Energy spectrum, exchange interaction and gate crosstalk in a pair of double-quantum-dot system: a molecular orbital calculation

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.