Mathematical Foundations of Quantum Computing: Editorial Reviews

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.

The QCI book (Quantum Computing and Information: A Scaffolding Approach) 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: A Scaffolding Approach), 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.

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.

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.

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 of anyone seeking a deeper understanding of quantum computing and its mathematical foundations.

This book provides a thorough explanation of the mathematics underlying quantum computing. Dirac (bra–ket) notation is introduced right at the beginning of Part II. Part III then offers a detailed treatment of matrix operations fundamental to quantum computing, with particular emphasis on tensor products. The text also gives careful attention to change of basis—crucial in applications such as quantum key distribution—and to the Kronecker product, which is central to describing composite quantum systems. Equally significant, Part IV presents an in-depth discussion of probability, an essential tool for understanding quantum computing in contrast to classical computing.