  It has been shown that a Weyl point in a superconducting nanostructure may
give rise to a Weyl disk where two quantum states are almost degenerate in a 2D
manifold in the parametric space. This opens up the possibility of a holonomic
quantum manipulation: a transformation of the wave function upon adiabatic
change of the parameters within the degenerate manifold. In this paper, we
investigate in detail the opportunities for holonomic manipulation in Weyl
disks.
  We compute the connection at the manifold in quasiclassical approximation to
show it is Abelian and can be used for a phase gate. To provide a closed
example of quantum manipulation that includes a state preparation and read-out,
we augment the holonomic gate with a change of parameters that brings the
system out of the degenerate subspace. For numerical illustrations, we use a
finite value of quasiclassical parameter and exact quantum dynamics. We
investigate the fidelity of an example gate for different execution times.
