  This paper explores the utility of the quantum phase estimation (QPE) in
calculating high-energy excited states characterized by promotions of electrons
occupying inner energy shells. These states have been intensively studied over
the last few decades especially in supporting the experimental effort at light
sources. Results obtained with the QPE are compared with various high-accuracy
many-body techniques developed to describe core-level states. The feasibility
of the quantum phase estimator in identifying classes of challenging shake-up
states characterized by the presence of higher-order excitation effects is also
discussed.
