  Skyrmions in frustrated magnets have the helicity degree of freedom, where
two different configurations of Bloch-type skyrmions are energetically favored
by the magnetic dipole-dipole interaction and characterized by opposite
helicities. A skyrmion must become a quantum-mechanical object when its radius
is of the order of nanometer. We construct a qubit based on the two-fold
degeneracy of the Bloch-type nanoscale skyrmions in frustrated magnets. It is
shown that the universal quantum computation is possible based on nanoscale
skyrmions in a multilayered system. We explicitly show how to construct the
$\pi /4$ phase-shift gate, the Hadamard gate, and the CNOT gate. The one-qubit
quantum gates are materialized by temporally controlling the electric field and
the spin current. The two-qubit gate is materialized with the use of the
Ising-type exchange coupling by controlling the distance between the skyrmion
centers in two adjacent layers. The merit of the present mechanism is that an
external magnetic field is not necessary. Our results may open a possible way
toward universal quantum computations based on nanoscale topological spin
textures.
