- 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

Head of the Group## Marek Kuś, Professor

Group memberI am a mathematical physicist, a professor at the Center for Theoretical Physics, Polish Academy of Sciences and a member of the Centre for Systemic Risk Analysis at University of Warsaw.

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. My PhD supervisor is Prof. Adam Sawicki.

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

## Jan Głowacki

PhD studentI am a PhD student at the Center for Theoretical Physics, Polish Academy of Sciences (Warsaw). My PhD supervisor is Prof. Marek Kuś. I am interested in a variety of topics in theoretical and mathematical physics, including:

The main topics of my current research are:

- relational approaches to quantum theory (quantum reference frames and beyond)
- reconstructions of (relational) quantum theory
- statistical (quantum) physics with Bayesian inference
- General Relativity as as emergent framework

# 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”, written under the supervision of Prof. Adam Sawicki, 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”, written under the supervision of Prof. Adam Sawicki, in October 2018.

## Lorenzo Mattioli

Former memberLorenzo was a PhD student in QuantMath group in 10/2018-10/2022. His PhD supervisor was Prof. Adam Sawicki. Lorenzo successfully defended thesis: “Quantum Universality and Membership Problems” in October 2022.