A Basic Mathematics Book for Learning Quantum Computing

In the previous article, we introduced a new book on quantum computing. However, many people may want to first learn basic mathematics before reading such books. I would like to briefly introduce the following book as one such book. Generally speaking, the relationship between this book and the previous one is as follows:

Peter Y. Lee, James M. Yu, Ran Cheng :Mathematical Foundations of Quantum Computing, Polaris QCI Publishing, 2025.

This book is a large volume of 539 pages. It provides a very thorough explanation of the basics of mathematics related to quantum computing. Parts 1 and 2 are basic mathematics, mainly linear algebra. However, since Dirac Notation (bra-ket) is already used here, it becomes clear that this is not purely basic mathematics, but is aimed at quantum computing. The authors explain that readers who have already mastered the basics of linear algebra can skip these parts and move on to Part 3. Even for such readers, Part 2 is very useful for reviewing points that they may have forgotten. In other words, this book also serves as an encyclopedia.

In the third and fourth parts, the most important operations in quantum computing are explained in detail, with a focus on "Tensor products". Although it is not very noticeable, it is worth noting that the "Change of Basis" introduced in the second part is explained in more detail in this third part. This will be important in many fields,  including quantum key distribution later. You will also see that the "Kronecker Product" is important in simplifying quantum computing. More advanced content such as "Singular Value Decomposition" is also included. Furthermore, one of the outstanding features of this book is that "Probability", another foundation of quantum computing, is dealt with extensively in the fourth part.

At the beginning, there is a "Level Indicator" explanation, which is useful for understanding the level of difficulty of the content. However, it would be even better if it had a marking to indicate which of the minimum necessary knowladge is required to read the second book, "Quantum Computing & Information." This is because this book contains a huge amount of content, and some people want to study efficiently. For example, it may be okay to skip "Discrete Fourier Transform" and "Markov Chains" for the time being.