[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-119548-en":3,"doc-seo-119548-105":30,"detail-sidebar-cat-0-en-105":91},{"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},119548,1374391974564,"Clementine","https://ap-avatar.wpscdn.com/avatar/14000253aa45c000a9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779874745381141002",8,"Research & Report","Can Atoms Learn how to Read? - On the use of Quantum Systems in Machine Learning","This master thesis investigates a novel machine learning approach that exploits the complex dynamics of small quantum systems driven by strong time-dependent electric fields to enable computations on ultrafast timescales. Training results obtained for simulated hydrogen atoms are compared across different machine learning frameworks using a handwritten digit recognition task. Geometric and chaos-theory tools quantify internal dynamical complexity and relate ordered-to-chaotic phase transitions to successful trainability. Similar “computation at the edge of chaos” behavior is discussed in broader contexts.","Faculty of Physics and Astronomy University of Heidelberg  \nMaster Thesis In Physics  \nsubmitted by Maurice Béringuier  \nborn in Berlin  \n2025  \nCan Atoms Learn how to Read?  \nOn the use of Quantum Systems in Machine Learning  \nThis Master Thesis has been carried out by  \nMaurice Béringuier  \nat the  \nMax Planck Institute for Nuclear Physics  \nDivision Quantum-Dynamics & -Control  \nunder the supervision of  \nProf. Dr. Thomas Pfeifer  \nand  \nPriv.-Doz. Dr. Christian Ott  \nZusammenfassung  \nKönnen Atome Lesen lernen? Über die Nutzung von Quantensystemen im Maschinellen Lernen: In dieser Arbeit erforschen wir einen neuen Ansatz für maschinelles Lernen, dessen Kernidee darin besteht, die Komplexität der Dynamik in kleinen Quantensystemen unter dem Einfluss zeitabhängiger Felder zu nutzen, um Berechnungen auf ultraschnellen Zeitskalen durchzuführen Wir vergleichen die Ergebnissedes Trainings von simulierten Wasserstoffatomen mithilfe verschiedener Frameworks des Maschinellen Lernens anhand der beispielhaften Aufgabe der Erkennung handgeschriebener Ziffern. Wir verwenden Methoden aus der Geometrie und der Chaostheorie, um die Komplexität der internen Dynamik von Quantensystemen zu quantifizieren und eine Beziehung zwischen Phasenübergängen von geordnetem zu chaotischem Verhalten und der Fähigkeit eines Quantensystems, erfolgreich trainiert zu werden, aufzuzeigen. Ähnliche Zusammenhänge wurden bereits in anderen Systemen beobachtet und mit dem Schlagwort \"Computation at the Edge of Chaos\" versehen.  \nAbstract  \nCan atoms learn how to read? On the use of quantum systems in machine learning: In this thesis we explore a novel approach to machine learning based on exploiting the complexity of the dynamics of small quantum systems evolving in strong time-dependent electric fields to perform computations on ultrafast time scales  We compare the results of training simulated hydrogen atoms in different machine learning frameworks on the exemplary task of recognizing handwritten digits. We use methods from geometry and chaos theory to quantify the complexity of the internal dynamics of quantum systems to demonstrate a relationship between phase transitions from ordered to chaotic behaviour and the ability of a quantum system to be trained successfully. Similar relationships have been observed in other systems before and been given the moniker \"Computation at the Edge of Chaos\".  \nDanksagung  \nFür ihre Unterstützung bin ich meinen Freunden und meiner Familie sehr dankbar, allen voran die meiner Partnerin Salo, die mich oft zur Arbeit angespornt, mich manchmal willkommenerweise von ihr abgelenkt und außerdem diesen Text probegelesen hat.  \nAm MPIK (und anderswo in Heidelberg) gibt es viele Menschen die mir mit wertvollen Diskussionen geholfen haben; Christian, Gergana, Alex, Erwin, Carl und Leonard sind nur ein paar davon. Besonderer Dank gebührt Annwoy den ich für (leider nur) kurze Zeit als Praktikant betreuen durfte und der einen kleinen Beitrag zu dieser Arbeit beigesteuert hat.  \nIch danke auch Rebekka und Alexandra, die mir halfen mich nicht in Bürokratiedschungeln zu verirren und Kevin, der die Lösung für alle Linuxprobleme kennt, meine Kommandozeilenbefehle korrigiert und mir zu Weihnachten längere Rechenzeit auf dem Cluster geschenkt hat.  \nZu guter Letzt gebührt natürlich Thomas eine Menge Dank, der es wunderbar versteht Menschen in ihren Leidenschaften zu fördern, wovon auch ich profitierendurfte.  \nContents  \n1 Introduction 4  \n1.1 Motivation ................................. 4  \n1.2 Previous Work .............................. 4  \n2 Methods 8  \n2.1 Modeling Atomic Physics ......................... 8  \n2.1.1 The Hydrogen Atom ....................... 8  \n2.1.2 Simple Models of Vibrating Molecules .............. 9  \n2.1.3 Solving the Time-Dependent Schrödinger Equation ...... 11  \n2.1.4 Absorption Spectra ........................ 13  \n2.2 Some Fundamentals of Machine Learning ................ 14  \n2.2.1 Training of Machine Learning M","cbCairVuja54uIJu","https://ap.wps.com/l/cbCairVuja54uIJu","pdf",5703389,1,52,"English","en",105,"# Introduction\n## Motivation\n## Previous Work\n# Methods\n## Modeling Atomic Physics\n## Some Fundamentals of Machine Learning\n## Quantifying Chaos\n## Learning Atoms\n# Results\n## Training of Atoms\n## Differentiable Simulators\n## Trainability as a Function of Electric Field Amplitudes\n## Computation at the Edge of Chaos\n# Discussion\n## Conclusion\n## Caveats and Considerations\n## Outlook\n## Appendix A Conventions, Units and Constants\n## Appendix B Additional Learning Curves\n## References","[{\"question\":\"What is the core idea of the thesis’s machine learning approach?\",\"answer\":\"The thesis uses atoms or molecules as nanoscale computers by leveraging the complex, nonlinear dynamics of small quantum systems under time-dependent electric fields for ultrafast computation.\"},{\"question\":\"How are the learning experiments evaluated?\",\"answer\":\"The work compares training outcomes for simulated hydrogen atoms across different machine learning frameworks using an example task: recognizing handwritten digits.\"},{\"question\":\"Which tools are used to analyze the quantum dynamics and learning success?\",\"answer\":\"Methods from geometry and chaos theory are used to quantify internal dynamical complexity and to link ordered-to-chaotic phase transitions with how successfully the quantum system can be trained.\"}]","Can Atoms Learn how to Read? 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