  This chapter is devoted to the recent theoretical results on the optical
quantum control over charges confined in quantum dots under influence of
phonons. We show that lattice relaxation processes lead to decoherence of the
confined carrier states. The theoretical approach leading to a uniform, compact
description of the phonon impact on carrier dynamics, perturbative in phonon
couplings but applicable to arbitrary unperturbed evolution, is described in
detail. Next, some applications are presented: phonon damping of Rabi
oscillations in quantum dots and phonon-induced error of a single-qubit gate
for an excitonic quantum dot qubit as well as for a semiconductor quantum dot
spin qubit operated via a STIRAP transfer.
