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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 (28 May, includes Chapter 1-4)

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.

Schedule:

Note that there is no class on Thu 28 May, Mon 9 June, Thu 12 June, and Thu 19 June due to holidays and lecture break.
Date Type Topic
Mon 26/05 L 4.1 Random Quantum Circuits
Mon 02/06 L 4.1 RQCs / 5.1 Anticoncentration
Thu 05/06 L 5.1 Anticoncentration
Mon 16/06 E Exercise sheet 4 (note the unusual day!)
Mon 23/06 L 5.1 Anticoncentration
Thu 26/06 L 5.1 Anticoncentration