北京雁栖湖应用数学研究院

We often hear about hot topics in quantum, such as quantum entanglement, quantum communication, and quantum computers. In this course, we will discuss the theory behind these concepts in detail. The goal is to help beginners gain a systematic understanding of the field of quantum computation. We will start with the mathematical basis of quantum mechanics to learn about quantum states, quantum evolution, quantum measurement, and quantum composite systems. We will then discuss quantum teleportation, superdense coding, and Bell inequality. Later, we introduce quantum circuits, the elementary unit for quantum computers, and present some famous quantum algorithms, such as Deutsch-Jozsa, Fourier transformation, phase estimation, Shor's factoring algorithm, HHL for solving linear equations, Grover's search, and quantum walk-based algorithms. Finally, we will also discuss some frontier research areas in quantum computation and leave some questions.