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Quantum computing education requires students to move beyond classical programming intuitions related to state, determinism, and debugging, and to develop reasoning skills grounded in probability, measurement, and interference. This paper…

Computers and Society · Computer Science 2026-01-27 Umar Farooq , Krishna Upadhyay

Optimizing quantum circuits is challenging due to the very large search space of functionally equivalent circuits and the necessity of applying transformations that temporarily decrease performance to achieve a final performance…

Quantum Physics · Physics 2023-07-20 Zikun Li , Jinjun Peng , Yixuan Mei , Sina Lin , Yi Wu , Oded Padon , Zhihao Jia

In quantum physics (QP) education, the use of representations such as diagrams and visual aids that connect to mathematical concepts is crucial. Research in representation theory indicates that combining symbolic-mathematical elements (e.g.…

Physics Education · Physics 2025-08-04 Linda Qerimi , Sarah Malone , Eva Rexigel , Sascha Mehlhase , Jochen Kuhn , Stefan Küchemann

Quantum machine learning is an approach that aims to improve the performance of machine learning methods by leveraging the properties of quantum computers. In quantum circuit learning (QCL), a supervised learning method that can be…

In classical theory, the physical systems are elucidated through the concepts of particles and waves, which aim to describe the reality of the physical system with certainty. In this framework, particles are mathematically represented by…

Quantum Physics · Physics 2024-09-25 Mohammad Vahid Takook , Ali Mohammad-Djafari

Quantum mechanics is a field often considered very mathematical, abstract, and unintuitive. One way some instructors are hoping to help familiarize their students with these complex topics is to have the students see quantum effects in…

Physics Education · Physics 2023-10-19 Victoria Borish , H. J. Lewandowski

Various physical constraints limit the number of qubits that can be implemented in a single quantum processor, and thus it is necessary to connect multiple quantum processors via quantum interconnects. While several compiler implementations…

Quantum Physics · Physics 2023-02-02 Shin Nishio , Ryo Wakizaka

Quantum process tomography (QPT) is a fundamental tool for fully characterizing quantum systems. It relies on querying a set of quantum states as input to the quantum process. Previous QPT methods typically employ a straightforward strategy…

Quantum Physics · Physics 2025-06-06 Jiaqi Yang , Xiaohua Xu , Wei Xie

One of the key considerations in the development of Quantum Machine Learning (QML) protocols is the encoding of classical data onto a quantum device. In this chapter we introduce the Matrix Product State representation of quantum systems…

Quantum Physics · Physics 2026-01-15 Chris Nakhl , Maxwell West , Muhammad Usman

Visual-graphical qubit representations offer a means to introduce abstract quantum concepts - such as quantum state, superposition, or measurement - in an accessible manner, particularly for learners with low prior knowledge. Building on a…

Physics Education · Physics 2025-07-30 Linda Qerimi , Sarah Malone , Eva Rexigel , Jochen Kuhn , Stefan Küchemann

Quantum Field Theory (QFT) is the basis of some of the most fundamental theories in modern physics, but it is not an easy subject to learn. In the present article we intend to pave the way from quantum mechanics to QFT for students at early…

Quantum Physics · Physics 2021-11-12 Helmut Linde

We explore the difficulties that advanced undergraduate and graduate students have with non-relativistic quantum mechanics of a single particle in one spatial dimension. To investigate these difficulties we developed a conceptual survey and…

Physics Education · Physics 2016-02-18 Guangtian Zhu , Chandralekha Singh

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

The expectation value of an observable is an important concept in quantum mechanics. However, upper-level undergraduate and graduate students in physics have both conceptual and procedural difficulties when determining the expectation value…

Physics Education · Physics 2017-01-06 Chandralekha Singh , Emily Marshman

Quantum Image Processing is a recent highlight in the quantum computing field. All previous methods for representing the images as quantum states were defined using qubits. One Quantum Image Representation (QIR) method using qutrits is…

Quantum Physics · Physics 2022-11-01 Ankit Khandelwal , M Girish Chandra

A survey was developed to probe student understanding of quantum mechanics at the beginning of graduate instruction. The survey was administered to 202 physics graduate students enrolled in first-year quantum mechanics courses from seven…

Physics Education · Physics 2016-02-23 Chandralekha Singh

We propose three core ideas: 1. the wave-particle duality of the qudit quantum space; 2. the classification of all elementary quantum gates by ordered pairs of qudit functionals; 3. a new type of quantum gates called the "quantum wave…

Quantum Physics · Physics 2022-12-22 Zixuan Hu , Sabre Kais

Quantum machine learning, as an extension of classical machine learning that harnesses quantum mechanics, facilitates effiient learning from data encoded in quantum states. Training a quantum neural network typically demands a substantial…

Quantum Physics · Physics 2026-02-17 Yongcheng Ding , Yue Ban , Mikel Sanz , José D. Martín-Guerrero , Xi Chen

Quantum entanglement remains a challenging concept to teach and visualise due to its microscopic and non-classical nature. We present innovative educational demonstration material consisting of electronic dice that simulate the properties…

Physics Education · Physics 2025-12-23 B. Folkers , A. van Rossum , A. Brinkman , H. K. E. Stadermann

Development of conceptual multiple-choice tests related to a particular physics topic is important for designing research-based learning tools to reduce the difficulties. We explore the difficulties that the advanced undergraduate and…

Physics Education · Physics 2016-02-22 Chandralekha Singh , Guangtian Zhu