  In the singlet-triplet qubit architecture, the two-qubit interactions
required in universal quantum computing can be implemented by capacitative
coupling, by exploiting the charge distribution differences of the singlet and
triplet states. The efficiency of this scheme is limited by decoherence, that
can be mitigated by stronger coupling between the qubits. In this paper, we
study the capacitative coupling of singlet-triplet qubits in different
geometries of the two-qubit system. The effects of the qubit-qubit distance and
the relative orientation of the qubits on the capacitative coupling strength
are discussed using an accurate microscopic model and exact diagonalization of
it. We find that the trapezoidal quantum dot formations allow strong coupling
with low charge distribution differences between the singlet and triplet
states. The analysis of geometry on the capacitative coupling is also extended
to the many-qubit case and the creation of cluster states.
