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

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.