Semiconductor quantum-dot spin qubits are one of the most promising candidates for hosting quantum computing devices, attributed to the long coherence time and scalability. Due to the relatively simple analytical models, earlier studies on spin qubits mostly focus on quantum-dot devices in which the maximum electron occupation in each dot is limited to two electrons. Recent experimental works show that, by entering the multielectron regime, electrons in a quantum dot exhibit interesting features in terms of the total spin. These initiate an open question of whether the variations of total spin can be utilized to improve the quantum-gate fidelities, which suffer from a great number of limitations in two-electron systems. In addition, previous works predominantly concentrate on the exchange interaction between nearest-neighbor spins with the intuition that one between distant spins is negligible and can be neglected. Focusing only on the nearest-neighbor exchange poses great restrains for realizing long-range interaction between remote spins, an essential building block to achieving large-scale qubit architectures. In this thesis, in response to the issues addressed above, we study several topics for the spin qubits.

First, we start with a summary of quantum computation and its implementation in semiconductor quantum dot devices, with an emphasis on spin qubits. We then introduce the method of full configuration interaction to simulate the energy diagrams of spin qubits.

Second, we study a singlet-triplet qubit formed by four electrons in an asymmetric double-quantum-dot. A conventional two-electron single-triplet qubit hosted in singly-occupied QDs in a symmetric double-quantum-dot device exhibit a monotonic behavior of the exchange energy, the qubit parameter. The monotonicity results in an increased exposure to charge noises when the exchange gate is driven faster. In contrast, we have found that a four-electron singlet-triplet qubit exhibits a non-monotonic behavior of the exchange energy, giving rise to sweet spots, the loci where exchange energies are first-order insensitive to detuning noises. In addition, the exchange energy is largely enhanced at the sweet spot. We proceed to provide a microscopic theory on the tuning of sweet spots by perpendicular magnetic field. In particular, we have identified that the tuning of sweet spots can be attributed to the orbital splitting occurring at the valence orbitals, which is tunable by perpendicular magnetic field. The tuning of sweet spots are also found to be directly related to the variation of total spin in the fully-occupied dot.

Third, following the novel results of a four-electron singlet-triplet qubit as described above, we consider the performance of a two-qubit gate in a pair of capacitively coupled four-electron singlet-triplet qubits. Due to the emergence of effective exchange energy sweet spots and the substantial enhancement of the capacitive coupling at sweet spots, we show that gate fidelities above 99% can be achieved in the proposed system.

Next, we study the superexchange energy between two singly-occupied outmost dots in a linear triple-quantum-dot device with an empty mediator dot. A previous experiment on this type of superexchange interaction has concluded that the superexchange energy is positive and monotonic with respect to the relative detuning between outmost dots. However, the superexchange interaction is only measured for two operating points while an extensive study on a larger range of the detuning regime is lacking. To explore further the physics of superexchange interaction for applications of spin-based quantum computing, we numerically study the superexchange energy using full Configuration Interaction calculations, which allow us to associate the behaviors of superexchange energy to the details of the dot parameters, i.e. confinement strengths and inter-dot distances. We have found that the superexchange energy can be tuned either by the relative detuning between two outmost dots or the middle dot detuning. In particular, the superexchange energy is found to be tuned to yield both signs, i.e. positive or negative values, which are important to realize universal control of superexchange gate between remote spins. In addition, we have found, in the charge regime of experimental interests, that sweet spots exist for the superexchange energy, which are crucial for high-fidelity superexchange operations.

Finally, we conclude our results provided in this thesis and discuss possible further studies on these research topics.