北京雁栖湖应用数学研究院

Quantum technologies have become a hot topic, with exciting advancements in quantum entanglement, quantum communication, and quantum computing. In this course, we will explore the fundamental theory behind these concepts, providing beginners with a structured and comprehensive introduction to quantum computation.

We begin by establishing the mathematical foundations of quantum mechanics, covering quantum states, quantum evolution, quantum measurement, and composite quantum systems. Building on this, we will examine key protocols such as quantum teleportation, superdense coding, and the Bell inequality.

Next, we introduce quantum circuits—the fundamental building blocks of quantum computers—and present several well-known quantum algorithms, including Deutsch-Jozsa, quantum Fourier transform, phase estimation, Shor’s factoring algorithm, HHL for solving linear equations, Grover’s search, and quantum walk-based algorithms.

Finally, we will explore some of the latest research directions in quantum computing and discuss open questions in the field. By the end of this course, students will have a solid theoretical foundation and a clearer perspective on the rapidly evolving landscape of quantum computation.