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Cognitive diagnosis, the goal of which is to obtain the proficiency level of students on specific knowledge concepts, is an fundamental task in smart educational systems. Previous works usually represent each student as a trainable…

Artificial Intelligence · Computer Science 2021-11-18 Hengyao Bao , Xihua Li , Xuemin Zhao , Yunbo Cao

In this paper we present a simple algorithm for representation of statistical data of any origin by complex probability amplitudes. Numerical simulation with Mathematica-6 is performed. The Bloch's sphere is used for visualization of…

Quantum Physics · Physics 2008-03-11 Andrei Khrennikov

Unlike classical bits that can only occupy one of two discrete states, quantum bits (qubits) can exist in arbitrary coherent superpositions of the ground and excited states. This fundamental distinction grants qubits enhanced capabilities…

Quantum Physics · Physics 2025-05-28 Xiao-Meng Zhang , Guang-Chen He , Zhao-Xian Chen , Ze-Guo Chen , Ming-Hui Lu , Yan-Feng Chen

The revolutionary new field of Quantum Computing (QC) continues to gain attention in industry, academia, and government in both research and education. At educational institutions, there is a proliferation of introductory courses at various…

Physics Education · Physics 2025-07-15 Beth Thacker , Jianlan Wang , Yuanlin Zhang , Quy Ban Tran , Divya Sree Vemula , Tunde Kushimo

The qutrit comes next in complexity after qubit as a resource for quantum information processing. The qubit density matrix can be easily visualized using Bloch sphere representation of its states. In contrast, this simplicity is in general…

Quantum Physics · Physics 2017-09-29 Vinod K. Mishra

Understanding the structure of multi-qubit quantum states is essential for both quantum information research and education, yet intuitive visualization beyond the single-qubit Bloch sphere remains challenging. In this work, we propose a…

Quantum Physics · Physics 2026-03-11 Satoru Shoji

The similarities between gated quantum dots and the transistors in modern microelectronics - in fabrication methods, physical structure, and voltage scales for manipulation - have led to great interest in the development of quantum bits…

Three unit spheres were used to represent the two-qubit pure states. The three spheres are named the base sphere, entanglement sphere, and fiber sphere. The base sphere and entanglement sphere represent the reduced density matrix of the…

Quantum Physics · Physics 2020-08-04 C. R. Wie

Research-validated multiple-choice questions comprise an easy-to-implement instructional tool that serves to scaffold student learning and formatively assess students' knowledge. We present findings from the implementation, in consecutive…

Physics Education · Physics 2024-05-30 Peter Hu , Yangqiuting Li , Chandralekha Singh

The Bloch Sphere visualization of the possible states of a single qubit has proved a useful pedagogical and conceptual tool as a one-to-one map between qubit states and points in a 3-D space. However, understanding many important concepts…

Quantum Physics · Physics 2024-05-31 Li-Heng Henry Chang , Shea Roccaforte , Ziyu Xu , Paul Cadden-Zimansky

In the field of quantum information science and technology, the representation and visualization of quantum states and related processes are essential for both research and education. In this context, a focus especially lies on ensembles of…

Transfer of learning is an important objective of education. However, students usually have difficulties in solving physics transfer tasks even after having solved similar problems previously. We investigated if instruction provided using…

Physics Education · Physics 2017-01-18 Tianlong Zu , Elise Agra , John Hutson , Lester C. Loschky , N. Sanjay Rebello

We provide new examples of pure entangled systems related to cluster state quantum computation that can be efficiently simulated classically. In cluster state quantum computation input qubits are initialised in the `equator' of the Bloch…

Quantum Physics · Physics 2024-02-07 Sahar Atallah , Michael Garn , Sania Jevtic , Yukuan Tao , Shashank Virmani

This paper presents the findings of pedagogical research on the efficacy of a virtual laboratory platform in general education courses on quantum information science. Specifically, a virtual laboratory activity based on the Bell test has…

Physics Education · Physics 2026-03-25 Hongbin Song

Visual methods are of great utility in understanding and interpreting quantum mechanics at all levels of understanding. The Bloch sphere, for example, is an invaluable and widely used tool for visualising quantum dynamics of a two level…

Quantum Physics · Physics 2023-04-26 Max Z. Festenstein

Quantum Information Science (QIS) is a vast, diverse, and abstract field. In consequence, learners face many challenges. Science, Technology, Engineering, and Mathematics (STEM) education research has found that visualizations are valuable…

An ability to describe quantum states directly by average values of measurement outcomes is provided by the Bloch vector. For an informationally complete set of measurements one can construct unique Bloch vector for any quantum state.…

Quantum Physics · Physics 2013-03-21 Pawel Kurzynski

Quantum computers may outperform classical computers on machine learning tasks. In recent years, a variety of quantum algorithms promising unparalleled potential to enhance, speed up, or innovate machine learning have been proposed. Yet,…

Quantum mechanics is difficult to learn because it is counterintuitive, hard to visualize, mathematically challenging, and abstract. The Physics Education Technology (PhET) Project, known for its interactive computer simulations for…

Physics Education · Physics 2009-11-13 S. B. McKagan , K. K. Perkins , M. Dubson , C. Malley , S. Reid , R. LeMaster , C. E. Wieman

The QuVis Quantum Mechanics Visualization project aims to address challenges of quantum mechanics instruction through the development of interactive simulations for the learning and teaching of quantum mechanics. In this article, we…

Physics Education · Physics 2015-06-11 Antje Kohnle , Charles Baily , Anna Campbell , Natalia Korolkova , Mark J. Paetkau