Quantum Computing with p-Wave Superfluid Vortices

It is shown that Majorana fermions trapped in three vortices in a p-wave superfluid implement a qubit for universal quantum computing. Several similar ideas have already been proposed: Ivanov [Phys. Rev. Lett. 86 (2001) 268] and Zhang et al. [Phys. Rev. Lett. 99 (2007) 220502] have proposed schemes in which a qubit is implemented with two and four Majorana fermions, respectively, where a qubit operation is performed by exchanging the positions of Majorana fermions. The set of gates thus obtained is a discrete subset of the relevant unitary group. We propose, in this paper, a new scheme, where three Majorana fermions form a qubit. We show that continuous 1-qubit gate operations are possible by exchanging the positions of Majorana fermions complemented with dynamical phase change. Two-qubit gates are realized through the use of the coupling between Majorana fermions belonging to different qubits.