  We investigate the effect of the Coulomb interaction on the applicability of
quantum gates on a system of two Coulomb-coupled quantum dots. We calculate the
fidelity for a single- and a two-qubit gate and the creation of Bell states in
the system. The influence of radiative damping is also studied. We find that
the application of quantum gates based on the Coulomb interaction leads to
significant input state-dependent errors which strongly depend on the Coulomb
coupling strength. By optimizing the Coulomb matrix elements via the material
and the external field parameters, error rates in the range of $10^{-3}$ can be
reached. Radiative dephasing is a more serious problem and typically leads to
larger errors on the order of $10^{-2}$ for the considered gates. In the
specific case of the generation of a maximally entangled Bell state, error
rates in the range of $10^{-3}$ can be achieved even in the presence of
radiative dephasing.
