  Majorana-based topological qubits are expected to exploit the nonabelian
braiding statistics of Majorana modes in topological superconductors to realize
fault-tolerant topological quantum computation. Scalable qubit designs require
several Majorana modes localized on quantum wires networks, with braiding
operations relying on the presence of the groundstate degeneracy of the
topologically nontrivial superconducting phase. However, this degeneracy is
lifted due to the hybridization between Majorana modes localized at a finite
distance. Here, we describe a braiding protocol in a trijunction where each
branch consists of a lattice of Majorana modes overlapping at a finite
distance. We find that the energy splitting between the groundstate and the
lowest-energy state decreases exponentially with the number of Majorana modes
if the system is in its topologically nontrivial regime. This result does not
rely on the specific braiding geometry and on the details of the braiding
scheme but is a consequence of the supersymmetry and nontrivial topology of the
effective low-energy Hamiltonian describing the Majorana lattice.
