In this study, we employed Fourier-based quantum phase estimation (QPE) to calculate x-ray absorption spectroscopy (XAS) spectra. The primary focus of this study is the calculation of the XAS spectra of transition metal $L_{2,3}$ edges, which are dominated by strong correlation effects. First, the $\mathrm{Fe}$ $L_{2,3}$-edge x-ray absorption near-edge structure of ${\mathrm{Fe}\mathrm{PO}}_4$ is calculated using a noiseless simulator. The present computation involves a comparison of three types of input states: a uniform superposition state, optimal entangled input state, and Slater function state. Subsequently, we investigated the resolution error of the QPE and statistical error attributed to the measurements. It was revealed that postprocessing to introduce Lorentzian broadening reduces the statistical error, which becomes a significant problem for a large number of qubits. Finally, we implemented QPE on a trapped-ion quantum computer, encompassing three orbitals within the active space. To this end, we implemented QPE using dynamic circuits to reduce ancilla qubits and $\text{⟦}k+2,k,2\text{⟧}$ quantum error-detection code to mitigate the quantum noise inherent in current quantum computers. As a result, it was demonstrated that hardware noise was reduced, and spectra close to the noiseless ones were obtained.

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• Electronic structure
• Quantum algorithms for chemical calculations
• Quantum information with trapped ions
• Quantum simulation
• Transition metal oxides
• X-ray absorption spectroscopy