  We investigate the influence of dissipation on one- and two-qubit rotations
in coupled semiconductor quantum dots, using a (pseudo) spin-boson model with
adiabatically varying parameters. For weak dissipation, we solve a master
equation, compare with direct perturbation theory, and derive an expression for
the `fidelity loss' during a simple operation that adiabatically moves an
electron between two coupled dots. We discuss the possibility of visualizing
coherent quantum oscillations in electron `pump' currents, combining quantum
adiabaticity and Coulomb blockade. In two-qubit spin-swap operations where the
role of intermediate charge states has been discussed recently, we apply our
formalism to calculate the fidelity loss due to charge tunneling between two
dots.
