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Abstract: It is shown that Majorana fermions trapped in three vortices in a p-wavesuperfluid form a qubit in a topological quantum computing TQC. Severalsimilar ideas have already been proposed: Ivanov Phys. Rev. Lett. {\bf 86},268 2001 and Zhang {\it et al.} Phys. Rev. Lett. {\bf 99}, 220502 2007have proposed schemes in which a qubit is implemented with two and fourMajorana fermions, respectively, where a qubit operation is performed byexchanging the positions of Majorana fermions. The set of gates thus obtainedis 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 thatcontinuous 1-qubit gate operations are possible by exchanging the positions ofMajorana fermions complemented with dynamical phase change. 2-qubit gates arerealized through the use of the coupling between Majorana fermions of differentqubits.

Autor: Tetsuo Ohmi, Mikio Nakahara


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