Introductory Guide to Classical and Quantum Computing

Introduction to Classical and Quantum Computing is a comprehensive text that caters to students interested in exploring quantum computing beyond a conceptual level, without the prerequisite of advanced mathematical training. The only requirement is a background in trigonometry, as the book covers the necessary mathematical concepts, including linear algebra. This book can be utilized as a course textbook or for independent study.

The text begins with a thorough overview of classical computing, from the fundamentals of number addition to the computational limits of classical systems. This lays the groundwork for the subsequent exploration of quantum computing topics. The journey into quantum computing starts with a single qubit and the various quantum gates that can operate on it, first using geometry and elementary algebra, and later introducing linear algebra techniques. The book leverages computer algebra systems, providing code examples for both Mathematica and SageMath.

After the introduction of a single qubit, the focus shifts to multi-qubit systems, covering topics such as quantum addition, universal gate sets, and error correction. Readers are then guided through the process of programming quantum circuits on actual quantum processors using the IBM Quantum Experience. This hands-on approach allows students to apply the theoretical concepts in a practical setting.

The book then delves into the concepts of entanglement and quantum protocols, providing a deeper understanding of the unique properties of quantum systems. The final chapters are dedicated to the examination of quantum algorithms, culminating in the study of Shor's algorithm for factoring. Throughout the text, the Quirk quantum simulator is extensively utilized to reinforce the learning experience.

The book concludes with a brief discussion on career opportunities in quantum computing, as well as suggestions for potential technical topics that readers may wish to explore further. This well-rounded approach ensures that readers not only gain a solid understanding of quantum computing but also have a roadmap for continued learning and professional development in this rapidly evolving field.

Overall, Introduction to Classical and Quantum Computing is a valuable resource for students and independent learners who seek to deepen their understanding of quantum computing beyond the conceptual level, while building a strong foundation in the underlying mathematical principles and practical applications.

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