Dynamics and Fusion of Majorana Zero Modes in Quantum-dot based Interacting Kitaev Chains

Motivated by the recent experimental realization of a minimal Kitaev chain in quantum dot systems, we present our theoretical findings on the dynamics and fusion of MZMs at or near the ``sweet spot" tₕ = (where the fermionic hopping tₕ and superconducting coupling are equal). We investigated the dynamics and fusion of MZMs using time-dependent real-space local density-of-states methods. The movement of Majoranas and the detection of fusion channels are crucial for topological quantum computations. Additionally, we discuss our recent discovery of exotic ``multi-site" MZMs in Y-shaped Kitaev wires, which is important for the potential braiding of Majoranas in Y-junctions formed from arrays of quantum dots. Finally, we present results on "non-trivial" fusion using canonical Kitaev wires at the sweet spot.