Semidefinite Programming & Quantum Information
CS 6604 (Fall 2026)
This seminar course introduces semidefinite programs, a powerful class of optimization problems with important applications in quantum information. The first part of the course covers the foundations of semidefinite programming, the second part focuses on applications in quantum information, and the final part consists of student presentations on related topics.
No previous knowledge of quantum theory or optimization is required.
This course does not require any coding, unless a student chooses to incorporate it into a course presentation.
Office hours: Immediately after lectures (other times and Zoom options available upon request)
Lectures: 11:15am-12:05pm Monday, Wednesday, Friday in Whittemore 257 (subject to change)
For CS Students: This is under Area 6: Data and Information
Lecture notes are forthcoming.
Part One: Semidefinite programming
Mathematical background, Positive semidefinite matrices, Real Analysis, Convex analysis, Semidefinite programming introduction, Standard form reductions and real vs. complex data, Duality theory, The dual of the dual, Lifehack: How to really take the dual, Slater's theorem and optimality conditions, Clark's theorem and ascent directions
Part Two: Quantum applications
Quantum states and measurements, Distinguishing between two states and the trace norm, Optimal measurements, Uhlmann's Theorem and Alberti's Theorem are dual, The completely bounded trace norm and properties of the fidelity function, Operator geometric means, Quantum entropy functions, Quantum nonlocal games, Quantum money