Braiding Majorana zero modes in a two-dimensional grid structure

Constructing Majorana zero modes (MZMs) is one of the most promising schemes for achieving topological quantum computing. However, recent research primarily focuses on preparing stable materials that carry MZMs and detecting their existence. Further combining structures that carry MZMs for quantum computing would facilitate the synergistic development of material fabrication and quantum computing. Here, we take the T-junction structure carrying MZMs as the basic unit to construct a two-dimensional (2D) grid structure. Based on this structure, the protocols for performing braiding operations for single-qubit and two-qubit gates are defined. Furthermore, the Deutsch-Jozsa (D-J) algorithm is derived to demonstrate the vast application potential of the 2D grid structure in more complex quantum algorithms.