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These lecture notes are an informal introduction to the theory of computational complexity and its links to quantum computing and statistical mechanics.

Statistical Mechanics · Physics 2009-09-25 Stephan Mertens

One hallmark of expertise in physics is the ability to translate between different representations of knowledge and use the representations that make the problem-solving process easier. In quantum mechanics, students learn about several…

Physics Education · Physics 2025-04-25 Emily Marshman , Alexandru Maries , Chandralekha Singh

The ZX-calculus was introduced as a graphical language able to represent specific quantum primitives in an intuitive way. The recent completeness results have shown the theoretical possibility of a purely graphical description of quantum…

Quantum Physics · Physics 2021-09-14 Titouan Carette , Yohann D'Anello , Simon Perdrix

We discuss the development and evaluation of quantum interactive learning tutorials (QuILTs) which are suitable for undergraduate courses in quantum mechanics. QuILTs are based on the investigation of student difficulties in learning…

Physics Education · Physics 2016-03-11 Chandralekha Singh

We introduce an abstract machine architecture for classical/quantum computations---including compilation---along with a quantum instruction language called Quil for explicitly writing these computations. With this formalism, we discuss…

Quantum Physics · Physics 2017-02-20 Robert S. Smith , Michael J. Curtis , William J. Zeng

We present an introduction to the Quantum Toolbox in Python (QuTiP) in the context of an undergraduate quantum mechanics class and potential senior research projects. QuTiP provides ready-to-use definitions of standard quantum states and…

Physics Education · Physics 2019-10-01 Andrew M. C. Dawes

These are a set of lecture notes for a mini-course I gave at The University of Warwick from October 30th to November 1st, 2024. Recordings of the lectures are available on Oleg Zaboronski's webpage at…

Probability · Mathematics 2025-12-08 Jeffrey Kuan

This article is a short review on the concept of information. We show the strong relation between Information Theory and Physics, beginning by the concept of bit and its representation with classical physical systems, and then going to the…

Physics Education · Physics 2007-05-23 F. L. Marquezino , R. R. Mello Junior

Quantum information science and technology is a rapidly growing interdisciplinary field drawing researchers from science and engineering fields. Traditional instruction in quantum mechanics is insufficient to prepare students for research…

Physics Education · Physics 2016-02-23 Chandralekha Singh

Quantum computing has shown great potential to revolutionize traditional computing and can provide an exponential speedup for a wide range of possible applications, attracting various stakeholders. However, understanding fundamental quantum…

Human-Computer Interaction · Computer Science 2025-03-04 Manusha Karunathilaka , Shaolun Ruan , Lin-Ping Yuan , Jiannan Li , Zhiding Liang , Kavinda Athapaththu , Qiang Guan , Yong Wang

We describe the difficulties advanced undergraduate and graduate students have with concepts related to addition of angular momentum in quantum mechanics. We also describe the development and implementation of a research-based learning…

Physics Education · Physics 2016-04-05 Guangtian Zhu , Chandralekha Singh

These lecture notes aim to provide a clear and comprehensive introduction to using open quantum system theory for quantum algorithms. The main arguments are Variational Quantum Algorithms, Quantum Error Correction, Dynamical Decoupling and…

Quantum Physics · Physics 2024-06-18 Matteo Carlesso

Lecture Notes of the Les Houches Summer School 2003 on Quantum entanglement and information processing to be published as P. Zoller, J. I. Cirac, Luming Duan and J. J. Garcia-Ripoll, in "Quantum entanglement and information processing",…

Quantum Physics · Physics 2009-09-29 P. Zoller , J. I. Cirac , Luming Duan , J. J. Garcia-Ripoll

This is an informal introduction to the ideas of decoherence and emergent classicality, including a simple account of the decoherent histories approach to quantum theory. It is aimed at undergraduates with a basic appreciation of quantum…

Quantum Physics · Physics 2009-11-11 J. J. Halliwell

The educational value of a fully diagrammatic approach in a scientific field has never been explored. We present Quantum Picturalism (QPic), an entirely diagrammatic formalism for all of qubit quantum mechanics. This framework is…

We describe the difficulties advanced undergraduate and graduate students have with quantum measurement. To reduce these difficulties, we have developed research-based learning tools such as the Quantum Interactive Learning Tutorial (QuILT)…

Physics Education · Physics 2016-02-19 Guangtian Zhu , Chandralekha Singh

The Institute of Physics New Quantum Curriculum consists of freely available online learning and teaching materials (quantumphysics.iop.org) for a first course in university quantum mechanics starting from two-level systems. This approach…

By popular request we post these old (from 2001) lecture notes of the Varenna Summer School Proceedings. The original was published as J. I. Cirac, L. M. Duan, and P. Zoller, in "Experimental Quantum Computation and Information" Proceedings…

Quantum Physics · Physics 2009-09-29 J. I. Cirac , L. M. Duan , P. Zoller

These lecture notes cover undergraduate textbook topics (e.g. as in Sakurai), and also additional advanced topics at the same level of presentation. In particular: EPR and Bell; Basic postulates; The probability matrix; Measurement theory;…

Quantum Physics · Physics 2018-08-30 Doron Cohen

These notes offer a basic introduction to the primary mathematical concepts of quantum physics, and their physical significance, from the operator and Hilbert space point of view, highlighting more what are essentially the abstract…

High Energy Physics - Theory · Physics 2008-12-04 Jan Govaerts