This course is scheduled as three parts: the mathematical formalism of quantum information, its applications in computing tasks, and its applications in information-processing and more advanced topics. Part I - Closed Quantum Systems 1. Foundations and Postulates for Closed Quantum Systems: Quantum States, Evolution, and Projective Measurements. 2. The Quantum No-Go Theorem: No-Cloning Theorem, No-Signaling Theorem, and No-Perfect Discrimination. 3. Basic Quantum Protocols: Teleportation, Dense Coding, Quantum Key Distribution. 4. Quantum Computation I: Quantum Circuit Model and Algorithms. 5. Quantum Computation II: Algorithms Based on Amplitude Amplification. 6. Quantum Computation III: Algorithms Based on Phase Estimation. 7. Quantum Computation IV: Integer Factorization Algorithm. 8. Quantum Non-Local Games. Part II - Open Quantum Systems 9. Foundations and Postulates for Open Quantum Systems: Density Operators, Quantum Channels, and Quantum Measurements. 10. Distance Measures: Quantum Fidelity, Trace Distance, and Quantum Entropies. 11. Quantum Shannon Theory I: Quantum Compression. 12. Quantum Shannon Theory II: Hypothesis Testing and Classical Communication over Quantum Channels. 13. Quantum Shannon Theory III: Quantum Communication over Quantum Channels. 14. Quantum Error Correction. 15. Advanced Topics: Quantum Machine Learning (as time permits).

1. Introduce fundamental concepts and mathematical framework of quantum information (the so-called quantum bits)---how to model it, process it, and measure it. 2. Present core quantum computing topics including quantum circuit models and basic quantum algorithms, and how to harness quantum computing power to speed-up classical computational tasks. 3. Learn compressing quantum information and communicating classical/quantum information through a quantum channel, and various quantum information-processing protocols. 4. Develop necessary abilities for students to independently study advanced topics in quantum information sciences and to innovate applications in quantum information technology. 5. Perform a term project on studying advanced topics of the latest research, experiment development, technologies of quantum information processing. 6. Equip students with sufficient backgrounds to self-study academic papers and self-learn in this field after taking this course.

The course is intended for graduate students (undergraduate students are very welcome) who have previously taken courses of linear algebra and basic probability theory. No previous background in quantum mechanics is required. The grading criterion is based on homework (45%), mid-term exam (25%), and final project (30%).

At least 10 hours

Course slides

[1] Michael Nielsen and Issac Chuang. Quantum Computation and Quantum Information, Cambridge University Press, 2009. [2] P. Kaye, R. Laflamme, M. Mosca. An Introduction to Quantum Computing, Oxford University Press, 2007. [3] Benjamin Schumacher and Michael Westmoreland. Quantum Processes systems, and Information, Cambridge Press, 2010. [4] Joseph M. Renes. Quantum Information Theory: Concepts and Methods, de Gruyter, 2022. [5] Mark M. Wilde. Quantum Information Theory, Cambridge University Press, 2018. [6] John Watrous. The Theory of Quantum Information, Cambridge University Press, 2018. [7] Mario Ziman and Teiko Heinosaari. The Mathematical Language of Quantum Theory: From Uncertainty to Entanglement, Cambridge University Press, 2011.