Calculation of SSVQE including shotnoise.
In this article, I have calculated the full potential of molecular hydrogen using the Subspace-Search Variational Quantum Eigensolver (SSVQE) method in a system with shot noise as in "Shot noise implemented in blueqat: excited state version by Hikaru Wakaura | blueqat". SSVQE is a method in which the evaluation function is not the energy but the sum of the energies in each state. SSVQE is a method that uses the sum of the energies in each state as the evaluation function instead of the energies, and optimizes multiple conceptions simultaneously by optimizing them in a common cluster. In this study, the ground state energy of molecular hydrogen was calculated by varying the distance between hydrogen atoms from 0.1 to 2.5 (Å) in increments of 0.1, with the number of shots = 100. The depths of both the Hamiltonian and the clusters were set to 2, UCCSD was used for the clusters, Newton's method was used for the optimization, and the number of iterations was set to 500.
Figure 1 shows the results without shot noise, and Figure 2 shows the results with shot noise. Clearly, the results with noise deviate from the exact solution. This is probably because in SSVQE, the SWAP-test is zero since the eigenstates are calculated by clustering the orthogonal initial states, but the shot noise makes it finite and non-negligible. However, the SWAP-test is zero because the shot noise makes it finite and non-negligible. Since it took two days to calculate, it is difficult to increase the number of SWAP-tests, but there seems to be no other way.
Figure 1: Each level of molecular hydrogen without shot noise.
Figure 2: Levels of molecular hydrogen with shot noise.