|Teaching⟩

SS 2025: Quantum Information Methods for Many-Body Physics

Lecturers: Xhek Turkeshi and Markus Heinrich
Course format: 3+1 hours per week (6 CP)
Times: Mondays 16:00 - 17:30 (Seminarraum II. Physik), Thursdays 10:00-11:30 (Seminarraum Theorie).
Registration: via KLIPS
Module: Primary/secondary area of specialization "Foundations of Quantum Technologies" or "Solid State Theory / Computational Physics" (Physics Master). External students are welcome.

External master students from ML4Q sites other than Cologne can also earn credits through the ML4Q Research School. Please send us an email if you are interested.

Prerequisites: Knowledge of quantum mechanics and many-body physics at the bachelor level. Completion of the "Quantum Information Theory" course and/or a many-body physics course at the master level (e.g. "Solid State Theory" or "Quantum Computational Physics") will be helpful, but is not required.

Content:

1. Introduction: Motivation & overview, linear algebra
2. Quantum randomness I: Haar integration, Weingarten calculus, unitary designs
3. Measuring properties of many-body states: Classical shadows and applications
4. Quantum randomness II: Random quantum circuits
5. Random dynamics in many-body systems: Entanglement dynamics, scrambling in chaotic systems

Lecture notes: Download here (8 April, includes Chapter 1 and most of Chapter 2)

Exercises: There will be exercises every two weeks on Thursdays, starting at 17 April. Exercises may include some numerical ones in the context of applications. Completed exercises should be uploaded via ILIAS.

• Exercise sheet 1 (due on 17 April, 10:00): Download here (Updated notation in exercise 3)