Holonomic quantum manipulation in the Weyl disk

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