It is shown that Majorana fermions trapped in three p-wave
superfluid vortices form a qubit in a topological quantum
computing (TQC). Several similar ideas have already been
proposed: Ivanov [Phys. Rev. Lett. 86, 268 (2001)] and
Zhang et al [Phys. Rev. Lett. 99, 220502 (2007)] suggested
schemes in which a qubit is implemented with two and four
Majorana fermions, respectively, where a qubit operation is
performed by braiding the world lines of these Majorana
fermions. Naturally the set of quantum gates thus obtained
is a discrete subset of the relevant unitary group.
We propose a new scheme, where three Majorana fermions
form a qubit. We show that continuous qubit operations are
made possible by braiding the Majorana fermions complemented
with dynamical phase change. Moreover, it is possible to
introduce entanglement between two such qubits by geometrical
manipulation of some vortices involved.