Tutorial housekeeping: Build repetition codes

[beckykd]

Closes #1137

FYI @RoyElkabetz

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[RoyElkabetz]

Hi @beckykd, could you please run the notebook and commit with fresh output so I could review the changes?

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[javabster]

Looks great! my comments:

• For the esitmated QPU usage can we use the same wording we used here (and make it italics): https://learning.quantum.ibm.com/tutorial/combine-error-mitigation-options-with-the-estimator-primitive
• For the background section are there any papers we could link to for people who want to explore QEC in more depth?
• for the requirements section we've been combining the qiskit sdk line with the visualisation support line (see tutorial linked above)
• in the optimize section could we add a link to the transpiler docs with more info on ISA circuits
• we probably don't need to print out the versions at the end, I dont think we do that in other tutorials and the required version is stated at the top
• Do you think it's possible to add a scale-up section to the end of this notebook, to show how this could be applied in a utility scale experiment?

[beckykd]

• add a scale-up section

I added all the updates except this. Working on figuring out an appropriate example.

[ihincks]

Do you think it's possible to add a scale-up section to the end of this notebook, to show how this could be applied in a utility scale experiment

My take on this is that it's not crucial to demonstrate utlity scale for QEC examples because that hasn't be the focus of IBM utility-scale experiments to date: they have all been about things like trotterized Hamiltonian simulations with mitigation.

If this direction is mandatory, the repetition code could be kept, but repeated to more than three qubits. The routing would get quite a bit more complicated. But also, there would be a tonne of conditional if statements which are quite slow especially when done serially, and degrade the quality of the experiment. However, pushing this strategy too far would make the example feel contrived, and the results would not be great, I expect.