This paper explores the implementation of non-Abelian statistics and topological quantum information processing in one-dimensional semiconductor wire networks. The authors demonstrate that Majorana fermions, which are their own antiparticles, can be manipulated in such networks to enable non-Abelian braiding and statistics, similar to those observed in a $ p + ip $ superconductor. The key idea is that networks of 1D semiconducting wires, when placed on an s-wave superconductor, can host Majorana fermions at their ends, which can be transported, created, and fused using locally tunable gates. The authors show that despite the absence of vortices in the wires, Majorana fermions in semiconducting wires exhibit non-Abelian statistics, transforming under exchange in a manner analogous to vortices in a $ p + ip $ superconductor. The paper discusses the physics of a single wire, showing that under specific conditions, the wire can be driven into a topological superconducting state with zero-energy Majorana modes at its ends. The authors then consider the T-junction, a simple network of wires, and show that it allows for the adiabatic exchange of Majorana fermions. They demonstrate that the exchange of Majorana fermions in such a network leads to non-Abelian statistics, with the transformation rules for the Majoranas being similar to those in a $ p + ip $ superconductor. The authors also propose experimental setups that enable the Majorana fusion rules to be probed, as well as networks that allow for efficient exchange of many Majorana fermions. The paper concludes that 1D semiconductor wire networks provide a promising platform for topological quantum information processing. The physical transparency of the manipulations and the experimental realism of the setups make them particularly appealing. While braiding alone does not permit universal quantum computation, the implementation of the ideas introduced here would constitute a critical step towards this ultimate goal. The authors also discuss the implications of their findings for the broader field of topological quantum computation, emphasizing the importance of non-Abelian statistics in enabling robust quantum information processing.This paper explores the implementation of non-Abelian statistics and topological quantum information processing in one-dimensional semiconductor wire networks. The authors demonstrate that Majorana fermions, which are their own antiparticles, can be manipulated in such networks to enable non-Abelian braiding and statistics, similar to those observed in a $ p + ip $ superconductor. The key idea is that networks of 1D semiconducting wires, when placed on an s-wave superconductor, can host Majorana fermions at their ends, which can be transported, created, and fused using locally tunable gates. The authors show that despite the absence of vortices in the wires, Majorana fermions in semiconducting wires exhibit non-Abelian statistics, transforming under exchange in a manner analogous to vortices in a $ p + ip $ superconductor. The paper discusses the physics of a single wire, showing that under specific conditions, the wire can be driven into a topological superconducting state with zero-energy Majorana modes at its ends. The authors then consider the T-junction, a simple network of wires, and show that it allows for the adiabatic exchange of Majorana fermions. They demonstrate that the exchange of Majorana fermions in such a network leads to non-Abelian statistics, with the transformation rules for the Majoranas being similar to those in a $ p + ip $ superconductor. The authors also propose experimental setups that enable the Majorana fusion rules to be probed, as well as networks that allow for efficient exchange of many Majorana fermions. The paper concludes that 1D semiconductor wire networks provide a promising platform for topological quantum information processing. The physical transparency of the manipulations and the experimental realism of the setups make them particularly appealing. While braiding alone does not permit universal quantum computation, the implementation of the ideas introduced here would constitute a critical step towards this ultimate goal. The authors also discuss the implications of their findings for the broader field of topological quantum computation, emphasizing the importance of non-Abelian statistics in enabling robust quantum information processing.