Quantum Computation Using Vortices and Majorana Zero Modes of a $p_x$ + $ip_y$ Superfluid of Fermionic Cold Atoms

Abstract

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.