Topological Quantum Computing with p-Wave Superfluid Vortices

Details Topological Quantum Computing with p-Wave Superfluid Vortices Topological Quantum Computing with p-Wave Superfluid Vortices

2009-06-24

arxiv.org/abs/0906.4444v2

Physics

Quantum Physics

5 pages, 2 figures. Two-qubit gate implementation is added.

Scientific paper

It is shown that Majorana fermions trapped in three vortices in a p-wave superfluid form a qubit in a topological quantum computing (TQC). Several similar ideas have already been proposed: Ivanov [Phys. Rev. Lett. {\bf 86}, 268 (2001)] and Zhang {\it et al.} [Phys. Rev. Lett. {\bf 99}, 220502 (2007)] 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. 2-qubit gates are realized through the use of the coupling between Majorana fermions of different qubits.

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