Hyperfine interactions in lanthanide-organic complexes for Quantum Information Processing

This thesis integrates quantum computing, optimal control theory, nuclear structure, hyperfine interactions, f-elements, crystal field theory, and molecular magnetism, focusing on lanthanide-organic complexes, particularly TbPc\textsubscript{2}, as potential molecular quantum processors. The research begins with a theoretical overview, highlighting the convergence of these fields and the role of lanthanide chemistry. Key properties of lanthanides are analyzed, including their atomic and ionic states, ligand field interactions, and responses to external fields. Detailed discussions cover non-interacting electrons, Coulomb repulsion, spin-orbit coupling, and hyperfine coupling, as well as the transition from crystal field theory to ligand field theory and the capabilities of ligand field DFT. The hyperfine interaction is examined through the Dirac equation, incorporating relativity into the Schrödinger equation. Topics include mass corrections, muonic atoms, and hyperfine constants. Quantum computing with nuclear spins in lanthanides is explored, introducing qubits, qudits, quantum gates, algorithms, and relevant timescales. Optimal gate generation is investigated, aiming to develop efficient qudit gates, with TbPc\textsubscript{2} as a practical example. ... mehrThe Prouhet-Thue-Morse sequence is analyzed for its properties and applications in quantum computing. The thesis concludes with future research directions, including decoherence studies, effects of ligand composition, hyperfine constant calculations, and qudit gate optimization