Migrate transpiler/synthesis

[prakharb10]

Summary

Closes #10819
Partially adresses #9667

Details and comments

I'm unable to build the docs locally so please let me know if any doc changes are required.

I have just copied the aqc directory and updated references. Is it okay that the code exists in two places right now or should the (soon-to-be) deprecated methods call the new methods internally?

Will add reno once changes are approved

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[coveralls]

Pull Request Test Coverage Report for Build 6602305890

• 839 of 879 (95.45%) changed or added relevant lines in 15 files are covered.
• 20 unchanged lines in 2 files lost coverage.
• Overall coverage increased (+0.07%) to 86.957%

---

Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/synthesis/unitary/aqc/cnot_unit_objective.py	135	136	99.26%
qiskit/synthesis/unitary/aqc/cnot_unit_circuit.py	42	44	95.45%
qiskit/synthesis/unitary/aqc/fast_gradient/layer.py	132	134	98.51%
qiskit/synthesis/unitary/aqc/fast_gradient/fast_gradient.py	112	116	96.55%
qiskit/synthesis/unitary/aqc/fast_gradient/pmatrix.py	100	104	96.15%
qiskit/synthesis/unitary/aqc/approximate.py	32	37	86.49%
qiskit/synthesis/unitary/aqc/fast_gradient/fast_grad_utils.py	75	80	93.75%
qiskit/synthesis/unitary/aqc/cnot_structures.py	106	114	92.98%
qiskit/synthesis/unitary/aqc/aqc_plugin.py	45	54	83.33%

Files with Coverage Reduction	New Missed Lines	%
crates/qasm2/src/lex.rs	2	91.16%
crates/qasm2/src/parse.rs	18	95.74%

Totals
Change from base Build 6594932071:	0.07%
Covered Lines:	74688
Relevant Lines:	85891

---

💛 - Coveralls

[ShellyGarion]

Hi @prakharb10 - Thank you very much for your contribution!

As for the docs, you can also see them in the build artifact here:
https://dev.azure.com/qiskit-ci/qiskit/_build/results?buildId=50719&view=results

Indeed, it's not enough to copy the aqc directory, you should remove the internal code and call the new methods internally.
See for example this PR: #10725

[ShellyGarion]

Hi @prakharb10 - are you still working on this PR?

[prakharb10]

Hi @ShellyGarion. I'm planning on completing this PR. I looked at the reference PR, but I had some questions. Posting here too
https://qiskit.slack.com/archives/C024ELK40TW/p1698781477136239

[ShellyGarion]

Another comment about the docs. If you want them to show up you need to update the __init__ file in qiskit.synthesis.

For example, please add this line:
.. autofunction:: synth_cnot_phase_aam
here:

qiskit/qiskit/synthesis/__init__.py

Line 46 in 2935f0d

[ShellyGarion]

Hi @prakharb10 - any progress with this PR?

[ShellyGarion]

Hi @prakharb10 - since there is no progress with this PR, and since we have a strict deadline for deprecations for Qiskit 1.0 release, I will have a close your PR and start another PR soon.

[prakharb10]

Hi @ShellyGarion
I'm sorry for not getting back to you sooner; I have been busy with school.
I understand. That sounds good.

[ShellyGarion]

Thank you @prakharb10 for your work, it is very much appreceated. I opened a new PR #11426 and added you as a co-author.