Update PQK tutorial to conform to new template

[MeltemTolunay]

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• @nathanearnestnoble

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[nathanearnestnoble]

Comment 1:
we do not seems to follow template of a small scale simulator example followed by larger hardware demonstration. For this particular tutorial, I think the point of it is improved scalaibility compared to the original kernel method. In that regard, my suggested update would be:

1. reference the quantum kernel tutorial and associated difficulty of scaling (large weight observable)
2. Include 'small scale simulator example' section and either fill it out or state 'we skip this section as the purpose of this tutorial is to demonstrate how a quantum kernel can scale' (Id probably pick the second)

Comment 2:
I would personally suggest pulling the step 3/4 explanatory text into the background section, as it helps make it more clear why scaling works

Comment 3:
I think the sentence This tutorial also assumes general familiarity with QML methods. For further exploration of QML, refer to the [Quantum machine learning](https://github.com/Qiskit/documentation/blob/d82972aee109f8a42d897f345139020b8dd8daf8/docs/tutorials/learning/courses/quantum-machine-learning) course in IBM Quantum Learning. is a bit redundant, given prereq section.

[MeltemTolunay]

Thank you for the review, here is the summary of updates:

1. Quantum kernel tutorial is linked, and I added a paragraph about scaling.
2. I added a paragraph to background section explaining 1-RDMs. I still kept the equation in Section 3, because I think it's better for the flow and right above the section where we actually compute the RDMs.
3. Removed the duplicate section.

Please let me know if any other changes are needed.

[abbycross]

duplicate?

[henryzou50]

Yes, this is a duplicate, I remove it on my latest commit.

[henryzou50]

LGTM! Thanks for the changes @MeltemTolunay! I added a review minor changes to make the tutorial more consistent with the template and the other tutorials.

[abbycross]

For consistency, we should put the "If you found this work interesting" line inside the Admonition box (so just switch lines 1501 and 1502). After that is done it's good from my end! @nathanearnestnoble do you need to review?

[henryzou50]

Got it, I will revert that change. I originally did that before since the tutorial template had it outside.