About the Book
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.
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.
About the Author :
Dr. 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. Dr. 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. Dr. Ran Cheng earned his Ph.D. in Physics with a focus on theoretical condensed matter physics from the University of Texas at Austin. Following his doctoral studies, he furthered his inquiry into magnetic materials and nanostructures as a postdoctoral researcher at Carnegie Mellon University. He is now a faculty member at the University of California, Riverside, where he actively explores three core research domains: spintronics, topological materials, and low-dimensional quantum magnets. A recognized pioneer in the burgeoning field of antiferromagnetic spintronics, Dr. Cheng was honored with the DOD MURI award alongside a cadre of distinguished physicists, furthering advancements in this innovative domain.
Review :
Leonard Kahn, Professor and Chair, Department of Physics, University of Rhode Island
With the move toward introducing quantum computing as a first-year course, the structure of Mathematical Foundations of Quantum Computing makes it a strong contender as a text that can be used throughout an academic career. The authors have successfully designed a text that can be used at multiple stages of development, from introductory, through intermediate and graduate levels, as well as a useful reference work. From the introduction of vectors and matrices, each topic is revisited with increasing complexity, an ideal implementation of the scaffolding approach. The layout of the text, accompanied by a variety of exercises, examples, and clear graphics, advances the authors' goal of creating a valuable learning and teaching aid. The text, along with its companion Quantum Computing and Information, deserves serious consideration by those who are designing a full-range quantum computing curriculum.
Ying Nian Wu, Professor, Department of Statistics and Data Science, University of California in Los Angeles
The QCI book (Quantum Computing and Information) presents quantum computing in a wonderfully friendly manner, making this complex field accessible to anyone with basic undergraduate math preparation. The companion text (Mathematical Foundations of Quantum Computing), with its comprehensive coverage of mathematical foundations, provides all the essential tools needed to dive into quantum concepts with confidence. I found the chapters on probability to be expertly written, offering a clear, engaging, and quantum-relevant introduction. Together, these books form an inviting and masterful gateway for learners eager to explore quantum computing.
Andrew Kent, Professor of Physics, The Center for Quantum Phenomena, New York University
This comprehensive and accessible text presents, in a single volume, the mathematical foundation of quantum information. Beginning with the essentials-linear algebra, probability, and matrix analysis-and advancing to topics like tensor products, spectral decompositions, and Markov Chain Monte Carlo simulations, the authors guide the reader with clarity and rigor. Rarely is so much mathematical depth presented in such a student-friendly way. This volume will serve both newcomers and experts alike, providing a strong foundation for gaining facility with the mathematics required to understand quantum systems.
Steven Frankel, Rosenblatt Professor, Faculty of Mechanical Engineering, Technion - Israel Institute of Technology
A beautiful, colorfully crystal clear, and veritable one-stop-shop, this resource offers everything mathematical essential to quantum computing. Covering vector spaces, matrix methods including tensor products, and probability theory, it is a must-read for quantum computing researchers and practitioners alike.
Tony Holdroyd, Retired Senior Lecturer in Computer Science and Mathematics
This book is a learned and thorough exposition of the mathematics that supports quantum computing. The authors have gone to great lengths to make it both learner-friendly and detailed while maintaining rigor. It covers topics ranging from the fundamentals of quantum mathematics to the complexities of vector and matrix algebra, as well as the probabilities central to quantum computing. The text is complemented by numerous supporting figures that effectively illustrate key concepts. Applications of quantum computing are introduced and seamlessly integrated throughout the book. This volume, along with its companion, Quantum Computing and Information - a Scaffolding Approach, is an essential addition to the bookshelf.
