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SS 2026: Advanced Seminar on Quantum Computing

Lecturers: Markus Heinrich and Felix Motzoi
Course format: 2 hours per week (3 CP)
Times: Thursdays 12:00-13:30 (Seminarraum 0.01).
Registration: via KLIPS. Interested students should come to the first meeting on 16 April for further organization and assignement of a topic.
Module: Primary/secondary area of specialization "Foundations of Quantum Technologies".
Notes: More information and course material on ILIAS.

Prerequisites: Completion of the "Quantum Information Theory" course will be helpful.

Content: This seminar will cover theoretical aspects of quantum computing and practical challenges. The topics will mostly focus on quantum algorithms and problems for which we expect computational advantages from quantum computing. Tangential topics touching quantum error correction, quantum learning, or experimental implementations may also be possible.

Topics (preliminary and incomplete):

  1. Quantum Phase Estimation and Quantum Chemistry Applications
  2. Hamiltonian Simulation I: Product formulas and Linear Combination of Unitaries
  3. Hamiltonian Simulation II: From Quantum Walks to Qubitization
  4. HHL and Linear Algebra
  5. Quantum Singular Value Transform / Quantum Signal Processing
  6. Variational Algorithms: Hype and Reality
  7. Quantum Optimization
  8. Decoded Quantum Interferometry
  9. Classical Shadows
  10. Quantum Machine Learning
  11. Quantum Random Sampling / Quantum Advantage Experiments
  12. Fault Tolerance and Resource Estimates
Most of these topics may be split in two or more.

SS 2025: Quantum Information Methods for Many-Body Physics

Lecturers: Markus Heinrich and Xhek Turkeshi
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 (26 September)

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 (random MPS)
Mon 16/06 E Exercise sheet 4 (note the unusual day!)
Mon 23/06 L 5.1 Anticoncentration (super brickwork circuits)
Thu 26/06 L 5.1 Anticoncentration (2-local brickwork circuits)
Mon 30/06 L 5.2 Entanglement dynamics
Thu 03/07 L 5.2 Entanglement dynamics
Mon 07/07 E Exercise class 5 (note the unusual day!)
Thu 10/07 L Research focus #1
Mon 14/07 L Research focus #2