Quantum Phase Estimation and its problems:part 2
In this article, we continue our discussion of the performance and limitations of quantum phase estimation. Figure 1 shows some of the results and the exact solution for the quantum phase estimation of the Hamiltonian of molecular hydrogen in the STO-3G basis. Unfortunately, the ability to display the phase together with the energy eigenvalues after determining the phase has not been implemented, so only the eigenvalues are shown. The ground state was not included, only the triplet, the doublet state between the ground state and the triplet, and the singlet state. I got the accuracy I wanted, but it took 21 hours to do this. Dr. Nakata has succeeded in high-precision calculations using Q# with lithium hydrogen. Either it is the technique of calculation or the limitation of the machine, but it still seems too early to simulate this.
Fig. 1 Difference between the 16 energy levels obtained and their exact solutions, and their accuracy.
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