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 π/4 phase-shift gate, the Hadamard gate, and
the CNOT gate. 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. We also propose a qubit based on a nanoscale meron in a magnetic nanodisk.