Theoretical Foundations of Quantum Computing

Theoretical Foundations of Quantum Computing is the essential textbook designed specifically for introductory courses in this groundbreaking discipline. Quantum computing represents a paradigm shift in how we understand computation itself. This textbook delves deep into the fundamental principles of quantum mechanics that underpin this revolutionary technology, making it an invaluable resource for both undergraduate and graduate students in computer science and related fields. Structured into eight meticulously crafted chapters, this textbook covers everything from the historical context of quantum computing to advanced theories and applications. Each chapter is designed to build upon the last, ensuring that students develop a robust understanding of both foundational concepts and cutting-edge research. Chapter 1 briefly introduces the development history, background, and current status of quantum computing, and points out its advantages and potential applications; Chapter 2 describes the basic concepts related to quantum computing and points out that classical computing is a special case of quantum computing; Chapter 3 provides an overview of linear algebra, systematically summarizing the relevant theorems on operator (matrix) decomposition and hyperoperators; Chapter 4 states the basic quantum cryptography and communication protocols; Chapter 5 elaborates on basic quantum computing models, including quantum finite automata, quantum Turing machines, and quantum circuits; Chapter 6 introduces the core content of quantum computing, including important quantum algorithms It also introduces hidden subgroup algorithms and summarizes the basic tools for designing quantum algorithms, namely quantum phase estimation method and quantum amplitude amplification method; Chapter 7 introduces the basic knowledge and methods of quantum computing complexity; Chapter 8 introduces the basic concepts and methods of quantum error correction codes, as well as their error correction principles. This textbook not only serves as a foundational resource for students but also acts as a comprehensive guide for researchers interested in quantum computing. Its clarity and thoroughness make it an excellent reference for those looking to deepen their understanding or engage in cutting-edge research.