Emerging quantum hybrid systems for non-Abelian-state manipulation

The non-Abelian state has garnered considerable interest in the field of fundamental physics and future applications in quantum computing. In this review, we introduce the basic ideas of constructing the non-Abelian states in various systems from 1D to 3D and discuss the possible approaches to detect these states, including the Majorana bound states in a hybrid device and the v = 5/2 state in a fractional quantum Hall system.