  The possibility of performing quantum chemical calculations using quantum
computers has attracted much interest. In this regard, variational quantum
deflation (VQD) is a quantum-classical hybrid algorithm for the calculation of
excited states with noisy intermediate-scale quantum (NISQ) devices. Although
the validity of this method has been demonstrated, there have been few
practical applications, primarily because of the uncertain effect of
calculation conditions on the results. In the present study, calculations of
the core-excited and core-ionized states for common molecules based on the VQD
method were simulated using a classical computer, focusing on the effects of
the weighting coefficients applied in the penalty terms of the cost function.
Adopting a simplified procedure for estimating the weighting coefficients based
on molecular orbital levels allowed these core-level states to be successfully
calculated. The O 1s core-ionized state for a water molecule was calculated
with various weighting coefficients and the resulting ansatz states were
systematically examined. The application of this technique to functional
materials was demonstrated by calculating the core-level states for titanium
dioxide (TiO2) and nitrogen-doped TiO2 models. The results demonstrate that VQD
calculations employing an appropriate cost function can be applied to the
analysis of functional materials in conjunction with an experimental approach.
