We present a survey of quantum algorithms, primarily for an intended audience of pure mathematicians. We place an emphasis on algorithms involving group theory.
Fundamentals of energy density functional in nuclear physics are presented. Much attention is paid to a mathematically rigorous treatment of deriving the energy density functional. The specific features of the density functional used in studying many-nucleon systems, which is quite different from that used in many-electron systems, are also shown. The intended audience are physicists, chemists and mathematicians. In particular those who will start to study the density functional theory are intended.
Contribution:In this study, an alternative educational approach for introducing quantum computing to a wider audience is highlighted. The proposed methodology considers quantum computing as a generalized probability theory rather than a field emanating from physics and utilizes quantum programming as an educational tool to reinforce the learning process.Background:Quantum computing is a topic mainly rooted in physics, and it has been gaining rapid popularity in recent years. A need for extending the educational reach to groups outside of physics has also been becoming a necessity.Intended Outcomes:This study aims to inform academics and organizations interested in introducing quantum computing to a diverse group of participants on an educational approach. It is intended that the proposed methodology would facilitate people from diverse backgrounds to enter the field.Application Design:The introductory quantum physics content is bypassed and the quantum computing concepts are introduced through linear algebra instead. Quantum programming tasks are prepared in line with the content. Pre/post-test design method and Likert scale satisfaction surveys are utilized to measure knowledge acquisition and to evaluate the perception of the learning process by the participants.Findings:Conducted pre/post-test design survey shows that there is a statistically significant increase in the basic knowledge levels of the participants on quantum computing concepts. Furthermore, no significant difference in the gain scores is observed between the participants from different STEM-related educational backgrounds. The majority of the participants were satisfied and provided positive feedback.
A survey of various concepts in quantum information is given, with a main emphasis on the distinguishability of quantum states and quantum correlations. Covered topics include generalized and least square measurements, state discrimination, quantum relative entropies, the Bures distance on the set of quantum states, the quantum Fisher information, the quantum Chernoff bound, bipartite entanglement, the quantum discord, and geometrical measures of quantum correlations. The article is intended both for physicists interested not only by collections of results but also by the mathematical methods justifying them, and for mathematicians looking for an up-to-date introductory course on these subjects, which are mainly developed in the physics literature.