Includes bibliographical references and index.

This chapter briefly introduces the origins, elements, and fundamental themes of quantum computers. In Section 1.1 we recount how successive observations by different scientists led to the concept of quantum computing. We also review the potential applications that propelled quantum computing from a nascent idea to a global enterprise. Section 1.2 distinguishes quantum computers from classical ones and outlines the five criteria for quantum computing. We introduce the standard model of quantum computation - the circuit model - in Section 1.3. Next, we explain why it's believed that quantum computers are (1) more powerful than classical ones (Section 1.4); and (2) physically realizable (Section 1.5)--. The global race to build the world's first quantum computer has attracted enormous investment from government and industry, and it attracts a growing pool of talent. As with many cutting-edge technologies, the optimal implementation is not yet settled. This important textbook describes four of the most advanced platforms for quantum computing: nuclear magnetic resonance, quantum optics, trapped ions, and superconducting systems. The fundamental physical concepts underpinning the practical implementation of quantum computing are reviewed, followed by a balanced analysis of the strengths and weaknesses inherent to each type of hardware. The text includes more than 80 carefully designed exercises with worked solutions available to instructors, applied problems from key scenarios, and suggestions for further reading, facilitating a practical and expansive learning experience. Suitable for senior undergraduate and graduate students in physics, engineering, and computer science, Building Quantum Computers is an invaluable resource for this emerging field.