147 research outputs found
On geometric phases for quantum trajectories
A sequence of completely positive maps can be decomposed into quantum
trajectories. The geometric phase or holonomy of such a trajectory is
delineated. For nonpure initial states, it is shown that well-defined
holonomies can be assigned by using Uhlmann's concept of parallel transport
along the individual trajectories. We put forward an experimental realization
of the geometric phase for a quantum trajectory in interferometry. We argue
that the average over the phase factors for all quantum trajectories that build
up a given open system evolution, fails to reflect the geometry of the open
system evolution itself.Comment: Submitted to the Proceedings of the 13th CEWQO 2006 in Vienn
Validity of rotating wave approximation in non-adiabatic holonomic quantum computation
We examine the validity of the rotating wave approximation (RWA) in
non-adiabatic holonomic single-qubit gates [New J. Phys. {\bf 14}, 103035
(2012)]. We demonstrate that the adoption of RWA may lead to a sharp decline in
fidelity for rapid gate implementation and small energy separation between the
excited and computational states. The validity of the RWA in the recent
experimental realization [Nature (London) {\bf 496}, 482 (2013)] of
non-adiabatic holonomic quantum computation for a superconducting qubit is
examined.Comment: Changes, old figure replaced two new figures, journal reference adde
Comment on `Detecting non-Abelian geometric phases with three-level systems'
In their recent paper, Yan-Xiong Du et al. [Phys. Rev. A 84, 034103 (2011)]
claim to have found a non-Abelian adiabatic geometric phase associated with the
energy eigenstates of a large-detuned three-level system. They
further propose a test to detect the non-commutative feature of this geometric
phase. On the contrary, we show that the non-Abelian geometric phase picked up
by the energy eigenstates of a system is trivial in the adiabatic
approximation, while, in the exact treatment of the time evolution, this phase
is very small and cannot be separated from the non-Abelian dynamical phase
acquired along the path in parameter space.Comment: Explicit proof that the non-Abelian geometric phase is trivial added,
journal reference adde
- …