|Teaching⟩

Lecturers: Markus Heinrich and Xhek Turkeshi
Course format: 3+1 hours per week (6 CP)
Times: Mondays 14:00 - 15:30 (Seminarraum II. Physik), Tuesdays 12:00-13:30 (SR 0.02).
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. Statistics of random unitaries: Haar integration, Weingarten calculus, unitary designs
3. Many-body properties from classical shadows
4. Quantum randomness from local gates: Random quantum circuits
5. Random dynamics in many-body systems: anticoncentration, magic and entanglement dynamics, scrambling in chaotic systems

Lecture notes: Will be available here.

Exercises: There will be exercises every second Monday, starting on 26 October. Exercise sheets will be released every second Thursday at 12:00, starting on 15 October, and shall be uploaded via ILIAS a week later. There will be 7 exercise sheets in total.

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

Slides of the seminar talks (incomplete):

1. Hamiltonian Simulation I: Linear Combination of Unitaries
2. Hamiltonian Simulation II: Qubitization and Quantum Signal Processing
3. Solving Differential Equations using Quantum Algorithms
4. Magic-State Model and Resource Estimates
5. Beyond factoring: the Hidden Subgroup Problem
6. Lower Bounds using Quantum Query Complexity
7. Quantum Machine Learning (PhD student talk)

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.