Basics of mathematical modeling of quantum computing processes. Textbook for universities.
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The textbook is dedicated to the issues of mathematical modeling of quantum processes. The main content of the textbook can be divided into three parts. The first part covers the basic questions of linear algebra necessary for further understanding of the material. Definitions of linear space, basis, transition matrix, linear operator, unitary space, adjoint space, Hermitian and unitary matrices, tensor product of linear spaces, operators, and vectors are provided. The second part introduces the basics of quantum mechanics, including definitions of qubit, multipartite quantum state, quantum entanglement, Landau density matrix, and quantum gates. The third part presents the Jaynes-Cummings model for a single atom and photon. The system's dynamics are studied using the general solution of the Schrödinger equation. The presence of Rabi oscillations in the system is demonstrated. The textbook offers many exercises, most of which are solved. The Appendix discusses the quantum dynamics of the system with model Hamiltonians. A set of programs written in Python is provided. The textbook is written in accordance with the requirements of the Federal State Educational Standard for the direction of training in "Applied Mathematics." It is intended for students of higher educational institutions studying in the fields of "Applied Mathematics," "Applied Informatics," and "Physics." It can also be used by students of other specialties interested in the applications of linear algebra to mathematical modeling of nanoprocesse
Author:
Author:Viktorova Nadezhda Borisovna
Cover:
Cover:softcover
Category:
- Category:Computer & Technology
- Category:Science & Math
Dimensions:
Dimensions:20x13x.5 cm
Series:
Series:Mathematics
ISBN:
ISBN:978-5-507-46185-1
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