# Quantum phase estimation, calculation of eigenvalues from phase.

In this article, I will show the results of calculating them using the method of calculating eigenvalues from phase in quantum phase estimation. In 'Quantum Phase Estimation and its problems by Hikaru Wakaura | blueqat', I showed the results of calculating eigenvalues from phase in quantum phase estimation. This time, the initial state of the quantum phase estimation is the ground state obtained by the VQE method, and the circuit depth of the Hamiltonian is set to 1. This time, we used the Hamiltonian in the STO-3G basis for molecular hydrogen, and only used the value of 0.1 (Å) for the distance between hydrogen atoms. Again, the number of ancillary bits was set to 10 and the number of observations was set to 16. The results are shown in Figure 1. In spite of the planning section and constant shift with the ground state as the initial state, the initial state was not observed. However, we were able to calculate the triplet, singlet, and two-electron excited states with a predetermined accuracy (the difference from the exact solution is within 0.01). However, the method of calculating the eigenenergy from the phase can only be done by calculating the maximum and minimum values in advance. For unknown systems, it is not possible to calculate the energy by quantum phase estimation at first. Moreover, the maximum precision of the quantum phase estimation depends on the precision of the calculated value. Therefore, other methods such as VQE will remain.

Figure 1: Calculated results and exact solution for molecular hydrogen at an interatomic distance of 0.1 (Å).