Research

Quantum isomorphism and symmetry

Nonlocal games provide a way to connect graph theory with quantum information. With Laura Mančinska, I developed a theory of quantum graph homomorphisms that brings together graph coloring, independent sets and zero-error communication.

One of our results gives a combinatorial characterization of quantum isomorphism in the quantum commuting model: two graphs are quantum isomorphic exactly when they have the same number of homomorphisms from every planar graph. This connects a notion defined using quantum measurements to ordinary graph counting.

I also study quantum automorphism groups. With Josse van Dobben de Bruyn and Simon Schmidt, I constructed asymmetric graphs with quantum symmetry: their classical automorphism groups are trivial, but their quantum automorphism groups are not.

Homomorphism counts and graph structure

How much of a graph can be recovered from the number of homomorphisms into it? I study how the answer depends on the graphs from which we count. For example, I showed that no fixed bound on their maximum degree is sufficient to distinguish all nonisomorphic graphs, even when arbitrarily large graphs are allowed.

This work introduced oddomorphisms, graph homomorphisms with additional parity conditions, and led to further questions about the distinguishing power of graph classes. In recent joint work, we prove the weak Roberson conjecture. My current work also explores topological and geometric approaches to homomorphism indistinguishability.

Semidefinite optimization and quantum information

Semidefinite programming provides useful relaxations of many graph problems. With collaborators, I have studied exact computation at fixed levels of the Lasserre and NPA hierarchies for classical and quantum graph isomorphism, connecting these relaxations to homomorphism counts. I also work on graph parameters such as vector colorings and projective packings, including their role in quantum communication.

Funding

I am the principal investigator of Quantum Graph Theory, supported by a Carlsberg Foundation Semper Ardens: Accelerate grant for 2022–2026. The project funded one PhD student and three postdoctoral researchers.

I also contribute to Lifelong Education in Quantum Science (2025–2027), supported by the Danish Agency for Higher Education and Science. My role is to develop a course on quantum nonlocality for the joint DTU–University of Copenhagen MSc in Quantum Information Science.

Academic activities