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Brief Introduction to Quantum Computing for Undergraduate Students: Lecture Three — Quantum Gates, Quantum Circuits, and Simple Quantum Algorithms

Li Chen

Published Sep 22, 2026• 0 citations
Publisher

Abstract

This lecture continues Lectures One and Two, where we introduced the basic concepts of quantum computing and reviewed the essential linear algebra background for undergraduate students. In this lecture, we focus on the basic computational units of quantum computation, known as quantum gates. Quantum gates play a central role in quantum algorithms, as each quantum algorithm can be implemented as a sequence of quantum gate operations. This idea has a close analogy with classical computing, where computations can be represented by Boolean circuits constructed from elementary logic gates. In principle, classical algorithms can be implemented through combinations of such logic gates. To establish this connection, we first review several fundamental logic gates in classical computing, including the AND, OR, and NOT gates. These elementary Boolean gates provide a useful foundation for understanding quantum gates and how classical computational concepts are extended into the quantum domain. In general, a quantum processing unit (QPU), which executes quantum gate operations, can be viewed as the quantum counterpart of a classical central processing unit (CPU), where computations are carried out through logical operations and circuits. This lecture establishes the foundation for understanding the quantum circuit model and for designing and analyzing quantum algorithms in subsequent lectures. To provide a smooth transition to the topics that follow, we also introduce several tiny quantum algorithms and examples in this lecture. These examples illustrate how quantum gates can be combined to perform meaningful computational tasks and prepare students for the more advanced quantum algorithms discussed later.

DOI
10.1145/3848065.3848069

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INTRODUCTION QUANTUM COMPUTING

Mr. V. PAVAN KUMAR, Mr. V. SURYANARAYANA REDDY, Mr. THAMBI VINOD KUMAR +2 more

Quantum computing has emerged as one of the most transformative technological developments of the twenty-first century. By exploiting the fundamental principles of quantum mechanics—namely superposition, entanglement, and measurement—quantum computers offer the potential to address problems that are beyond the practical reach of classical computing systems. As the field advances from theoretical exploration to real-world implementation, the demand for clear, structured, and comprehensive educational resources continues to grow. This book presents a systematic and accessible introduction to quantum computing, beginning with the essential concepts of classical information and computation and progressively advancing toward modern quantum algorithms and communication protocols. The initial chapters establish a strong foundation in classical bits, logic gates, Boolean algebra, reversible logic, and computational complexity, providing the conceptual bridge necessary to understand quantum computation. The discussion then moves to the quantum bit (qubit), examining its behavior through superposition, measurement, Bloch sphere representation, and physical realization. Special emphasis is placed on linear algebra as the mathematical framework underpinning quantum computing. Through this approach, readers are guided to develop an intuitive yet rigorous understanding of quantum states, quantum gates, and circuit-based computation. The text further extends these ideas to multi-qubit systems, quantum entanglement, universal gate sets, and quantum error correction, integrating theoretical principles with practical insights. To support experiential learning, the book incorporates hands-on exposure to leading quantum programming platforms, including IBM Quantum, OpenQASM, and Qiskit. These sections connect theory with practice, enabling readers to design, simulate, and execute quantum circuits on both simulators and real quantum hardware. Subsequent chapters explore key quantum communication protocols such as superdense coding, quantum teleportation, and quantum key distribution, followed by an in-depth treatment of foundational quantum algorithms including Deutsch–Jozsa, Grover’s search, Simon’s algorithm, and Shor’s factoring algorithm. This text is intended for undergraduate and postgraduate students, research scholars, and industry professionals seeking a coherent and structured pathway into quantum computing. No prior knowledge of quantum mechanics is assumed, although familiarity with linear algebra and classical computation will enhance comprehension. Each chapter is carefully organized to promote conceptual clarity, supported by illustrative examples, circuit diagrams, and concise summaries. Beyond explaining the principles and mechanisms of quantum computation, this book aims to inspire readers to engage with the future of the field—whether through academic research, industrial application, or interdisciplinary innovation. As quantum technologies continue to evolve, it is hoped that this text will serve as a dependable guide and a meaningful entry point into the quantum era.

•Feb 12, 2026•0 citations
This lecture continues Lectures One and Two, where we introduced the basic concepts of quantum computing and reviewed the essential linear algebra background for undergraduate students. In this lecture, we focus on the basic computational units of quantum computation, known as quantum gates. Quantum gates play a central role in quantum algorithms, as each quantum algorithm can be implemented as a sequence of quantum gate operations. This idea has a close analogy with classical computing, where computations can be represented by Boolean circuits constructed from elementary logic gates. In principle, classical algorithms can be implemented through combinations of such logic gates. To establish this connection, we first review several fundamental logic gates in classical computing, including the AND, OR, and NOT gates. These elementary Boolean gates provide a useful foundation for understanding quantum gates and how classical computational concepts are extended into the quantum domain. In general, a quantum processing unit (QPU), which executes quantum gate operations, can be viewed as the quantum counterpart of a classical central processing unit (CPU), where computations are carried out through logical operations and circuits. This lecture establishes the foundation for understanding the quantum circuit model and for designing and analyzing quantum algorithms in subsequent lectures. To provide a smooth transition to the topics that follow, we also introduce several tiny quantum algorithms and examples in this lecture. These examples illustrate how quantum gates can be combined to perform meaningful computational tasks and prepare students for the more advanced quantum algorithms discussed later.
Aimed at advanced undergraduate and graduate-level students, this textbook covers the core topics of quantum computing in a format designed for a single-semester course. It will be accessible to learners from a range of disciplines, with an understanding of linear algebra being the primary prerequisite. The textbook introduces central concepts such as quantum mechanics, the quantum circuit model, and quantum algorithms, and covers advanced subjects such as the surface code and topological quantum computation. These topics are essential for understanding the role of symmetries in error correction and the stability of quantum architectures, which situate quantum computation within the wider realm of theoretical physics. Graphical representations and exercises are included throughout the book and optional expanded materials are summarized within boxed 'Remarks'. Lecture notes have been made freely available for download from the textbook's webpage, with instructors having additional online access to selected exercise solutions.
Aimed at advanced undergraduate and graduate-level students, this textbook covers the core topics of quantum computing in a format designed for a single-semester course. It will be accessible to learners from a range of disciplines, with an understanding of linear algebra being the primary prerequisite. The textbook introduces central concepts such as quantum mechanics, the quantum circuit model, and quantum algorithms, and covers advanced subjects such as the surface code and topological quantum computation. These topics are essential for understanding the role of symmetries in error correction and the stability of quantum architectures, which situate quantum computation within the wider realm of theoretical physics. Graphical representations and exercises are included throughout the book and optional expanded materials are summarized within boxed 'Remarks'. Lecture notes have been made freely available for download from the textbook's webpage, with instructors having additional online access to selected exercise solutions.
Aimed at advanced undergraduate and graduate-level students, this textbook covers the core topics of quantum computing in a format designed for a single-semester course. It will be accessible to learners from a range of disciplines, with an understanding of linear algebra being the primary prerequisite. The textbook introduces central concepts such as quantum mechanics, the quantum circuit model, and quantum algorithms, and covers advanced subjects such as the surface code and topological quantum computation. These topics are essential for understanding the role of symmetries in error correction and the stability of quantum architectures, which situate quantum computation within the wider realm of theoretical physics. Graphical representations and exercises are included throughout the book and optional expanded materials are summarized within boxed 'Remarks'. Lecture notes have been made freely available for download from the textbook's webpage, with instructors having additional online access to selected exercise solutions.
Quantum computing has emerged as one of the most transformative technological developments of the twenty-first century. By exploiting the fundamental principles of quantum mechanics—namely superposition, entanglement, and measurement—quantum computers offer the potential to address problems that are beyond the practical reach of classical computing systems. As the field advances from theoretical exploration to real-world implementation, the demand for clear, structured, and comprehensive educational resources continues to grow. This book presents a systematic and accessible introduction to quantum computing, beginning with the essential concepts of classical information and computation and progressively advancing toward modern quantum algorithms and communication protocols. The initial chapters establish a strong foundation in classical bits, logic gates, Boolean algebra, reversible logic, and computational complexity, providing the conceptual bridge necessary to understand quantum computation. The discussion then moves to the quantum bit (qubit), examining its behavior through superposition, measurement, Bloch sphere representation, and physical realization. Special emphasis is placed on linear algebra as the mathematical framework underpinning quantum computing. Through this approach, readers are guided to develop an intuitive yet rigorous understanding of quantum states, quantum gates, and circuit-based computation. The text further extends these ideas to multi-qubit systems, quantum entanglement, universal gate sets, and quantum error correction, integrating theoretical principles with practical insights. To support experiential learning, the book incorporates hands-on exposure to leading quantum programming platforms, including IBM Quantum, OpenQASM, and Qiskit. These sections connect theory with practice, enabling readers to design, simulate, and execute quantum circuits on both simulators and real quantum hardware. Subsequent chapters explore key quantum communication protocols such as superdense coding, quantum teleportation, and quantum key distribution, followed by an in-depth treatment of foundational quantum algorithms including Deutsch–Jozsa, Grover’s search, Simon’s algorithm, and Shor’s factoring algorithm. This text is intended for undergraduate and postgraduate students, research scholars, and industry professionals seeking a coherent and structured pathway into quantum computing. No prior knowledge of quantum mechanics is assumed, although familiarity with linear algebra and classical computation will enhance comprehension. Each chapter is carefully organized to promote conceptual clarity, supported by illustrative examples, circuit diagrams, and concise summaries. Beyond explaining the principles and mechanisms of quantum computation, this book aims to inspire readers to engage with the future of the field—whether through academic research, industrial application, or interdisciplinary innovation. As quantum technologies continue to evolve, it is hoped that this text will serve as a dependable guide and a meaningful entry point into the quantum era.