This is a comprehensive introduction for senior undergraduate and graduate students to modern quantum computing and information processing. The author innovatively incorporates the rich legacy of classical books such as Nielsen and Chuang [1] and von Neumann [2] into this work for students, providing a smooth introduction to learning quantum theory. After reading this book, readers will have gained a comprehensive understanding of quantum theory from the foundation to practical applications and beyond. More ambitious readers can freely go on to read the references at the end of the book for further study.

This work is well partitioned into four parts. The first part begins with basic notations including bits and qubits. The Stern-Gerlach experiment is inserted as a vivid illustration. Quantum states are also introduced.

The second part is the theoretical foundation of quantum computing. Chapter 3 covers the fundamental knowledge of quantum mechanics. The qubits are formularized in Hilbert space. Related operators are introduced such as the inner product and Dirac product. Chapter 4 further elaborates the properties of qubits. Important definitions include the Bloch sphere (the front face figure), cloning, and entanglement. Chapter 5 is a slightly advanced chapter on the use of the density matrix approach to introduce mixed states and open systems. Chapter 6 is more computer related and elaborates preliminaries in computation theories. It starts with the definition of the Turing machine (TM) to introduce the quantum Turing machine, the halting problem, and complexity classes. This chapter also includes fundamental concepts of universal binary logic gates, circuits, and reversible computation.

The third part focuses on the quantum aspects of computing. Starting with universal classic gates, chapter 7 introduces the quantum gates from single and multiqubit gates to universal quantum gates. Chapter 8 introduces various examples of quantum algorithms such as the Deutsch-Josza algorithm, the Bernstein-Vazirani algorithm, and Simon’s algorithm. The more interesting part of this chapter is the quantum translation of the fast Fourier transform (FFT) algorithm, namely QFT. Finally, Grover’s search algorithm and quantum counting are introduced. This chapter shows the power of using quantum theories in solving modern computation problems.

Part 4 is about quantum information. Chapter 9 introduces quantum applications in modern cryptography. The author specially elaborates the quantum key distribution (QKD) and possible attacks and solutions. Chapter 10 introduces the quantum application of error correction in information transportation. Chapter 11 introduces Shannon’s information theory to describe the information contents of a quantum system.

There are many other good features in this book. The author includes a rich list of references of classic works for readers’ further study. At the end of most chapters, the author thoughtfully designs problems for students to practice. There are many well-designed examples with illustrative figures included in each chapter to make the reading interesting and fun. The author also allocates spaces in different sections to introduce important related history.

To fully understand this book, readers should be equipped with basic knowledge in the following fields: complex analysis, general college-level physics, probability, discrete math, cryptography, and information theory.

In general, this work is an excellent introduction to the foundation of quantum computing. Compared with other dedicated monographs, this book provides much easier access and an overall picture of the field. Students and researchers who want to learn about quantum computing will be very interested in this book.