It develops a Koopman operator–based framework to improve quantum optimization strategies within quantum machine learning algorithms.\"},{\"question\":\"How does the Koopman operator contribute to representing classical dynamics for quantum computation?\",\"answer\":\"The method uses a pipeline to encode classical dynamical systems into quantum-accessible representations, enabling state-space modeling suited for quantum processing.\"},{\"question\":\"How is the proposed approach implemented for quantum machine learning frameworks?\",\"answer\":\"The paper provides a programmatic framework for employing the Koopman operator in QML workflows using the IBM Qiskit environment.\"}]","Quantum machine learning optimization using Koopman operator technique | 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problem does this paper address in quantum machine learning optimization?","Question",{"text":76,"@type":77},"It develops a Koopman operator–based framework to improve quantum optimization strategies within quantum machine learning algorithms.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"How does the Koopman operator contribute to representing classical dynamics for quantum computation?",{"text":81,"@type":77},"The method uses a pipeline to encode classical dynamical systems into quantum-accessible representations, enabling state-space modeling suited for quantum processing.",{"name":83,"@type":74,"acceptedAnswer":84},"How is the proposed approach implemented for quantum machine learning frameworks?",{"text":85,"@type":77},"The paper provides a programmatic framework for employing the Koopman operator in QML workflows using the IBM Qiskit 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