Abstract: Quantum information is an interdisciplinary science involving quantum mechanics, information theory, and computer science. It is of strategic importance and has far-reaching influence. Born in the late 1970s, it has developed very fast since the mid-1990s. Quantum information science includes quantum computing, quantum communication, and so on. The combination of different branches of science has led to many new research topics in science and technology, and many remarkable achievements have been made. This paper will introduce the basics of quantum information science, including some very important quantum algorithms such as Shor’s algorithm and Grover’s algorithm. The former factorizes an integer in polynomial steps, while the latter finds a marked item with a square-root increase in speed compared to classical algorithms. Other recent studies of quantum algorithms will also be reviewed.