  We present a theoretical study of a four-electron four-quantum-dot system
based on molecular orbital methods, which hosts a pair of singlet-triplet spin
qubits. We explicitly take into account of the admixture of electron wave
functions in all dots, and have found that this mixing of wave functions has
consequences on the energy spectrum, exchange interaction and the gate
crosstalk of the system. Specifically, we have found that when the two
singlet-triplet qubits are close enough, some of the states are no longer
dominated by the computational basis states and the exchange interaction can
not simply be understood as the energy difference between the singlet and
triplet states. Using the Hund-Mulliken calculation of the Hubbard parameters,
we characterize the effective exchange interaction of the system and have found
good agreement with results calculated by taking energy differences where
applicable. We have studied the two commonly conceived schemes coupling two
qubits, the exchange and capacitive coupling, and have found that when the
inter-qubit distance is at certain intermediate values, the two kinds of
coupling are comparable in strength, complicating analyses of the evolution of
the two qubits. We also investigate the gate crosstalk in the system due to the
quantum mechanical mixing of electron states and have found that while this
effect is typically very weak, it should not be ignored if the spacing between
the qubits are similar to or less than the distance between the double dots
that constitute the qubit.
