Realistic Modeling of Decoherence in Molecular Spin Qubits

Quantum coherence is a key resource for emerging quantum science and tech- nologies. Its preservation in solid-state systems is inevitably hampered by inter- actions with complex environments. In this context, molecular nanomagnets offer a particularly appealing platform, combining long coherence times with an excep- tional degree of chemical and structural tunability. Understanding the microscopic mechanisms that govern decoherence in these systems is therefore crucial for their controlled use as quantum devices. In this thesis, we investigate decoherence processes in lanthanide-based molecular spin systems, with a primary focus on pure dephasing mechanisms at cryogenic temperatures and spin-phonon relaxation at higher temperatures. A realistic theoretical and computational framework is developed to describe the interaction between a central electronic spin and its surrounding nuclear and elec- tronic spin baths. The analysis is carried out using the Cluster Correlation Ex- pansion and its generalized formulation, which allow for a controlled inclusion of many-body correlations within the environment. Using Yb(trensal) as a repre- sentative molecular spin qudit, we analyze the respective roles of nuclear and elec- tronic spin baths, identify the dominant decoherence channels in different regimes, and assess the convergence and robustness of the adopted methods. Strategies for mitigating decoherence through Hamiltonian engineering are also discussed, in order to provide a complementary strategy to the active dynami- cal decoupling techniques commonly employed in experiments. In particular, we identify a necessary and sufficient condition for coherence preservation based on the commutation properties of the Hamiltonians responsible for the conditional bath dynamics. For molecular spin systems, this condition translates into requir- ing identical expectation values of local spin operators for the two eigenstates and provides a microscopic interpretation of decoherence-free subspaces. Finally, spin–phonon relaxation mechanisms are addressed by extending the anal- ysis to higher temperatures. The theoretical approach employed to simulate this processes is based on ab initio calculation of spin-phonon coupling coefficients, combined with a perturbative treatment within the Redfield theory. This method- ology is applied to a series of lanthanide-based molecular nanomagnets, establish- ing a link between lattice dynamics, spin–phonon coupling, and spin relaxation rates. Overall, this work provides a unified microscopic picture of decoherence and re- laxation in molecular nanomagnets, offering insights that are relevant for both the interpretation of experiments and the design of molecular spin systems with enhanced quantum coherence.