This introductory course to quantum algorithms is concise but comprehensive, covering many key algorithms. It is mathematically rigorous but requires minimal background and assumes no knowledge of quantum theory or quantum mechanics. We will explain quantum computation in terms of elementary linear algebra. We assume the students have some familiarity with vectors, matrices, and their basic properties, but offers a review of all the relevant material from linear algebra. By emphasizing computation and algorithms rather than physics, the objective of this course is to make quantum algorithms accessible to students in computer science without the complications of quantum mechanical notation, physical concepts, and philosophical issues.

After explaining the development of quantum operations and computations based on linear algebra, we will present the major quantum algorithms, from seminal algorithms by Deutsch, Jozsa, and Simon through Shor’s and Grover’s algorithms to recent quantum walks. It covers quantum gates, computational complexity, and some graph theory.