When geometric phases turn topological

@article{Aguilar2020WhenGP,
  title={When geometric phases turn topological},
  author={Pedro Aguilar and Chryssomalis Chryssomalakos and E Guzm{\'a}n-Gonz{\'a}lez and L Hanotel and E Serrano-Ens{\'a}stiga},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2020},
  volume={53}
}
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… 
2 Citations

Toponomic Quantum Computation

Holonomic quantum computation makes use of non-abelian geometric phases, associated to the evolution of a subspace of quantum states, to encode logical gates. We identify a special class of

Stellar Representation of Multipartite Antisymmetric States

Pure quantum spin- s states can be represented by 2 s points on the sphere, as shown by Majorana (Nuovo Cimento 9:43–50, 1932)—the description has proven particularly useful in the study of

References

SHOWING 1-10 OF 46 REFERENCES

Quantum Kinematic Approach to the Geometric Phase. II. The Case of Unitary Group Representations

The quantum kinematic approach to geometric phases, developed in a preceding paper, is applied to the case of phases arising from unitary representations of Lie groups on Hilbert space. Specific

Quantum Kinematic Approach to the Geometric Phase. I. General Formalism

A new approach to the theory of the geometric phase in quantum mechanics, based entirely on kinematic ideas, is developed. It is shown that a gauge and reparametrization invariant phase can be

A geometric phase for m = 0 spins

A mod jm) spin state in an adiabatically-cycled magnetic field acquires a geometric phase of m times the solid angle described by B, so that for m=0 states the geometric phase vanishes. However, if B

QUANTUM HOLONOMIES FOR QUANTUM COMPUTING

Holonomic Quantum Computation (HQC) is an all-geometrical approach to quantum information processing. In the HQC strategy information is encoded in degenerate eigen-spaces of a parametric family of

Geometric phase of a spin-1 2 particle coupled to a quantum vector operator

We calculate Berry’s phase when the driving field, to which a spin-1 2 is coupled adiabatically, rather than the familiar classical magnetic field, is a quantum vector operator, of noncommuting, in

Measurement of a vacuum-induced geometric phase

TLDR
The ability to control the appearance of a vacuum-induced Berry phase in an artificial atom, a superconducting transmon, interacting with a single mode of a microwave cavity opens new possibilities for the geometric manipulation of atom-cavity systems also in the context of quantum information processing.

Geometry of spin coherent states

Spin states of maximal projection along some direction in space are called (spin) coherent, and are, in many respects, the ‘most classical’ available. For any spin s, the spin coherent states form a

Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase

It is shown that the "geometrical phase factor" recently found by Berry in his study of the quantum adiabatic theorem is precisely the holonomy in a Hermitian line bundle since the adiabatic theorem

Noise fluctuations and the Berry phase: Towards an experimental test

Abstract.Due to its geometric nature Berry's geometric phase exhibits stability to a great extent when exposed to parametric noise fluctuations. Considering an adiabatic evolution of a