Adding a convergence threshold to VQD to filter non-sensible values

[tnemoz]

Summary

As mentioned here, some optimizers don't work well with shots-based samplers. This leads to VQD returning sometimes absurd values, as shown here.

This Pull Request adds a convergence_threshold to VQD to test whether the optimization converged well.

It also paves the road for adapting VQD to V2 primitives.

Details and comments

Changes that were made:

• a convergence_threshold parameter now tests whether the average fidelity of the $k$-th eigenstate w.r.t. the previously found eigenstates is larger than this threshold, indicating that not only the eigenvalue returned is likely to be false, but the next iterations won't make sense either.
• if the convergence_threshold test passes, VQD now returns $\left\langle\psi_k\middle|H\middle|\psi_k\right\rangle$ instead of $\left\langle\psi_k\middle|H\middle|\psi_k\right\rangle+\sum\limits_{i=1}^{k-1}\beta_i\left|\left\langle\psi_k\middle|\psi_i\right\rangle\right|^2$, which not only makes more sense, but also allows to get decent values even when using gradients-based optimizers such as SLSQP.
• the tutorial has been updated to use COBYLA and a value of betas that are closer to real-world use cases.
• the tests have been updated. In particular, the values of betas have been updated from 50 to 3. A too large value with shot noise made the optimizers focus solely on the fidelity part, forgetting about the energy part.