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

Holonomic quantum manipulation in the Weyl Disk