4EU+: Quantum Information and Quantum Many-Body Theory

Education

The course is not mandatory in any master's education but is part of the 4EU+ Alliance and offered in collaboration with the DigiQ network. The course is given in collaboration with the University of Warsaw, the University of Milan, the University of Geneva, Heidelberg University, Sorbonne University and Charles University.

Target Groups

Master students and PhD students. The course is open to all interested students, as well as students outside the 4EU+ Alliance. Travel grants are, however, only available to students from within the alliance and the DigiQ network. Priority will be given to students from our partner universities, the University of Milan, the University of Warsaw, the University of Geneva, Heidelberg U University, Sorbonne University and Charles University.

Requirements

Expected minimal requirements: Linear algebra some elementary quantum knowledge, e.g., elementary quantum computing or elementary quantum mechanics.

Registration

Registration before Friday February 19, 2026. The online registration will open in the beginning of January 2026.

ECTS Credits

ECTS credits are allocated locally. The registration form is the standard form used at UCPH, where students will be awarded 7.5 ECTS credits. Students from other universities will receive their ECTS credits through their local study administration. Please contact your local contact person (see list of contact persons below).

Master students enrolled at the University of Copenhagen must apply to the Study Board to transfer the course credits as part of their master's program. The course responsible can help with the application to the Study Board. Please contact Albert Werner or Jan Philip Solovej.

Placement

Spring and Block 4, February 26- June 19, 2026.

Schedule

The course will consist of three phases:
  • Phase 1: 25 February-23 April, 2026. Introduction to the course on February 25, 2026.Tentative lecture dates:  February: 26. March: 5, 12, 9, 26. April: 9,16. Introduction to projects  on April 23, 2026. 
    Online lectures     (approximately one two-hour lecture every other week, in total 7 lectures)
  • Phase 2: 23 April-31 May, 2026. Students work on assignments which will be presented at a poster session at the physical meeting.
  • Phase 3: 15-19 June, 2026. Physical Master Class in Paris. The location is to be confirmed. (Approximately 24 hours of lectures plus 5 hours of exercises).

Content

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 includes:

  • Entanglement/Non-Locality:
    Lecture 1: States, Measurement, Tensor Product, Maximally Entangled State
    Lecture 2: Tensor Product (contd.), Density Matrices, Reduced States, Entropy, Entanglement Entropy.
    Lecture 3: Bell-inequalities, Bell’s Theorem, Non-local Games/Protocols.

  • Quantum Spin-System
    Lecture 1: Spin Hamiltonians, Spin-½ Heisenberg Model, SU(2), Ground States, Ground State Energy
    Lecture 2: Free Energy, Thermodynamic Limit, Thermal State
    Lecture 3: Symmetry Breaking, Mermin-Wagner
    Lecture 4: AKLT, Matrix Product States

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 of the latest developments in those fields. 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 and 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. 

Registration before 19 February, 2026. Students who register for the course will get access to the Absalon course webpage before the course starts.

Contact Persons

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

University of Milan:
Professor Niels Benedikter, Dipartimento di Matematica

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

University of Geneva: 
Assistant Professor Géraldine Haack, Department of Applied Physics 
Professor Nicholas Brunner, Department of Applied Physics

Heidelberg University:
Professor Manfred Salmhofer, Department of Physics

Sorbonne University:
Frédéric Grosshans, CNRS Researcher at LIP6

Vincent Petit,

Associate Professor Marco Túlio Quintino, Department of Engineering and LIP6

Charles University: 
Professor Martin Loebl, Department of Applied Mathematics