- description of quantum entanglement in many body systems and quantum marginal problem
- classification of quantum statistics (anyons) on quantum graphs and quantum networks
- characterisation of isospectral/isoscattering quantum graphs using representation theory of finite groups
- universality criteria for quantum gates
- t-designs and ε-nets
- efficiency of quantum gates and random walks on compact groups
- membership problem for quantum gate-sets

# Faculty

## Adam Sawicki, Professor

Group Leader## Marek Kuś, Professor

Group memberI am a mathematical physicist. I am a professor at the Center for Theoretical Physics, Polish Academy of Sciences and at International Center for Formal Ontology at Warsaw Technical University

My areas of scientific activities encompass:

- Quantum information theory (in particular, theory of quantum correlations),
- Quantum chaos (transitions from quantum to classical in quantum nonlinear systems),
- Information geometry
- Fundamentals of quantum mechanics and philosophy of mathematics and physics

# PhD Students

## Oskar Słowik

PhD StudentBy education, I am a mathematician, theoretical physicist and computer scientist. My scientific interests span a wide range of topics within those three subjects. My main area of research is mathematical and quantum physics, specifically applications of geometry and topology in quantum information and computation.

The main topics of my current research are:

- efficient quantum gates and quantum compilers
- shallow quantum circuits and random walks on compact groups
- geometry and topology of quantum correlations
- the computational complexity of chosen problems in quantum information
- elements of Quantum Machine Learning

# Former Members

## Tomasz Maciążek

Former MemberTomasz was a PhD student in QuantMath group in 10/2015-10/2018. He successfully defended thesis: “Topology of configuration spaces for particles on graphs” in October 2018. Currently he is a Vice Chancellor’s Fellow, School of Mathematics, University of Bristol.

## Katarzyna Karnas

Former MemberKatarzyna was a PhD student in QuantMath group in 09/2016-10/2018. She successfully defended thesis: “Universality in quantum computation” in October 2018.