Fix Sphinx-execution & other minor circuit updates

[Cryoris]

Summary

Blocks qiskit-community/qiskit-aqua#1374.

• Unblock Aqua CI by using jupyter-execute instead of >>> style examples. The latter is run and tested by Aqua's CI and but hasn't been designed to be valid code in our docs.
• Remove the 4-months deprecated mirror method
• Update the existing_gate_names in qasm()
• Remove the outdated default gates names in draw() and redirect to the DefaultStyle class instead

[mtreinish]

LGTM, just a couple of small inline comments, also this needs an upgrade release note because you're removing a deprecated method which has upgrade impact for users.

[mtreinish]

I don't actually think this is a valid docs link right now. I'm not able to find this path in the documentation https://qiskit.org/documentation/apidoc/visualization.html it probably means we need to add this to the docs first.

[Cryoris]

That just means adding it in the __init__ docstring or do I also need to create a new apidocs file?

[Cryoris]

I referenced the module for now, and added the module to the __init__

[mtreinish]

Yeah, you just need it in the qiskit.visualization __init__ module. There's no need to add a new apidocs.rst unless you want to create a new top page in the docs tree. (which for qcstyle I don't think makes sense, at least not yet until we improve the interface around it).

[mtreinish]

I think we might need to add some additional setup or docstrings to make this work. Looking at the rendered output from sphinx of this it doesn't contain any real details:

[enavarro51]

In working on #5223 I was updating the docs for circuit_drawer and QuantumCircuit.draw, which are duplicates except for 1 param each. I talked to @1ucian0 about having the QC.draw docs link to the circuit_drawer docs, but ultimately decided not do it. I like the idea though of referring both to new docs in qcstyle for the style dict, which is where they probably belong.

From what I see here, it looks like you are only moving the color references to qcstyle, not the whole style dict. It seems like we would want the whole style dict documented in qcstyle and then put links to this in QC.draw and circuit_drawer.

[Cryoris]

@enavarro51 if you're planning to take care of this I'll revert the changes here 👍

[mtreinish]

LGTM. I just checked the 0.15.0 release went out on August 6th, so the deprecation minimum is still 11 days away. Normally I'd say lets wait 11 days to merge this, but I think it it's probably pretty unlikely that we'll release before Nov 6th. Since this is blocking aqua I think it's fine to let that slide this time.