Study on the non-Abelian properties of Majorana zero modes assisted by quantum-dot

Majorana zero modes, characterized by non-Abelian exchange statistics, have been widely viewed as prime candidates for implementing topological quantum computing. The associated braiding and fusion operations realize topologically protected quantum gates and qubit measurements, thus providing a feasible pathway toward intrinsically fault-tolerant quantum computation. However, the experimental realization of controllable braiding and fusion of Majorana zero modes remains one of the most formidable challenges in the field.In this paper, building upon recent theoretical advances in quantum-dot-assisted schemes for realizing the braiding and fusion of Majorana zero modes, we provide a systematic introduction to the underlying theoretical foundations and detailed operational procedures, and further elucidate the experimental feasibility of the approach.Furthermore, this paper presents two lines of investigation developed within the proposed framework. Firstly, based on the quantum-dot-assisted braiding scheme, the dynamical evolution of Andreev bound states in Majorana nanowires is revealed. Secondly, employing the quantum-dot-assisted fusion scheme, numerical simulations of charge transfer along different fusion paths clarify the nontrivial fusion rules of Majorana zero modes and the corresponding operational procedures.