  In this paper we present a hybrid scheme for topological quantum computation
in a system of cold atoms trapped in an atomic lattice. A topological qubit
subspace is defined using Majorana fermions which emerge in a network of atomic
Kitaev one-dimensional wires. We show how braiding can be efficiently
implemented in this setup and propose a direct way to demonstrate the
non-Abelian nature of Majorana fermions via a single parity measurement. We
then introduce a proposal for the efficient, robust and reversible mapping of
the topological qubits to a conventional qubit stored in a single atom. There,
well-controlled standard techniques can be used to implement the missing gates
required for universal computation. Our setup is complemented with an efficient
non-destructive protocol to check for errors in the mapping.
