# When geometric phases turn topological

## TL;DR

This paper demonstrates that for certain spin states, geometric phases become topological invariants, making them robust against noise and deformation, which is promising for quantum computing applications.

## Contribution

It introduces a class of spin states called anticoherent states where geometric phases depend only on topological properties, enhancing noise immunity.

## Key findings

- Geometric phases for anticoherent states are topologically protected.
- Path dependence reduces noise sensitivity in quantum phases.
- Topological phases are invariant under continuous deformations.

## Abstract

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.