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The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual…

Mathematical Physics · Physics 2009-11-13 Eduardo J. S. Villaseñor

Here we review some of the recent developments in Quantum Optics. After a brief introduction to the historical development of the subject, we discuss some of the modern aspects of quantum optics including atom field interactions, quantum…

Quantum Physics · Physics 2019-02-25 Subhashish Banerjee , Arun Jayannavar

In this introductory review, we focus on applications of quantum computation to problems of interest in physics and chemistry. We describe quantum simulation algorithms that have been developed for electronic-structure problems,…

Quantum Physics · Physics 2014-04-16 Man-Hong Yung , James D. Whitfield , Sergio Boixo , David G. Tempel , Alán Aspuru-Guzik

Quantum information science is presented in a fashion that may be useful to a device or materials engineer. Spintronic implementations are emphasized.

Mesoscale and Nanoscale Physics · Physics 2007-05-23 S. Bandyopadhyay

Quantum computing is a highly abstract scientific discipline, which, however, is expected to have great practical relevance in future information technology. This forces educators to seek new methods to teach quantum computing for students…

Software Engineering · Computer Science 2026-03-11 Juha Reinikainen , Vlad Stirbu , Teiko Heinosaari , Vesa Lappalainen , Tommi Mikkonen

Quantum Computing is an exciting field that draws from information theory, computer science, mathematics, and quantum physics to process information in fundamentally new ways. There is an ongoing race to develop practical quantum computers…

Physics Education · Physics 2023-05-16 Tunde Kushimo , Beth Thacker

The quantum mechanical commutation relations, which are directly related to the Heisenberg uncertainty principle, have a crucial importance for understanding the quantum mechanics of students. During undergraduate level courses, the…

Physics Education · Physics 2018-04-10 A. Alper Billur , Serkan Akkoyun , Murat Bursal

Quantum algorithms are demonstrated to outperform classical algorithms for certain problems and thus are promising candidates for efficient information processing. Herein we aim to provide a brief and popular introduction to quantum…

Quantum Physics · Physics 2022-12-22 Shihao Zhang , Lvzhou Li

We review some applications of entanglement to improve quantum measurements and communication, with the main focus on the optical implementation of quantum information processing. The evolution of continuos variable entangled states in…

Quantum Physics · Physics 2007-05-23 M. G. A. Paris , G. M. D'Ariano , P. Lo Presti , P. Perinotti

Quantum computing has recently appeared in the headlines of many scientific and popular publications. In the context of quantitative finance, we provide here an overview of its potential.

Mathematical Finance · Quantitative Finance 2023-11-14 Antoine Jacquier , Oleksiy Kondratyev , Gordon Lee , Mugad Oumgari

A systematic method for simulating small-scale quantum circuits by use of linear optical devices is presented. It relies on the representation of several quantum bits by a single photon, and on the implementation of universal quantum gates…

Quantum Physics · Physics 2009-10-30 N. J. Cerf , C. Adami , P. G. Kwiat

Following the B. Hiley belief that unresolved problems of conventional quantum mechanics could be the result of a wrong mathematical structure, an alternative basic structure is suggested. Critical part of the structure is modification of…

General Physics · Physics 2017-03-03 Alexander Soiguine

Using quantum theory, we study the propagation of an optical field in an inhomogeneous dielectric, and apply this scheme to traveling optical fields in a waveguide. We introduce a field-atom interaction Hamiltonian and derive the refractive…

Quantum Physics · Physics 2015-10-26 Akira Kitagawa

Quantum machine learning (QML) is a promising early use case for quantum computing. There has been progress in the last five years from theoretical studies and numerical simulations to proof of concepts. Use cases demonstrated on…

Quantum Physics · Physics 2024-04-30 Daniel Goldsmith , M M Hassan Mahmud

Quantum computing is a growing field at the intersection of physics and computer science. The goal of this article is to highlight a successfully trialled quantum computing course for high school students between the ages of 15 and 18 years…

Physics Education · Physics 2024-06-19 Ciaran Hughes , Joshua Isaacson , Anastasia Perry , Ranbel Sun , Jessica Turner

Quantum state tomography is a fundamental task in quantum computing, involving the reconstruction of an unknown quantum state from measurement outcomes. Although essential, it is typically introduced at the graduate level due to its…

Quantum Physics · Physics 2025-07-14 Mohammad Aamir Sohail , Ranga Sudharshan , S. Sandeep Pradhan , Arvind Rao

This review presents an introduction to Quantum Cosmology, including the mathematical methods essential to the canonical approach, some of the existing conceptual problems and the connection of the models to possible observables.

General Relativity and Quantum Cosmology · Physics 2023-09-19 Paola C. M. Delgado

This paper provides an introduction to quantum machine learning, exploring the potential benefits of using quantum computing principles and algorithms that may improve upon classical machine learning approaches. Quantum computing utilizes…

Quantum Physics · Physics 2024-02-23 Ethan N. Evans , Dominic Byrne , Matthew G. Cook

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

This tutorial intends to introduce readers with a background in AI to quantum machine learning (QML) -- a rapidly evolving field that seeks to leverage the power of quantum computers to reshape the landscape of machine learning. For…