Advancing Quantum Chemistry Simulations with Relativistic Electronic Structure and Quantum Computation

Abstract

This dissertation covers two main topics: relativistic Hamiltonians for quantum chemistry, and quantum computation. The main theme of the work presented within is the development of higher accuracy ab initio quantum chemistry simulations within the context of relativistic theory, and the theoretical analysis of quantum computational algorithms. In the first chapter, approximate density functionals are calibrated with a variational two-component relativistic Hamiltonian for the prediction of excited state X-ray absorption spectra. The second chapter presents a new method for computing four-component Dirac Hartree--Fock ground states of molecules, with an emphasis on its practical efficiency for large heavy element molecular systems in the future. The third and final chapter goes beyond the realm of Dirac Hartree--Fock theory, and analyzes how one could model the fully correlated molecular Hamiltonian including second order effective quantum electrodynamic effects within the digital model of quantum computation.