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. 

Instructor: Jamie Sikora 

Email: sikora@vt.edu (please include "6604" in the subject line)

Office hours: Immediately after lectures (other times and Zoom options available upon request) 

Syllabus: pdf (tagged for accessibility)   

Lectures: 11:15am-12:05pm on Mondays, Wednesdays, and Fridays in Whittemore 257 (subject to change)

For CS students: This course falls 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