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 on Mondays, Wednesdays, and Fridays in Whittemore 257
For CS students: This course falls under Area 6: Data and Information
AI policy and academic integrity
You can use AI however you wish except during your presentation to answer questions.
You cannot simply get slides from an external source, but you can help create them with AI. You are responsible for knowing the content on your slides.
Lecture notes can be found here. These will be updated throughout the course. All comments are welcome!
Canvas-approved accessible notes can be found here.
A special thanks to Alice Zheng for putting these notes together!
Mathematical Background ✅
Semidefinite Programming ✅
3.4 Duality of Uhlmann's and Alberti's theorems (time-permitting)
Student Project Presentations (Tentative) 🆕
October 16 - Probabilistic cloning
October 23 - Lovasz theta function
October 26 - Comb decoupling
October 28 - Second-order cones
October 30 - SDPs in computer graphics
November 06 - Ellipsoid method
November 09 - State readout
November 13 - Quantum money
November 30 - SDPs and quaternions/octurnions
December 02 - Dimension reduction via symmetry
Possible Student Projects 👀
SDPs in [insert your favourite topic here] - The open-ended option
Not (necessarily) quantum
Linear programming and how it differs/relates to semidefinite programming - A classic framework for optimization
Clark's theorem and ascent directions* - Duality theory
SDP relaxations for combinatorial optimization problems (must come after MAX CUT) - A fun, but challenging topic
Product theorems* - A nice foundational theorem about tensor products of SDPs
CVX [or some other solver] - Numerical algorithm(s) for solving SDPs
Entanglement + PPT criterion* - A nice basic quantum problem
Symmetric extensions (must come after Entanglement + PPT criterion)* - An elegant solution to the entanglement problem
Compatibility - A nice basic quantum problem
Operator geometric means* - A matrix analog of a nice mathematical operation
Entropy functions (must come after Operator geometric means)* - Popular quantum functions
QMA is in EXP (must come after Ellipsoid method)* - Computational complexity theory
Perfect parellel repetition of QMA* - Computational complexity theory
Quantum Wasserstein distances - A quantum machine learning distance function
Nonlocal games (this is advanced, and might be a team-up project) - A go-to setting for studying quantum phenomena. A Nobel prize-winning topic.