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 computers are being developed to solve certain problems faster than classical computers. Instead of using classical bits, they use quantum bits (qubits) that utilize quantum effects. At Chalmers University of Technology, researchers have already built a quantum chip consisting of two superconducting transmon qubits and are trying to build systems with more qubits. To assist in that process, they make numerical simulations of the quantum systems. However, these simulations face an intrinsic computational limitation: the Hilbert space of the system grows exponentially with the number of qubits. In order to mitigate the problem: the simulations should be made as efficient as possible, by applying certain approximations, while still obtaining accurate results. The aim of this project is to compare several of these approximations, to see how accurate they are and how fast they run on a classical computer. This is done by modelling the qubits as quantum anharmonic oscillators and testing several cases: varying the energy levels of the qubits, increasing the number of qubits, and testing the rotating-wave approximation (RWA). These cases were tested by implementing two-qubit gates on the system. The simulations were all made using the Python library QuTiP. The results show that one should simulate using at least one energy level higher than the maximum energy level required for the gate to function. For larger systems, the RWA will make a big difference in simulation times, while still giving relatively accurate results. When using the RWA, the number of levels used does not seem to affect the results significantly and one could therefore use the lowest possible energy levels that can simulate the system.

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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 défauts ponctuels dans les semi-conducteurs sont étudiés pour la réalisation de bits quantiques d’information (Qubit). A ce jour, le système le plus développé est le centre NV dans le diamant. Récemment, les défauts ponctuels du carbure de silicium (SiC) ont été identifiés comme prometteurs pour la réalisation de Qubit en raison de leur long temps de cohérence de spin et du fonctionnement à température ambiante. Dans ce contexte, nous étudions la formation, la caractérisation optique et magnétique des défauts ponctuels dans SiC, ainsi que l’amélioration de la collection de leur luminescence. Nous commençons par une description des différents critères qui font du SiC un matériau clé pour les applications Qubit. Ensuite, nous présentons une étude bibliographique sur les principaux défauts ponctuels dans SiC en nous focalisant sur les centres : VSi, VSiVC, NV. Nous portons par la suite notre étude sur les conditions optimales d’irradiation ioniques/électroniques et de recuit post-irradiation pour la formation de défauts ponctuels luminescents dans le polytype cubique de SiC. Nous avons identifié les différents types de défauts dans le visible. Dans l’infra-rouge, nous n’avons détecté que le centre VSiVC en trouvant les conditions optimales de sa luminescence dans le cas d’implantation par les protons (dose 1016 cm-2 et le recuit à 750 °C). Puis, nous avons comparé les résultats obtenus par des irradiations aux électrons à ceux obtenus avec les protons en précisant les différents types de défauts ponctuels détectés par deux méthodes: la photoluminescence et la résonance paramagnétique électronique. Enfin, nous avons développé un processus technologique qui consiste en la fabrication de nano-piliers en SiC-4H. Nous avons montré les avantages de leur réalisation sur l’efficacité de la collection de PL des défauts ponctuels comme VSi et VSiVC. Une amélioration d’un facteur 25 pour le centre VSi et d’un facteur 50 pour le centre VSiVC a été obtenue. / Point defects in semiconductor materials are studied for the realization of quantum information bits (Qubit). Nowadays, the most developed system is based on the NV center in diamond. Recently, point defects in silicon carbide (SiC) have been identified as promising for the realization of Qubit due to the combination of their long spin coherence time and room temperature operation. In this context, this thesis studies the formation, optical and magnetic characterization of point defects in SiC, as well as the improvement of their luminescence collection. We begin with a general introduction to SiC in which we describe the different criteria that make SiC a key material for Qubit applications. Next, we present a bibliographical study on the main point defects in SiC, focusing on the centers: VSi, VSiVC, NV. We have studied the optimal conditions of ionic/electronic irradiation and post-irradiation annealing for the formation of luminescent point defects in the cubic polytype of SiC. We have identified the different types of visible range defects. In the infra-red range, we detected only the Ky5 center (VSiVC) by finding the optimal luminescence conditions of this center in the case of implantation by protons (dose 1016 cm-2 and annealing at 750 °C). Then, we compared the results obtained by electron irradiations with those obtained with protons specifying the different types of point defects detected by two methods: photoluminescence and electronic paramagnetic resonance. Finally, we have developed a technological process that consists of nano-pillars fabrication in SiC-4H. We have shown the advantages of realizing these pillars on the efficiency of the PL collection of point defects like VSi and VSiVC : an improvement of a factor of 25 for the VSi center and a factor of 50 for the VSiVC center was obtained.

The work presented in this thesis investigates transitions between quantum states in superconducting double dots (SDDs), a nanoscale device consisting of two aluminium superconducting islands coupled together by a Josephson junction, with each dot connected to a normal state lead. The energy landscape consists of a two level manifold of even charge parity Cooper pair states, and continuous bands corresponding to charge states with single quasiparticles in one or both islands. These devices are fabricated using shadow mask evaporation, and are measured at sub Kelvin temperatures using a dilution refrigerator. We use radio frequency reflectometry to measure quantum capacitance, which is dependent on the quantum state of the device. We measure the quantum capacitance as a function of gate voltage, and observe capacitance maxima corresponding to the Josephson coupling between even parity states. We also perform charge sensing and detect odd parity states. These measurements support the theoretical model of the energy landscape of the SDD. By measuring the quantum capacitance in the time domain, we observe random switching of capacitance between two levels. We determine this to be the stochastic breaking and recombination of single Cooper pairs. By carrying out spectroscopy of the bath responsible for the pair breaking we attribute it to black-body radiation in the cryogenic environment. We also drive the breaking process with a continuous microwave signal, and find that the rate is linearly proportional to incident power. This suggests that a single photon process is responsible, and demonstrates the potential of the SDD as a single photon microwave detector. We investigate this mechanism further, and design an experiment in which the breaking rate is enhanced when the SDD is in the antisymmetric state rather than the symmetric state. We also measure the quantum capacitance of a charge isolated double dot. We observe 2e periodicity, indicating the tunnelling of Cooper pairs and the lack of occupation of quasiparticle states. This work is relevant to the range of experiments investigating the effect of non-equilibrium quasiparticles on the operation of superconducting qubits and other superconducting devices.

Superconducting qubits are a promising technology for building a scalable quantum computer. An important architecture employed in the field is called Circuit Quantum Electrodynamics (circuit QED), where such qubits are combined with high quality microwave cavities to study the interaction between artificial atoms and single microwave photons. The ultra-strong coupling achieved in these systems allows for control and readout of the quantum state of qubits to perform quantum information processing. The work on circuit QED performed in this thesis consisted of realizing an experimental setup for qubit experiments in a new laboratory, investigating the coherence and decay of higher energy levels of superconducting transmon qubits and finally demonstrating a novel coaxial form of circuit QED. Designing and building a 3D circuit QED setup involved the following main accomplishments: producing high quality 3D cavities; designing and installing the cryogenic microwave setup as well as the room temperature amplification and data acquisition circuitry; successfully developing a recipe for the fabrication of Josephson junctions; controlling and measuring superconducting 3D transmon qubits at 10mK. Several qubits were fully characterised and have shown coherence times of several microseconds and relaxation times up to 25μs. Superconducting qubits in fact possess higher energy levels that can provide significant computational advantages in quantum information applications. In experiments performed at MIT, preparation and control of the five lowest states of a transmon qubit was demonstrated, followed by an investigation of the phase coherence and decay dynamics of these higher energy levels. The decay was found to proceed mainly sequentially with relaxation times in excess of 20μs for all transitions. A direct measurement of the charge dispersion of these levels was performed to explore their characteristics of dephasing. This experiment was also reproduced on a 3D transmon fabricated and measured in Oxford, where due to a higher effective qubit temperature a multi-level decay model including thermal excitations was developed to explain the observed relaxation dynamics. Finally, a coaxial transmon, which we name the coaxmon, is presented and measured with a coaxial LC readout resonator and input/output coupling ports placed inline along the third dimension. This novel coaxial circuit QED architecture holds great promise for developing a scalable planar grid of qubits to build a quantum computer.