add SHVQE script

[royess]

As mentioned in Issue #190, I want to contribute a script of Schrodinger-Heisenberg quantum variational eigensolver (SHVQE) with quantum architecture search.

[refraction-ray]

Thanks for the contribution. If applicable, do you have some remarks on the accuracy performance?

[refraction-ray]

please use black to format the code

[royess]

please use black to format the code

It is solved in the new commit.

Thanks for the contribution. If applicable, do you have some remarks on the accuracy performance?

I haven't done a performance benchmark on H6 Hamiltonian, provided in the examples directory.

Based on my previous experiments on OH Hamiltonian and also the data in the original paper, SHVQE features provide higher accuracy when circuit depth is limited. The accuracy grows when (Schrodinger) circuit depth increases.

[refraction-ray]

LGTM

[refraction-ray]

@all-contributors please add @royess for example

[allcontributors[bot]]

@refraction-ray

I've put up a pull request to add @royess! :tada: