Ajc/qedma qesem

[abbycross]

Supersedes #4003

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[abbycross]

@miamico @oria-qedma @talishnaider-qedma @pandasa123 The tutorial is now passing lint. One outstanding to-do is fitting the headers to the Qiskit patterns framework. I got one but don't want to arbitrarily add the others 😆 can someone suggest where exactly to put the next three steps (Optimize for target hardware, Execute on target hardware, Post-process results)?

[miamico]

Here's how I'd fix these headers:

• "Step 2: QPU time estimation with and without OBP" rename to "Step 2: Optimize problem for quantum hardware execution"
• "Step 3: Run the QESEM function" rename to "Step 3: Execute using Qiskit primitives"
• "Step 4: Run on real hardware" rename this header to: "Scale it up! Step 2 and 3"
• "Step 5: Visualize results" rename this to: "Step 4: Post-process and return result in desired classical format"

It's a little non-trivial to map it to the standard sequence of 1,2,3,4 as there is a scaled up example ran in the middle (under Step 4) instead of doing 1,2,3,4 for the small example and then repeating 1,2,3,4 for the scaled up example as we'd done in other examples. I think this is ok for now!

[talishnaider-qedma]

@abbycross @miamico @pandasa123 @oria-qedma I think there was some kind of a mix up here. The version in this PR is definitely not the last version I uploaded to the previous PR #4003. The version here is the first version we sent you.
The latest version has 4 steps and they are named according to your convention and a bunch of other changes... Could you address this? and update the notebook? :)

[abbycross]

I'll take a look and sort it out!