Quantum dots are attractive due to their potential technological applications and the opportunity they provide for study of fundamental physics in the mesoscopic scale. This dissertation studies optically controlled spins in quantum dots in connection to quantum information processing. The physical realization of the quantum bit (qubit) consists of the two spin states of an extra electron confined in a quantum dot. Spin rotations are performed optically, by use of an intermediate charged exciton (trion) state. The two spin states and the trion form a $\Lambda$-type system. The merits of this system for quantum information processing include integrability into a solid-state device, long spin coherence time, and fast and focused optical control. In this dissertation, we study the optical decay mechanisms of the trion state in the quantum dot. Using a master-equation approach, we derive microscopically the optical decay of the three- level system and find a novel term, the so-called spontaneously generated coherence (SGC). The latter, though predicted more than a decade ago for atomic $\ Lambda$-systems satisfying certain conditions, had not been detected yet in any system. We found that in quantum dots, these conditions can be satisfied. We present the experiment which, in collaboration with our theory, constituted the first measurement of SGC. We establish the unification of SGC, polarization entanglement, and two- pathway decay. By keeping track of the spontaneously emitted photon dynamics, we find the conditions on the couplings that determine which effect will take place. We have thus placed SGC in a more quantum informational framework, characterizing it as lack of entanglement between the emitted photon and the three-level system. We develop a theory of ultrafast optical single-qubit rotations by use of 2$\pi$ pulses, which have the two-fold advantage of minimal trion excitation and negligible spin precession. The analytically solvable hyperbolic secant pulses of Rosen and Zener for the two-level system are investigated in the context of the three-level system. Ultrafast rotations about the quantum dot growth direction are designed, the angle of spin rotation is expressed analytically, and the fidelity is studied by simulations. Adaptive feedback loops are employed to correct for unintended dynamics

Computational models are an essential tool for the design, characterization, and discovery of novel materials. Computationally hard tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their resources for simulation, analysis, and data processing. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions.