Quantum Algorithm for the Direct Calculations of Vertical Ionization Energies

Recently, a quantum algorithm that is capable of directly calculating the energy gap between two electronic states having different spin quantum numbers without inspecting the total energy of the individual electronic states was proposed. This quantum algorithm guarantees an exponential speedup, like quantum phase estimation (QPE)-based full-CI, with much lower costs. In this work, we propose a modified quantum circuit for the direct calculations of spin state energy gaps to reduce the number of qubits and quantum gates, extending the quantum algorithm to the direct calculation of vertical ionization energies. Numerical quantum circuit simulations for the ionization of light atoms (He, Li, Be, B, C, and N) and small molecules (HF, BF, CF, CO, O2, NO, CN, F2, H2O, and NH3) revealed that the proposed quantum algorithm affords the vertical ionization energies within 0.1 eV of precision.