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Capacitative coupling of singlet-triplet qubits in different inter-qubit geometries

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.