  We propose to use the recently predicted two-dimensional `weak-pairing' $p_x
+ ip_y$ superfluid state of fermionic cold atoms as a platform for topological
quantum computation. In the core of a vortex, this state supports a zero-energy
Majorana mode, which moves to finite energy in the corresponding topologically
trivial `strong-pairing' state. By braiding vortices in the `weak-pairing'
state, unitary quantum gates can be applied to the Hilbert space of Majorana
zero-modes. For read-out of the topological qubits, we propose realistic
schemes suitable for atomic superfluids.
