QMATH Masterclass on Representation Theory in Quantum Information Science
Copenhagen, 18 to 22 August 2025
Quantum information theory has seen much development over the past 30 years, and is becoming ever more important with the upcoming access to intermediate-scale quantum hardware.
Representation theory is a very successful branch of mathematics that has been extensively studied over the years. It finds many applications in quantum theory, where physical operations correspond linear transformations and thus has naturally played a very influential role in quantum mechanics.
Recently, interest in representation theory has skyrocketed, because it is an important tool to elegantly describe various tasks at the intersection of many-body quantum physics, quantum information, and quantum computing. Key examples are tasks involving independent copies of the same state (e.g., state tomography), the study of averaged properties of random states and/or circuits, which appear in a multitude of settings from black hole physics to cryptography, and randomized benchmarking of quantum devices, which is of key practical interest.
The aim of this course is to present these developments in a coherent way, identifying the key ingredients from the representation theory of the unitary and Clifford groups, as well as showcasing some of the many interesting applications in quantum information theory.
Target audience
This master class will be of interest for PhD students and advanced master students in mathematics, physics or computer science. It should serve as a way of entering the broad and vibrant field of quantum simulation. The masterclass will consist of blackboard lectures, giving an introduction in the mathematical theory of quantum simulation. The emphasis is on theoretical rather than practical aspects.
There will be a poster session, where all participants have the opportunity to present their research.
It is not required to have in-depth previous knowledge about representation theory. We do expect that students have basic knowledge about quantum information theory. Don't hesitate to get in touch with the organizers if you have questions!
Location
The master class will take place at the University of Copenhagen, Denmark. Copenhagen is a beautiful harbor city, famous for being among the safest and most enjoyable places to live in the world.
Participants of the master class will have the opportunity to explore the city from the water during an excursion. August is the second warmest month of the year in Copenhagen with about 14 hours of daylight.
The deadline for application is June 8th. Note that there is no participation fee.
In case of questions or if you missed the registration deadline, you are welcome to reach out to Daniel Malz (malz@math.ku.dk) or Albert H. Werner (werner@math.ku.dk).
We are happy to already announce the following leading experts to give lectures in the school:
- David Gross (University of Cologne)
- Michael Walter (Ruhr University of Bochum)
These will be supplemented by the local speakers:
- TBA
TBA
TBA
The conference/masterclass will take place at the Department of Mathematical Sciences, University of Copenhagen. See detailed instructions on how to reach Copenhagen and the conference venue. Directions to the MATH department, and several other useful locations, can be found here.
Tickets and passes for public transportation can be bought at the Copenhagen Airport and every train or metro station. You can find the DSB ticket office on your right-hand side as soon as you come out of the arrival area of the airport. DSB has an agreement with 7-Eleven, so many of their shops double as selling points for public transportation. Copenhagen is a very bike-friendly city, and you could consider renting a bike.
A journey planner in English is available.
We kindly ask the participants to arrange their own accommodation.
A good option can be Hotel 9 Små Hjem, which is pleasant and inexpensive and offers rooms with a kitchen. Other alternatives are Steelhouse Copenhagen and CabInn, which has several locations in Copenhagen: the Hotel City (close to Tivoli), Hotel Scandivania (Frederiksberg, close to the lakes), and Hotel Express (Frederiksberg) are the most convenient locations; the latter two are 2.5-3 km from the math department. Another hostel option is Hub - CityHub in Vesterbro. Somewhat more expensive – and still recommended – options are Hotel Nora and Ibsen's Hotel.
An additional option is to combine a stay at the CabInn Metro Hotel with a pass for Copenhagen public transportation (efficient and reliable). See information about tickets & prices.
The masterclass is organized by the Villum Centre for the Mathematics of Quantum Theory (QMATH) and the Quantum for Life center at the Department of Mathematical Sciences. The local organizers are:
Albert H. Werner
Any questions about the masterclass can be directed to Suzanne Andersen at suzanne@math.ku.dk