In linear control, balanced truncation is known as a powerful technique to
reduce the state-space dimension of a system. Its basic principle is to
identify a subspace of jointly easily controllable and observable states and
then to restrict the dynamics to this subspace without changing the overall
response of the system. This work deals with a first application of balanced
truncation to the control of open quantum systems which are modeled by the
Liouville-von Neumann equation within the Lindblad formalism. Generalization
of the linear theory has been proposed to cope with the bilinear terms arising
from the coupling between the control field and the quantum system. As an
example we choose the dissipative quantum dynamics of a particle in an
asymmetric double well potential driven by an external control field,
monitoring population transfer between the potential wells as a control
target. The accuracy of dimension reduction is investigated by comparing the
populations obtained for the truncated system versus those for the original
system. The dimension of the model system can be reduced very efficiently
where the degree of reduction depends on temperature and relaxation rate
