rename internal add_control to _add_control

[1ucian0]

Summary

The internal function add_control seems to create confusion among users. Here some examples:

• sympy2symengine error in circuit transpilation #13161
• Invalid Parameters with CU gate in AerSimulator #12625
• Running a specific quantum circuit multiple times gets different state vectors #11458
• https://stackoverflow.com/a/59545389/8146172
• https://stackoverflow.com/q/71108162/8146172

I think it can be renamed to mitigate that effect.

[qiskit-bot]

One or more of the following people are relevant to this code:

• @Qiskit/terra-core

[jakelishman]

I don't think we need to do this. It's not in the public interface, and I think changing its name like this risks suggesting that naming is what defines the public interface.

If we were going to do it, it'd probably be the module we renamed - the function itself is public within ourselves as a package (evidenced by how it's used in more than one file), and it's the module that's private to users.

[coveralls]

Pull Request Test Coverage Report for Build 11092537542

Warning: This coverage report may be inaccurate.

This pull request's base commit is no longer the HEAD commit of its target branch. This means it includes changes from outside the original pull request, including, potentially, unrelated coverage changes.

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Details

• 100 of 103 (97.09%) changed or added relevant lines in 1 file are covered.
• 987 unchanged lines in 29 files lost coverage.
• Overall coverage increased (+0.5%) to 88.851%

---

Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/circuit/gate.py	100	103	97.09%

Files with Coverage Reduction	New Missed Lines	%
qiskit/transpiler/passes/layout/disjoint_utils.py	1	96.83%
qiskit/pulse/instructions/directives.py	1	97.22%
qiskit/pulse/transforms/alignments.py	1	96.45%
crates/accelerate/src/two_qubit_decompose.rs	1	91.45%
qiskit/qasm3/init.py	1	95.0%
qiskit/circuit/library/pauli_evolution.py	2	96.15%
qiskit/transpiler/passes/synthesis/unitary_synthesis.py	2	88.26%
qiskit/primitives/containers/data_bin.py	2	96.36%
crates/circuit/src/imports.rs	2	77.78%
qiskit/quantum_info/operators/symplectic/sparse_pauli_op.py	3	93.98%

Totals
Change from base Build 10919208944:	0.5%
Covered Lines:	74103
Relevant Lines:	83401

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💛 - Coveralls

[1ucian0]

I inlined/moved the code from qiskit/circuit/add_control.py to qiskit/circuit/gate.py. I assume refactoring the control thing makes little sense because oxidation, right? Otherwise, I can have a look on that in follow up PR.