Increasing ubiquity of computational resources has enabled simulation of complex electronic systems and modern materials. The PAOFLOW software package is a tool designed to construct and analyze tight binding Hamiltonians from the solutions of DFT calculations. PAOFLOW leverages localized basis sets to greatly reduce computational costs of post-processing QE simulation results, enabling efficient determination of properties such as electronic density, band structures in the presence of electric or magnetic fields, magnetic or spin circular dichroism, spin-texture, Fermi surfaces, spin or anomalous Hall conductivity (SHC or AHC), electronic transport, and more. PAOFLOW's broad functionality is detailed in this work, and several independent studies where PAOFLOW's capabilities directly enabled research on promising candidates for ferroelectric and spintronic based technologies are described. Today, Quantum computers are at the forefront of computational information science. Materials scientists and quantum chemists can use quantum computers to simulate interacting systems of fermions, without having to perform the iterative methods of classical computing. This dissertation also describes a study where the band structure for silicon is simulated for the first time on quantum hardware and broadens this concept for simulating band structures of generic crystalline structures on quantum machines.

Significant sub-systems were created and others enhanced providing a platform for an order of magnitude precision increase of the small 4He interval - 23P1→23P2 laser spectroscopy measurement, as well as other helium transitions. These measurements serve as tests of helium theory and quantum electro-dynamics in general. Many improvements to the original experiment are discussed and characterized. In particular, counting speed increased 10x, the signal level was doubled, a novel Doppler shift minimization technique was implemented, a control node re-architecture was realized along with many useful features, and the development environment was updated. An initial 28% precision improvement was achieved also providing a foundation for additional gain via a created smaller and more heavily windowed vacuum cavity and picomotor controls.

Networks that self-organize in response to information are one of the most central studies in complex systems theory. A new time series analysis tool for studying self-organizing systems is developed and demonstrated. This method is applied to interacting complex swarms to explore the connection between information transport and group size, providing evidence for Dunbar's numbers having a foundation in network dynamics. A complex network model of information spread is developed. This network infodemic model uses reinforcement learning to simulate connection and opinion adaptation resulting from interaction between units. The model is applied to study polarized populations and echo chamber formation, exploring strategies for network resilience and weakening. The model is straightforward to extend to multilayer networks and networks generated from real world data. By unifying explanation and prediction, the network infodemic model offers a timely step toward understanding global collective behavior.