4EU+: Quantum Mechanics from Condensed Matter to Computing


The course is not mandatory in any master education but is part of the 4EU+ Alliance. The course is given in collaboration with University of Warsaw and University of Milan.

Target Groups

Master students and PhD students. The course is open to all interested students, also students outside the 4EU+ Alliance. Travel grants are, however, only available to students from within the alliance. Priority will be given to students from our partner universities, University of Milan and University of Warsaw.


Master students enrolled at University of Copenhagen must apply to the
Study Board to transfer the course credits as part of their master programme.
The course responsibles can help with the application to the Study Board.

Spring and Block 4
March 1- June 17, 2022


The course will consist of three phases.
Phase 1: March 1- May 13, 2022: Online lectures (approximately one two hour lectures every other week, in total 6 lectures)
Phase 2: May 13- June 13, 2022: Students work on assignments which will be presented at a poster session at the physical meeting.
Phase 3: June 13 -June 17, 2022: Physical Master Class (Approximately 24 hours of lectures plus 5 hours exercises)


We are currently witnessing the second quantum revolution and with it the advent of quantum technological devices for information processing purposes. Understanding these systems and their capabilities as well as developing robust algorithms for them, requires a fundamental understanding of complex quantum many-body systems as well as ways to characterize their properties efficiently. Within this course, we will help the participants to obtain proficiency in all of these aspects of quantum theory. A tentative list of topics include

  • Complex quantum many-body systems: 
    • Mathematical description of many-body systems
    • Properties of Fermi and Bose gases
  • Identification and certification of quantum systems
    • Quantum state tomography
    • Self-testing

For each of these topics, we will provide introductory lectures to get students acquainted with the topics before entering into the in-person phase, where experts and practitioners of these fields will give further insight.

Learning Outcome

The goal is to provide the students with a blended learning approach to the course content on the mathematics of quantum theory with special emphasis on complex quantum many-body systems and quantum information theory. The Main intended learning outcomes include an overview over the latest developments in those fields, the capability to analyze the performance and complexity of a given quantum optimization algorithm as well as how to efficiently benchmark and certify the functioning of a quantum information processing device. Furthermore, the course will help the participants to develop competencies to engage in self-organized cross-university and interdisciplinary collaborations via online groupwork as well as to give an receive peer-feedback on results. Inviting external experts in the field will also give young researchers in the field the opportunity to grow their professional network considerably. 

Contact Persons

University of Copenhagen: 
Associate Professor Albert Werner and Professor Jan Philip Solovej, Department of Mathematical Sciences (Project Coordinator)

University of Milan:
Associate Professor Niels Benedikter, Dipartimento di Matematica

University of Warsaw:
Assistant Professor Marcin Napiórkowski, Faculty of Physics