Beijing Institute of Mathematical Sciences and Applications

This course provides a comprehensive introduction to open quantum systems and quantum error correction, addressing the fundamental challenge of preserving quantum information in the presence of environmental noise. We begin with the theoretical framework of quantum operations and quantum channels, exploring how real quantum systems interact with their environment through models such as depolarizing and amplitude damping channels. The course covers essential distance measures for quantum states and operations, including trace distance and fidelity, which serve as tools for quantifying information loss. The core focus is on quantum error correction theory, from basic three-qubit codes to advanced stabilizer codes and CSS constructions, providing students with the mathematical foundation for fault-tolerant quantum computation. The course concludes with practical applications, including the BB84 quantum key distribution protocol, demonstrating how theoretical principles translate into real-world quantum technologies. Students will gain the essential theoretical tools needed to analyze and design noise-resilient quantum information processing systems.