Abstract
Topological concepts have profoundly changed our perspective on phases of matter, phase transitions, and the protection and processing of quantum information. In this Agora Talk, we explore the role of vortices and skyrmions in two-dimensional superfluids and magnets, as well as how novel quantum states, such as fractional quantum Hall systems, can non-locally store quantum information in a way that protects it from the environment while it is being processed. New discoveries have shown that fractional quantum Hall states can occur even without magnetic fields, opening new possibilities for their realization.
