  Quantum chemistry is one of the most promising near-term applications of
quantum computers. Quantum algorithms such as variational quantum eigen solver
(VQE) and variational quantum deflation (VQD) algorithms have been mainly
applied for molecular systems and there is a need to implement such methods for
periodic solids. Using Wannier tight-binding Hamiltonian (WTBH) approaches, we
demonstrate the application of VQE and VQD to accurately predict both
electronic and phonon bandstructure properties of several elemental as well as
multi-component solid-state materials. We apply VQE-VQD calculations for 307
spin-orbit coupling based electronic WTBHs and 933 finite-difference based
phonon WTBHs. We establish a workflow for using VQD with lattice Greens
function that can be used for solving dynamical mean-field theory problems. The
WTBH model solvers can be used for testing other quantum algorithms also.
