When geometric phases turn topological. (arXiv:1903.05022v2 [quant-ph] UPDATED)

Geometric phases, accumulated when a quantum system traces a cycle in quantum
state space, do not depend on the parametrization of the cyclic path, but do
depend on the path itself. In the presence of noise that deforms the path, the
phase gets affected, compromising the robustness of possible applications,
e.g., in quantum computing. We show that for a special class of spin states,
called anticoherent, and for paths that correspond to a sequence of rotations
in physical space, the phase only depends on topological characteristics of the
path, in particular, its homotopy class, and is therefore immune to noise.