In this article, we will show how to calculate the full potential in VQE in the presence of shot noise and the results. To do this, the conditional term and the deflation term can be made in the form with noise. The conditional term has the same form as the Hamiltonian, and the deflation term can be reduced to a finite number of shots in the SWAP test. It is derived for molecular hydrogen, and the values for each variable are shown for the ground state, triplet state, singlet state, and two-electron excited state.The depths of both the Hamiltonian and the clusters are set to 2, and the clusters are used only for the other states, not for the ground state.UCCSD was used for the clusters, and BFGS was used as the optimization method with 50 iterations.The number of shots was set to 100. Looking at Figure 1, we can see that the solution deviates significantly from the exact solution up to the ground state. This is because the conditional term and the deflation term are also calculated in the ground state. As you can see from the shape of the shot noise, this becomes larger as the number of terms in the evaluation function increases. Therefore, the accuracy in the ground state is poor, and the higher the level, the more the number of terms increases, and the more the excited state is trapped, resulting in low accuracy.<img src="https://assets.blueqat.com/public/uploads/us-east-2:62eba507-efdc-48b7-85a9-2f09d417847c/2021/07/22/Figure_1noise.png"/>Figure 1: Each level of molecular hydrogen in the presence of shot noise. In this calculation, we found out that the previous method does not work. From now on, we would like to try to minimize the noise by using shot noise proposal using sum operator calculation method to achieve high accuracy in simulations where noise is present. I will also try to check the effect of shot noise on the method of sci-fi, such as SSVQE, which requires a small number of terms.

Shot noise implemented in blueqat: excited state version

Hikaru Wakaura