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Semiconductor quantum dot systems offer a promising platform for quantum computation. And these quantum computation candidates are normally based on spin or charge properties of electrons. In these systems, we focus on quantum computation based on electron spins since these systems has good scalability, long coherence times, and rapid gate operations. And this thesis focuses on building a theoretical description of quantum dot systems and the link between theory and experiments. In many quantum dot systems, exchange interactions are the primary mechanism used to control spins and generate entanglement. And exchange energies are normally positive, which limits control flexibility. However, recent experiments show that negative exchange interactions can arise in a linear three-dot system when a two-electron double quantum dot is exchange coupled to a larger quantum dot containing on the order of one hundred electrons. The origin of this negative exchange can be traced to the larger quantum dot exhibiting a spin triplet-like rather than singlet-like ground state. Here we show using a microscopic model based on the configuration interaction (CI) method that both triplet-like and singlet-like ground states are realized depending on the number of electrons. In the case of only four electrons, a full CI calculation reveals that triplet-like ground states occur for sufficiently large dots. These results hold for symmetric and asymmetric quantum dots in both Si and GaAs, showing that negative exchange interactions are robust in few-electron double quantum dots and do not require large numbers of electrons. Recent experiments also show the potential to utilize large quantum dots to mediate superexchange interaction and generate entanglement between distant spins. This opens up a possible mechanism for selectively coupling pairs of remote spins in a larger network of quantum dots. Taking advantage of this opportunity requires a deeper understanding of how to control superexchange interactions in these systems. Here, we consider a triple-dot system arranged in linear and triangular geometries. We use CI calculations to investigate the interplay of superexchange and nearest-neighbor exchange interactions as the location, detuning, and electron number of the mediating dot are varied. We show that superexchange processes strongly enhance and increase the range of the net spin-spin exchange as the dots approach a linear configuration. Furthermore, we show that the strength of the exchange interaction depends sensitively on the number of electrons in the mediator. Our results can be used as a guide to assist further experimental efforts towards scaling up to larger, two-dimensional quantum dot arrays. / Doctor of Philosophy / Semiconductor quantum dot systems offer a promising platform for quantum computation. And these quantum computation candidates are normally based on spin or charge properties of electrons. In these systems, we focus on quantum computation based on electron spins since these systems has good scalability, long coherence times, and rapid gate operations. And this thesis focuses on building a theoretical description of quantum dot systems and the link between theory and experiments. A key requirement for quantum computation is the ability to control individual qubits and couple them together to create entanglement. In quantum dot spin qubit systems, the exchange interaction is the primary mechanism used to accomplish these tasks. This thesis is about attaining a better understanding of exchange interactions in quantum dot spin qubit systems and how they can be manipulated by changing the configuration of the system and the number of electrons. In this thesis, we show negative exchange energy can arise in large size quantum dots. This result holds for symmetric and asymmetric shape of the large dots. And we also provide a quantitative analysis of how large quantum dots can be used to create long-distance spin-spin interactions. This capability would greatly increase the flexibility in designing quantum processors built by quantum dot spins. The interplay of these systems with different geometry can serve as a guide to assist further experiments and may hopefully be the basis to build two-dimensional quantum dot arrays.

In this thesis, I present a microscopic theory of quantum circuits based on interacting electron spins in quantum dot molecules. We use the Linear Combination of Harmonic Orbitals-Configuration Interaction (LCHO-CI) formalism for microscopic calculations. We then derive effective Hubbard, t-J, and Heisenberg models. These models are used to predict the electronic, spin and transport properties of a triple quantum dot molecule (TQDM) as a function of topology, gate configuration, bias and magnetic field. With these theoretical tools and fully characterized TQDMs, we propose the following applications: 1. Voltage tunable qubit encoded in the chiral states of a half-filled TQDM. We show how to perform single qubit operations by pulsing voltages. We propose the "chirality-to-charge" conversion as the measurement scheme and demonstrate the robustness of the chirality-encoded qubit due to charge fluctuations. We derive an effective qubit-qubit Hamiltonian and demonstrate the two-qubit gate. This provides all the necessary operations for a quantum computer built with chirality-encoded qubits. 2. Berry's phase. We explore the prospect of geometric quantum computing with chirality-encoded qubit. We construct a Herzberg circuit in the voltage space and show the accumulation of Berry's phase. 3. Macroscopic quantum states on a semiconductor chip. We consider a linear chain of TQDMs, each with 4 electrons, obtained by nanostructuring a metallic gate in a field effect transistor. We theoretically show that the low energy spectrum of the chain maps onto that of a spin-1 chain. Hence, we show that macroscopic quantum states, protected by a Haldane gap from the continuum, emerge. In order to minimize decoherence of electron spin qubits, we consider using electron spins in the p orbitals of the valence band (valence holes) as qubits. We develop a theory of valence hole qubit within the 4-band k.p model. We show that static magnetic fields can be used to perform single qubit operations. We also show that the qubit-qubit interactions are sensitive to the geometry of a quantum dot network. For vertical qubit arrays, we predict that there exists an optimal qubit separation suitable for the voltage control of qubit-qubit interactions.

In this thesis, I present a microscopic theory of quantum circuits based on interacting electron spins in quantum dot molecules. We use the Linear Combination of Harmonic Orbitals-Configuration Interaction (LCHO-CI) formalism for microscopic calculations. We then derive effective Hubbard, t-J, and Heisenberg models. These models are used to predict the electronic, spin and transport properties of a triple quantum dot molecule (TQDM) as a function of topology, gate configuration, bias and magnetic field. With these theoretical tools and fully characterized TQDMs, we propose the following applications: 1. Voltage tunable qubit encoded in the chiral states of a half-filled TQDM. We show how to perform single qubit operations by pulsing voltages. We propose the "chirality-to-charge" conversion as the measurement scheme and demonstrate the robustness of the chirality-encoded qubit due to charge fluctuations. We derive an effective qubit-qubit Hamiltonian and demonstrate the two-qubit gate. This provides all the necessary operations for a quantum computer built with chirality-encoded qubits. 2. Berry's phase. We explore the prospect of geometric quantum computing with chirality-encoded qubit. We construct a Herzberg circuit in the voltage space and show the accumulation of Berry's phase. 3. Macroscopic quantum states on a semiconductor chip. We consider a linear chain of TQDMs, each with 4 electrons, obtained by nanostructuring a metallic gate in a field effect transistor. We theoretically show that the low energy spectrum of the chain maps onto that of a spin-1 chain. Hence, we show that macroscopic quantum states, protected by a Haldane gap from the continuum, emerge. In order to minimize decoherence of electron spin qubits, we consider using electron spins in the p orbitals of the valence band (valence holes) as qubits. We develop a theory of valence hole qubit within the 4-band k.p model. We show that static magnetic fields can be used to perform single qubit operations. We also show that the qubit-qubit interactions are sensitive to the geometry of a quantum dot network. For vertical qubit arrays, we predict that there exists an optimal qubit separation suitable for the voltage control of qubit-qubit interactions.

This thesis describes experiments on quantum dots made by locally gating one-dimensional quantum wires. The first experiment studies a double quantum dot device formed in a Ge/Si core/shell nanowire. In addition to measuring transport through the double dot, we detect changes in the charge occupancy of the double dot by capacitively coupling it to a third quantum dot on a separate nanowire using a floating gate. We demonstrate tunable tunnel coupling of the double dot and quantify the strength of the tunneling using the charge sensor. The second set of experiments concerns carbon nanotube double quantum dots. In the first nanotube experiment, spin-dependent transport through the double dot is compared in two sets of devices. The first set is made with carbon containing the natural abundance of \(^{12}C\) (99%) and \(^{13}C\) (1%), the second set with the 99% \(^{13}C\) and 1% \(^{12}C\). In the devices with predominantly \(^{13}C\), we find evidence in spin-dependent transport of the interaction between the electron spins and the \(^{13}C\) nuclear spins that was much stronger than expected and not present in the \(^{12}C\) devices. In the second nanotube experiment, pulsed gate experiments are used to measure the timescales of spin relaxation and dephasing in a two-electron double quantum dot. The relaxation time is longest at zero magnetic field and goes through a minimum at higher field, consistent with the spin-orbit-modified electronic spectrum of carbon nanotubes. We measure a short dephasing time consistent with the anomalously strong electron-nuclear interaction inferred from the first nanotube experiment. / Physics

In this thesis, I present a microscopic theory of quantum circuits based on interacting electron spins in quantum dot molecules. We use the Linear Combination of Harmonic Orbitals-Configuration Interaction (LCHO-CI) formalism for microscopic calculations. We then derive effective Hubbard, t-J, and Heisenberg models. These models are used to predict the electronic, spin and transport properties of a triple quantum dot molecule (TQDM) as a function of topology, gate configuration, bias and magnetic field. With these theoretical tools and fully characterized TQDMs, we propose the following applications: 1. Voltage tunable qubit encoded in the chiral states of a half-filled TQDM. We show how to perform single qubit operations by pulsing voltages. We propose the "chirality-to-charge" conversion as the measurement scheme and demonstrate the robustness of the chirality-encoded qubit due to charge fluctuations. We derive an effective qubit-qubit Hamiltonian and demonstrate the two-qubit gate. This provides all the necessary operations for a quantum computer built with chirality-encoded qubits. 2. Berry's phase. We explore the prospect of geometric quantum computing with chirality-encoded qubit. We construct a Herzberg circuit in the voltage space and show the accumulation of Berry's phase. 3. Macroscopic quantum states on a semiconductor chip. We consider a linear chain of TQDMs, each with 4 electrons, obtained by nanostructuring a metallic gate in a field effect transistor. We theoretically show that the low energy spectrum of the chain maps onto that of a spin-1 chain. Hence, we show that macroscopic quantum states, protected by a Haldane gap from the continuum, emerge. In order to minimize decoherence of electron spin qubits, we consider using electron spins in the p orbitals of the valence band (valence holes) as qubits. We develop a theory of valence hole qubit within the 4-band k.p model. We show that static magnetic fields can be used to perform single qubit operations. We also show that the qubit-qubit interactions are sensitive to the geometry of a quantum dot network. For vertical qubit arrays, we predict that there exists an optimal qubit separation suitable for the voltage control of qubit-qubit interactions.

In this thesis, I present a microscopic theory of quantum circuits based on interacting electron spins in quantum dot molecules. We use the Linear Combination of Harmonic Orbitals-Configuration Interaction (LCHO-CI) formalism for microscopic calculations. We then derive effective Hubbard, t-J, and Heisenberg models. These models are used to predict the electronic, spin and transport properties of a triple quantum dot molecule (TQDM) as a function of topology, gate configuration, bias and magnetic field. With these theoretical tools and fully characterized TQDMs, we propose the following applications: 1. Voltage tunable qubit encoded in the chiral states of a half-filled TQDM. We show how to perform single qubit operations by pulsing voltages. We propose the "chirality-to-charge" conversion as the measurement scheme and demonstrate the robustness of the chirality-encoded qubit due to charge fluctuations. We derive an effective qubit-qubit Hamiltonian and demonstrate the two-qubit gate. This provides all the necessary operations for a quantum computer built with chirality-encoded qubits. 2. Berry's phase. We explore the prospect of geometric quantum computing with chirality-encoded qubit. We construct a Herzberg circuit in the voltage space and show the accumulation of Berry's phase. 3. Macroscopic quantum states on a semiconductor chip. We consider a linear chain of TQDMs, each with 4 electrons, obtained by nanostructuring a metallic gate in a field effect transistor. We theoretically show that the low energy spectrum of the chain maps onto that of a spin-1 chain. Hence, we show that macroscopic quantum states, protected by a Haldane gap from the continuum, emerge. In order to minimize decoherence of electron spin qubits, we consider using electron spins in the p orbitals of the valence band (valence holes) as qubits. We develop a theory of valence hole qubit within the 4-band k.p model. We show that static magnetic fields can be used to perform single qubit operations. We also show that the qubit-qubit interactions are sensitive to the geometry of a quantum dot network. For vertical qubit arrays, we predict that there exists an optimal qubit separation suitable for the voltage control of qubit-qubit interactions.

Quantum information technologies include secure quantum communications and ultra precise quantum sensing that are significantly more efficient than their classical counterparts. To enable such technologies, we need a scalable quantum platform in which qubits are con trollable. Color centers provide controllable optically-active spin qubits within the coherence time limit. Moreover, the nearby nuclear spins have long coherence times suitable for quantum memories. In this thesis, I present a theoretical understanding of and control protocols for various color centers. Using group theory, I explore the wave functions and laser pumping-induced dynamics of VSi color centers in silicon carbide. I also provide dynamical decoupling-based high-fidelity control of nuclear spins around the color center. I also present a control technique that combines holonomic control and dynamically corrected control to tolerate simultaneous errors from various sources. The work described here includes a theoretical understanding and control techniques of color center spin qubits and nuclear spin quantum memories, as well as a new platform-independent control formalism towards robust qubit control. / Doctor of Philosophy / Quantum information technologies promise to offer efficient computations of certain algorithms and secure communications beyond the reach of their classical counterparts. To achieve such technologies, we must find a suitable quantum platform to manipulate the quantum information units (qubits). Color centers host spin qubits that can enable such technologies. However, it is challenging due to our incomplete understanding of their physical properties and, more importantly, the controllability and scalability of such spin qubits. In this thesis, I present a theoretical understanding of and control protocols for various color centers. By using group theory that describes the symmetry of color centers, I give a phenomenological model of spin qubit dynamics under optical control of VSi color centers in silicon carbide. I also provide an improved technique for controlling nuclear spin qubits with higher precision. Moreover, I propose a new qubit control technique that combines two methods - holonomic control and dynamical corrected control - to provide further robust qubit control in the presence of multiple noise sources. The works in this thesis provide knowledge of color center spin qubits and concrete control methods towards quantum information technologies with color center spin qubits.

Les qubits de spin sont des candidats prometteurs pour le traitement de l’information quantique en raison de leurs longs temps de cohérence. Les deux principaux qubits présents dans un système à trois spins ont été démontré au cours des dernières années dans la boîte quantique latérale triple. Le diagramme des niveaux d’énergie de quelques électrons dans la boîte quantique triple est beaucoup plus complexe que son homologue à deux ou à une boîte. Il en résulte des possibilités de fuites hors des qubits ciblés. Dans ce mémoire, nous présenterons une nouvelles technologie pour améliorer le contrôle des états de spin et augmenter le temps de cohérence des qubits. Nous avons effectué des mesures préliminaires sur des échantillons sur lesquels a été incorporé un microaimant. Ce microaimant crée un champ magnétique non-uniforme au niveau des boîtes quantiques qui sera utilisé pour effectuer une rotation de spin et pour améliorer certains types d’oscillations. Nous avons optimisé la forme des géométries afin de créer des gradients de champ magnétique optimaux spécifiquement pour la boîte quantique triple. Différents problèmes ont été encourus et la stratégie que nous avons adoptée pour les régler sera présentée. De plus, nous avons analysé les phénomènes de fuites entre les états quantiques en étudiant la réponse d’un système à trois spins en fonction de différentes impulsions électriques. Nous présentons deux processus d’interférence jamais répertoriés entre les qubits de la boîte quantique triple. Afin d’identifier l’origine de ces interférences, nous avons utilisé leur dépendance en champ magnétique.