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arXiv:2011.01029

Quanteninformationsverarbeitung in der Gymnasialen Oberstufe

Andreas J. C. Woitzik

Published Oct 29, 2020• 3 citations
arXivHTMLPDF

Abstract

Quantum Information Processing is usually taught as an elective in the master's degree in physics. We argue that a basic understanding of Quantum Information Processing can already be achieved by high school juniors and seniors. Moreover, we explain why it is useful to teach Quantum Information at this level and describe a teaching unit which has already been tested in the classroom. We will hereby focus on didactical reductions and describe some physical basics.

DOI
10.48550/arxiv.2011.01029

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Quantum Information Processing is usually taught as an elective in the master's degree in physics. We argue that a basic understanding of Quantum Information Processing can already be achieved by high school juniors and seniors. Moreover, we explain why it is useful to teach Quantum Information at this level and describe a teaching unit which has already been tested in the classroom. We will hereby focus on didactical reductions and describe some physical basics.
We present a simple, accessible, yet rigorous outreach/educational program focused on quantum information science and technology for high-school and early undergraduate students. This program allows students to perform meaningful hands-on calculations with quantum circuits and algorithms, without requiring knowledge of advanced mathematics. A combination of pen-and-paper exercises and IBM Q simulations helps students understand the structure of quantum gates and circuits, as well as the principles of superposition, entanglement, and measurement in quantum mechanics.
Quantum physics is a long established content in high school curricula. More recently, alternative approaches based on information-theoretical formulations of quantum theory have been discussed, in which conceptual emphases change in comparison to established didactical approaches. In particular, the notions of "superposition" and "entanglement" are brought into the center of discussion in these approaches. Likewise, there is a broad public interest in the new applications of quantum physics such as quantum computing, which has led to a variety of popular depictions. In this paper we identify common inaccuracies and errors in these representations, explain the technical background and make first recommendations to avoid misunderstandings. Our initial focus is on the notion of "superposition". -- Die Quantenphysik ist seit vielen Jahren ein etablierter Inhalt der Oberstufenphysik. In jüngerer Zeit werden alternative Zugänge über die informationstheoretische Formulierung der Quantentheorie diskutiert, bei denen sich konzeptionelle und begriffliche Schwerpunkte im Vergleich zu etablierten Elementarisierungen verändern. Im Besonderen die Begriffe "Superposition" und "Verschränkung" werden bei diesen Zugängen in das Zentrum der Diskussion gerückt. Ebenfalls besteht ein breites öffentliches Interesse an den neuen Anwendungen der Quantenphysik wie dem Quanten-computer, das zu einer Vielzahl populärer Darstellungen geführt hat. In dieser Arbeit identifizieren wir verbreitete Ungenauigkeiten und Fehler in diesen Darstellungen, erläutern den fachlichen Hintergrund und machen erste Empfehlungen, um Missverständnisse zu vermeiden. Unser Schwerpunkt liegt dabei zunächst auf dem Begriff der "Superposition".
This bachelor thesis deals with the creation of a Czech didactic text for teaching quantum algorithms at high schools. The thesis describes five basic quantum algorithms, namely Deutsch's, Deutsch-Jozsa, Bernstein-Vazirani, Simon's, and Grover's, which uti- lize a quantum oracle and form a theoretical foundation for more complex quantum algorithms. The theoretical explanation is supplemented with motivational and illustra- tive examples. The individual procedures are elaborated in such a way that the text is fully comprehensible to students at an upper secondary school level of knowledge. To facilitate orientation in the subject matter, an introductory chapter was created, summa- rizing the reader's expected knowledge and the necessary mathematical apparatus. The thesis concludes with a chapter providing a comprehensive summary of all the described algorithms.
Abstract Based on a series of courses taught by the authors, this theoretical-physics textbook takes the reader on a journey from the beginnings of quantum theory in the early twentieth century to the realm of quantum-information processing in the twenty-first. It provides an introductory text on quantum mechanics and quantum information theory for undergraduate students in physics and related subjects, but also serves as a resource for graduate students who want to engage with more advanced topics, while offering a collection of derivations, proofs, technical methods, and references for graduate students and more experienced readers engaged with teaching and active research.
Teaching and learning QM at high school as well as the undergraduate level is a highly non-trivial task. Indeed, major changes are required in understanding the new physical reality, and students have to deal with counterintuitive concepts such as uncertainty and entanglement as well as advanced mathematical tools. In order to overcome these critical issues, a simple approach is presented here, which is based solely on two-vector and 2 × 2 matrix algebra. Furthermore, it could also enable educational institutions to fill the gap between high school curricula and the current scientific and technological advances in physics by allowing students to gain some insight into topics such as qubits and quantum computers. The inspiration behind our proposal as well as its firm theoretical foundation are based on the famous Umdeutung (reinterpretation) paper by W. Heisenberg, which introduces QM in matrix form.
Discover the foundations of quantum mechanics, and explore how these principles are powering a new generation of advances in quantum engineering, in this ground-breaking undergraduate textbook. It explains physical and mathematical principles using cutting-edge electronic, optoelectronic and photonic devices, linking underlying theory with real-world applications; focuses on current technologies and avoids historic approaches, getting students quickly up-to-speed to tackle contemporary engineering challenges; provides an introduction to the foundations of quantum information, and a wealth of real-world quantum examples, including quantum well infrared photodetectors, solar cells, quantum teleportation, quantum computing, band gap engineering, quantum cascade lasers, low-dimensional materials, and van der Waals heterostructures; and includes pedagogical features such as objectives and end-of-chapter homework problems to consolidate student understanding, and solutions for instructors. Designed to inspire the development of future quantum devices and systems, this is the perfect introduction to quantum mechanics for undergraduate electrical engineers and materials scientists.