docs(notebooks): add long range CNOT notebook

[dsvandet]

Summary

Adds the long range CNOT notebook

Details and comments

The notebook is contained in the long-range-cnot branch. This is an updated version from the one currently on the learning website. This notebook adds:

• Common utility methods so that that experiments can use the same code with different parameters
• Added functionality for dynamic decoupling support for all experiments
• Updated for Qiskit1.0

Note: The notebook does not currently use primitives or services as extra support is needed that should be available mid year.

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Covered Lines:	290
Relevant Lines:	290

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💛 - Coveralls

[miamico]

The notebook is looking much more polished than before, I think we're almost at a final stage! Some comments on the overall picture:

• Simulations vs Experiment: I'm not sure whether we can run meaningful simulations for this but we should either settle on running the experiment with the notebook itself (and loading the data) or run some simulations. I find it is missing something if we only provide code without showing what it will output
• Organization in Qiskit Patterns: Right now the material is organized as 3 different experiments that go through 1-4. I would actually re-organize the material. The experiment is only one: long range CX. Now the notebook shows 3 possible optimized implementation (unitary on a line, meas-based with post-processing on a line, meas-based with feed-forward on a line). We could have a single step 1 where we set the long-range CX experiment and 3 different steps 2,3,4 for each of the optimizations
• There is lots of code written specifically for the experiment. So much that I think it's worth to create some modules to collect the functions developed. I actually even think that the fidelity estimation part deserves its own how to guide

Awesome work, this is the first tutorial we have which could actually be a proper utility-scale experiment!

[miamico]

It would be good to have also a "Load data" option for people who don't want to run the experiment. In this way we can show what kind of results can be expected from using this notebook (it is not clear whether what kind of results we'd get if we actually run this)

[dsvandet]

I am running a 83 qubit data set that could be added to get this. It may take some time. in the mean time users can look at the paper data.

[miamico]

Ok, let's wait a little more on the experiment data if we are able to collect them in a reasonable time

[miamico]

Adding a reference to the bug encountered when executing this notebook

[miamico]

Updated the notebook to include experimental data obtained by running it. Added some functionalities to save/load data. In my opinion, the last outstanding item is to convert backend.run to the primitives (blocker: currently buggy).