Lecture and tutorial classes

Characterization and verification of quantum simulations

(Summer term 2019)

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 working, 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 included 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 and verification, and first ways to solve them. Moreover, the course will provide an over the latest developments in this still young and very active research field. The approaches of the course will be mainly of conceptual and mathematical nature.


  • Fidelity estimation and certification of quantum state preparations

  • Quantum state tomography (based on compressed sensing)

  • Randomized benchmarking for quantum dynamics

Formal things

  • Prerequisites for attending are basic knowledge

    • Linear algebra,

    • Calculus, and

    • Quantum mechanics.

  • Assignments will be uploaded every two weeks.

  • There might be lecture notes.

Preliminary schedule


  • ?? | VL (Motivation, course outline, formalities), exercise 1 handed out

  • | Ü (Introduction, student questions & discussion)

  • | VL (Basics of probability theory)

  • | Ü (Discussion of exercise 1, exercise 2 handed out)

  • | VL (Tail bounds for iid. random variables)

  • | Ü, (Student questions & discussion)

  • |VL


  • ... to be uploaded ...