Mathematical Foundations of Quantum Computing: Book Information
Summary
Essential Mathematics for Quantum Computing
This focused guide connects key mathematical principles with their specialized applications in quantum computing, equipping students with the essential tools to succeed in this transformative field. It is ideal for educators, students, and self-learners seeking a strong mathematical foundation to master quantum mechanics and quantum algorithms.
Features
- Covers key mathematical concepts, including matrix algebra, probability, and Dirac notation, tailored for quantum computing.
- Explains essential topics like tensor products, matrix decompositions, Hermitian and unitary matrices, and their roles in quantum transformations.
- Offers a streamlined introduction to foundational math topics for quantum computing, with an emphasis on accessibility and application.
Authors
- Dr. Peter Y. Lee (Ph.D., Princeton University) – Expert in quantum nanostructures with extensive experience in teaching and academic program leadership.
- Dr. James M. Yu (Ph.D., Rutgers University) – Expert in mathematical modeling, applied mathematics, and quantum computing, with extensive teaching experience.
- Dr. Ran Cheng (Ph.D., University of Texas at Austin) – Specialist in condensed matter theory and an award-winning physicist.
Formats and Ordering Info
- ISBN 978-1-961880-08-5 (ebook, color): Amazon, Perlego, VitalSource, EBSCO
- ISBN 978-1-961880-09-2 (paperback, b/w): Amazon
- ISBN 978-1-961880-10-8 (hardcover, b/w): Amazon
- Library of Congress Control Number (LCCN) 2024947285
Synopsis
Quantum Computing and Information (QCI) requires a shift in mathematical thinking, going beyond the traditional applications of linear algebra and probability. This book focuses on building the specialized mathematical foundation needed for QCI, explaining the unique roles of matrices, outer products, tensor products, and the Dirac notation. Special matrices crucial to quantum operations are explored, and the connection between quantum mechanics and probability theory is made clear.
Recognizing that diving straight into advanced concepts can be overwhelming, this book starts with a focused review of essential preliminaries like complex numbers, trigonometry, and summation rules. It serves as a bridge between traditional math education and the specific requirements of quantum computing, empowering learners to confidently navigate this fascinating and rapidly evolving field.
Recommended Use
This book provides the foundational mathematics necessary for further study in quantum computing and quantum algorithms. It serves both as a stepping stone to the second and third books in this series and as a standalone reference.
To fully engage with the material, students are encouraged to complete the exercises and problems at the end of each chapter. For a two-semester course, this approach allows for a comprehensive exploration of the content. However, students already familiar with basic linear algebra may complete the book in a single semester by focusing primarily on Parts III and IV.
Furthermore, while not all topics covered here are essential for the second book, Quantum Computing and Information, they will be important for the third book, Quantum Algorithms and Applications. These topics can be deferred until studying the third book or specific quantum algorithms that require them. They include:
- Discrete Fourier Transform (§ 11.2.5)
- Pauli String Basis (§ 12.4) and Pauli Groups (§ 12.5)
- Jordan, Singular Value, and Schmidt Decompositions (Chapter 13)
- Markov Chains (Chapter 16) and Monte Carlo Methods (Chapter 17)
Key Features
- Pedagogically sound approach
- Up-to-date information
- Navigational aids
- Clean and clear layout
- Engaging exercises
- Suitable for senior undergraduates and early graduates
- 570 pages, 100+ illustrations
Authors
Peter Y. Lee: Holds a Ph.D. in Electrical Engineering from Princeton University. His research at Princeton focused on quantum nanostructures, the fractional quantum Hall effect, and Wigner crystals. Following his academic tenure, he joined Bell Labs, making significant contributions to the fields of photonics and optical communications and securing over 20 patents. Dr. Lee's multifaceted expertise extends to educational settings; he has a rich history of teaching, academic program oversight, and computer programming.
James M. Yu: Earned his Ph.D. in Mechanical Engineering from Rutgers University at New Brunswick, specialized in mathematical modeling and simulation of biophysical phenomena. Following his doctorate studies, he continued to conduct research as a postdoctoral associate at Rutgers University. Currently, he is a faculty member at Fei Tian College, Middletown where he dedicates to teaching mathematics, statistics, and computer science.
Ran Cheng: Earned his Ph.D. in Physics from the University of Texas at Austin, with a specialization in condensed matter theory, particularly in spintronics and magnetism. Following a postdoctoral position at Carnegie Mellon University, he joined the faculty at the University of California, Riverside, where he was honored with the NSF CAREER and DoD MURI awards.
Contents
Preface
Reviews
I. Preliminaries
1. Summation and Product Notations
2. Trigonometry
3. Complex Numbers
4. Sets, Groups, and Functions
II. Vectors, Matrices, and Linear Spaces
5. Vectors and Vector Spaces
6. Inner Product Spaces
7. Fundamentals of Matrix Algebra
8. Matrices as Linear Operators
9. Spectral Decomposition of Matrices
III. Matrix Methods for Quantum Computing
10. Tensor Products of Vector Spaces
11. Functions of Vectors and Matrices
12. Pauli Matrices, Strings, and Groups
13. Advanced Matrix Decompositions
IV. A Probability Primer for Quantum Computing
14. Fundamentals of Probability
15. Stochastic Processes
16. Markov Chains
17. Monte Carlo Methods
V. Supporting Materials
Key Formulas and Concepts
Bibliography
List of Figures
List of Tables
Index
Journey Forward