Constructing Hamiltonians Using a Wannier Basis Set to Study Localized Electronic Interactions Using a Variational Quantum Eigensolver

In this study, I demonstrate how Wannier basis sets can be used to construct a tight binding Hamiltonian that is localized in real space. This Hamiltonian can then be studied using the Variational Quantum Eigensolver (VQE), which is able to extract the minimized energy of the system. Unlike Bloch functions, Wannier functions are localized in real space, allowing each Hamiltonian element to represent orbital overlaps between neighboring atomic orbitals. This locality enables a substantial reduction in the Hamiltonian’s size by including only the orbital projections that contribute meaningfully to localized interaction energies, such as those involved in adsorption. As a result, the number of qubits required for quantum simulation via VQE is significantly reduced, as the required number of qubits is equivalent to the dimension of the Hamiltonian matrix. This thesis provides background on Density Functional Theory (DFT) and details how maximally localized Wannier functions are constructed. The workflow is described comprehensively, from atomic structure preparation to the extraction of the Hamiltonian via wannierization. I specifically investigate how including/excluding specific projections allows one to reduce the Hamiltonian size and study specific orbital interactions inside a material. The implementation of the VQE algorithm is reviewed and finally, I show that the VQE successfully captures the energy landscape associated with OH molecule adsorption on an aluminum surface. This work highlights a scalable pathway for using quantum-classical hybrid algorithms to study localized interactions with quantum efficiency, paving the way for practical quantum simulations of complex materials phenomena.