  We investigate the tunability of electrostatic coupling between solid state
quantum dots as building blocks for quantum bits. Specifically, our analysis is
based upon two-dimensional electron systems (2DEG) and depletion by top gates.
We are interested in whether the Coulomb interaction between qubits can be
tuned by electrical means using screening effects. The systems under
investigation are analyzed numerically solving the Poisson equation in 3D via
relaxation techniques with optimized algorithms for an extended set of boundary
conditions. These include an open outer boundary, simulation of 2DEG systems
and dielectric boundaries like the surface of a physical sample. The results
show that for currently lithographically available feature sizes, the Coulomb
interaction between the quantum bits is weak in general due to efficient
screening in the planar geometry of 2DEG and top gates. The evaluated values
are on the order of 1 $\mu$eV. Moreover, while it is not possible to turn off
the qubit interaction completely, an effective tunability on the order of 50%
is clearly realizable while maintaining an intact quantum bit structure.
