Quantum computers are machines that exploit the rules of quantum mechanics to potentially outperform even the fastest supercomputers. However, due to the interferences of the chaotic external world, quantum computers corrupt easily making it difficult to perform computations accurately. This makes it important to study the phenomenon of quantum scarring where some quantum states manage to escape chaos. Mathematics of quantum scarring is mostly studied in single body systems such as billiards or flows on surfaces. The purpose of this project in Aalto is to design new tools in mathematics that give us a new fundamental understanding of how chaos manifests in mathematical models of quantum systems. Our plan is to bridge the ideas from large single body quantum systems to many body systems, which will help us discover mechanisms to escape chaos. Our methods draw ideas from the rapidly advancing theory of large networks, which are ubiquitous in the modern day world of big data.

2022

2027