Finding order in large-scale structures by quantum computing
Quantum computing is an emerging, interdisciplinary field of science in the intersection of computer science, mathematics and physics. Recent experimental advances in building a physical quantum computer show the urgency of finding possible applications. On the other hand to date we only have very small quantum computers, which are mostly useful for proof of concept demonstrations, thus for the time being one needs to focus on building and understanding the underlying mathematical theory. A particularly interesting aspect of quantum computing is quantum machine learning, which also needs a more firm theoretical understanding, because many of the recent developments are based on heuristic approaches which cannot be properly tested yet, due to the limitations of the available hardware.

This proposal outlines new approaches and ideas for quantum algorithm development, and attempts to improve some aspects of the theory of quantum machine learning, while also encompasses some fundamental theoretical questions. The described ideas are all related to the problem of finding large-scale structures in various objects. Since quantum computers tend to be quite efficient at recognizing patterns, it is a promising angle of approach. The relevant ideas are inspired by multiple related disciplines, and several of the proposed tools were recently co-developed by the applicant.

The supervisor has an outstanding track record in developing the mathematical theory of large-scale structures emerging in graphs, groups and networks, while the applicant has demonstrated strong problem solving skills and the ability of developing novel quantum algorithms, which promises a fruitful collaboration in the implementation of the proposed action.