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Topological features in quantum computing provide controllability and noise error avoidance in the performance of logical gates. While such resilience is favored in the manipulation of quantum systems, it is very hard to identify topological features in nature. This paper proposes a scheme where holonomic quantum gates have intrinsic topological features. An ion trap is employed where the vibrational modes of the ions are coherently manipulated with lasers in an adiabatic cyclic way producing geometrical holonomic gates. A crucial ingredient of the manipulation procedures is squeezing of the vibrational modes, which effectively suppresses exponentially any undesired fluctuations of the laser amplitudes, thus making the gates resilient to control errors., 9 pages, 4 figures, REVTEX

We propose a possible scheme for generating spin-J geometric phases using a coupled two-mode Bose-Einstein condensate (BEC). First we show how to observe the standard Berry phase using Raman coupling between two hyperfine states of the BEC. We find that the presence of intrinsic interatomic collisions creates degeneracy in energy that allows implementation of the non-Abelian geometric phases as well. The evolutions produced can be used to produce interference between different atomic species with high numbers of atoms or to fine control the difference in atoms between the two species. Finally, we show that errors in the standard Berry phase due to elastic collisions may be corrected by controlling inelastic collisions between atoms., Comment: 6 pages, 2 figures

In this paper the idea of holonomic quantum computation is realized within quantum optics. In a non-linear Kerr medium the degenerate states of laser beams are interpreted as qubits. Displacing devices, squeezing devices and interferometers provide the classical control parameter space where the adiabatic loops are performed. This results into logical gates acting on the states of the combined degenerate subspaces of the lasers, producing any one qubit rotations and interactions between any two qubits. Issues such as universality, complexity and scalability are addressed and several steps are taken towards the physical implementation of this model., 16 pages, 3 figures, REVTEX