  We investigate the dynamics of a double quantum dot charge qubit which is
coupled to piezoelectric acoustic phonons, appropriate for GaAs
heterostructures. At low temperatures, the phonon bath induces a non-Markovian
dynamical behavior of the oscillations between the two charge states of the
double quantum dot. Upon applying the numerically exact quasiadiabatic
propagator path-integral scheme, the reduced density matrix of the charge qubit
is calculated, thereby avoiding the Born-Markov approximation. This allows a
systematic study of the dependence of the Q-factor on the lattice temperature,
on the size of the quantum dots, as well as on the interdot coupling. We
calculate the Q-factor for a recently realized experimental setup and find that
it is two orders of magnitudes larger than the measured value, indicating that
the decoherence due to phonons is a subordinate mechanism.
