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Continuously ongoing

Group seminar: Theoretical quantum science and technology

Group members present and discuss their latest progress and results and give tutorial talks. Some talks will also be given by (external) visitors.
Interested students are always very welcome.

Time and place: Thursdays 14:30h-16:00h, seminar room in or on Webex.

See www.mkliesch.eu/seminar.html for details.

Summer term 2022

Lecture: Quantum computing

Tuesday 12:30pm, room 25.32 HS 5K
Thursday 12:30pm, room 25.22 HS 5H

Quantum computing is among the most exciting applications of quantum mechanics. Quantum algorithms can solve computational problems efficiently that have a prohibitive runtime on traditional computers. Such problems include, for instance, factoring of integer numbers or energy estimation problems from quantum chemistry.
This course provides an introduction to quantum computing and discusses some challenges ahead.
An emphasize will be put on conceptual and mathematical aspects.

See www.mkliesch.eu/qc.html for the course homepage.

Winter term 2019/2020

Statistische Mechanik

3. Prüfung

Die 3. Klausur findet am 19. Oktober um 8:15h im Hörsaal 6F im Gebäude 26 statt.


  • Grundlagen der Wahrscheinlichkeitstheorie
  • Informationsmaße
  • Jaynes'sches Prinzip
  • Ensembles der Statistischen Physik
  • Ideale Quantengase, Bose-Einstein-Kondensation
  • Thermodynamik (Potentiale, Eulergleichung, Gibbs-Duhem-Relation, Maxwellbeziehungen, thermodynamische Prozesse, Hauptsätze)
  • Phasenübergänge (Van-der-Waals-Gleichung, Ising-Modell, kritische Phänomene)


  • Ein Skript zur Vorlesung kann hier gefunden werden.
    Auf Anfrage versende ich (teaching@mkliesch.eu) auch gerne eine Version des Skripts, welche die Bilder enthält.

Summer term 2019

Lecture: Characterization and verification of quantum simulations

Monday 8:30am, room (lecture)
Tuesday 10:30am, room (tutorial class)

Quantum simulations and quantum computing are among the most exciting applications of quantum mechanics. More generally, in the quantum technology research field one aims to develop new devices using quantum superposition and entanglement. In a popular wording, these anticipated developments will lead to the second quantum revolution.

A main milestone is the use of quantum capabilities to solve a (computational) problem that cannot practically be solved otherwise. Theoretical proposals include integer factoring (Shor's algorithm), speed-ups for optimization and machine learning algorithms, the simulation of complex quantum systems, and certain sampling experiments specifically tailored to that milestone.

But if one cannot obtain the output of a quantum simulation or computation by conventional means how can one make sure that the outcome is correct? The output of integer factorization can efficiently be checked but, for instance, for the estimation of energies in quantum many-body systems, or outcomes of dynamical simulations, the situation is much less clear. Hence, for the development of trusted quantum technologies special characterization and verification techniques are urgently required.

This course gives an introduction to the research field, to the problems of characterization, validation, and verification, and first ways to solve them. More specifically, quantum state tomography, quantum states certification, quantum process tomography, and randomized benchmarking will be covered. In particular, the course provides an overview of the latest developments in this still young and very active research field. The approaches of the course are mainly of conceptual and mathematical nature. 


  • Quantum state tomography
  • Fidelity estimation and certification of quantum state preparations
  • Randomized benchmarking for quantum dynamics
  • Quantum process tomography


Winter term 2018/2019

Machine learning in quantum physics

Quantum machine learning is an emerging research field. This first course focuses on the subfield where classical machine learning is applied in quantum physics. The goal of this course is to provide the students with the necessary skills to understand the main ideas and some details of the ongoing research in that area.


  1. Introduction to neural networks and deep learning
  2. Applications in quantum physics