SQD tutorial: add section on passing initial occupancies

[kevinsung]

Adds a section showing how to pass initial occupancies, which allows SQD to run even if there are no valid configurations. It may also improve convergence.

[qiskit-bot]

One or more of the following people are relevant to this code:

• @kevinsung
• @miamico

[review-notebook-app]

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[nathanearnestnoble]

Thank you for adding this component @kevinsung , I think it will help some issues which a few users have raised.

• Naive question: is there a scenario in which a user would not have the ability to guess the initial occupancies? If not, perhaps it can just be the default workflow rather than an "advanced section"
• Perhaps just adding a sentence which briefly explains the initial occupancy you selected?

[kevinsung]

Thank you for adding this component @kevinsung , I think it will help some issues which a few users have raised.

* Naive question: is there a scenario in which a user would not have the ability to guess the initial occupancies?  If not, perhaps it can just be the default workflow rather than an "advanced section"

* Perhaps just adding a sentence which briefly explains the initial occupancy you selected?

I've edited the notebook to just change the existing workflow, and expanded on the explanation for choosing the Hartree-Fock configuration. I've also added a cell that counts the number of valid configurations returned by the hardware. The diff seems to render incorrectly on GitHub, but it looks fine on ReviewNB.

Currently the notebook is showing a warning due to Qiskit/qiskit-addon-sqd#274. I will investigate that.

[kevinsung]

Ok I've fixed the warning in Qiskit/qiskit-addon-sqd#276 and re-run the notebook with that PR. @caleb-johnson agreed to cut a new release of the SQD addon shortly.

I've also updated the reference energy with the results of an improved SCI calculation, and added print statements that print the number of sampled valid bitstrings as well as the final energy error, like this:

Fraction of sampled configurations that are valid: 0.00065

Final energy error: 0.03878764275833646

[kaelynj]

Naive question about this PR @kevinsung. Does this address #4430 at all? Or is that something that'll have to be done separately?

[kevinsung]

Naive question about this PR @kevinsung. Does this address #4430 at all? Or is that something that'll have to be done separately?

No, this PR does not address #4430.