Move mcx synthesis methods with ancillas to the synthesis library

[ShellyGarion]

Summary

See details in issue #12863.
In this PR we transfer the mcx synthesis methods with clean and dirty ancillas to the synthesis library.

Details and comments

Added 3 functions in the qiskit/synthesis/multi-controlled library:

• synth_mcx_1_clean_b95
• synth_n_dirty_i15
• synth_n_clean_m15

[qiskit-bot]

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

• @Cryoris
• @Qiskit/terra-core
• @ajavadia

[coveralls]

Pull Request Test Coverage Report for Build 10338784669

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

• 112 of 116 (96.55%) changed or added relevant lines in 4 files are covered.
• 299 unchanged lines in 15 files lost coverage.
• Overall coverage decreased (-0.006%) to 89.745%

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Changes Missing Coverage	Covered Lines	Changed/Added Lines	%
qiskit/synthesis/multi_controlled/mcx_with_ancillas_synth.py	101	105	96.19%

Files with Coverage Reduction	New Missed Lines	%
crates/qasm2/src/expr.rs	1	94.02%
qiskit/primitives/statevector_estimator.py	3	94.44%
crates/qasm2/src/lex.rs	3	91.98%
qiskit/primitives/estimator.py	3	96.2%
qiskit/transpiler/passes/optimization/consolidate_blocks.py	5	95.28%
crates/accelerate/src/synthesis/clifford/greedy_synthesis.rs	5	97.34%
crates/qasm2/src/parse.rs	6	97.61%
crates/circuit/src/parameter_table.rs	7	93.27%
qiskit/transpiler/passes/basis/basis_translator.py	8	97.44%
qiskit/transpiler/preset_passmanagers/builtin_plugins.py	12	96.45%

Totals
Change from base Build 10222290210:	-0.006%
Covered Lines:	67411
Relevant Lines:	75114

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💛 - Coveralls

[Cryoris]

Nice, thanks for the effort! Should we already pending-deprecate the gate classes and refer to the synthesis functions? Once we have the MCX HLS by Sasha we can extend the deprecation message to state that users can also use the HLS plugin.

[ShellyGarion]

Note that in commit 7b68e57 I had to revert the new synthesized circuit names since QASM based tests are failing.
Should I update the names and fix the tests? or is it considered breaking API?

[alexanderivrii]

Thanks, this looks great! The new function names, such as synth_mcx_n_dirty_i15, synth_mcx_1_clean_b95, etc. are reasonable. One small question: once we integrate these into plugins, would it make sense for the plugin names to be n_dirty_i15, 1_clean_b95, etc. as in hls = HLSConfig(mcx=['1_clean_b95`])?

[alexanderivrii]

Thanks @ShellyGarion! This looks very good. I had a few minor comments about explicitly adding the information about the total numbers of qubits to the new synthesis function docstrings and to the release notes , moving imports to the top-level, and providing more explicit links to the papers in the release notes. After this is addressed, I would be happy to merge.

[alexanderivrii]

Would it be possible to import this at the top-level, and instead add disable=cyclic-import to x.py?

[ShellyGarion]

no, this will not work, since there is a real cyclic import here

[alexanderivrii]

LGTM, thanks for making the changes!