  We study the evolution of a quantum dot controlled by a frequency-swept
(chirped), linearly polarized laser pulse in the presence of carrier-phonon
coupling. The final occupation of the exciton state is limited both due to
phonon-induced transitions between the adiabatic spectral branches and because
of phonon-assisted transitions to the biexciton state. When the biexciton shift
is large enough, the quantum dot can be modeled as a two-level system, which
corresponds to excitation with circularly polarized light. For this case, we
compare different methods of simulations: (i) a time convolutionless method,
(ii) correlation expansion and (iii) path integrals. We show that results
obtained from these methods agree perfectly at low temperatures.
