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Deprecate qiskit/quantum_info/synthesis and move to qiskit/synthesis (backport #11460) (#11635)

* Deprecate qiskit/quantum_info/synthesis and move to qiskit/synthesis (#11460)

* remove deprecated code in clifford_decompose and cnotdihedral_decompose

* move tests from test/python/quantum_info to test/python/synthesis

* move the Quaternion class from quantum_info/synthesis to quantum_info

* deprecate cnot_rxx_decompose, and move to an internal code in the equivalence_library

* deprecate cnot_rxx_decompose

* move qsd from qiskit/quantum_info/synthesis to qiskit/synthesis/unitary

* handle lint and docs errors in qsd

* handle lint and docs errors in qsd

* handle lint and docs errors in qsd

* handle lint and docs errors in qsd

* handle lint and docs errors in qsd

* handle cyclic imports in qsd

* minor

* update qsd docs

* move one_qubit_decompose from qiskit/quantum_info/synthesis to qiskit/synthesis/one_qubit

* move xx_decompose from qiskit/quantum_info/synthesis to qiskit/synthesis/two_qubits

* handle cyclic imports

* move two-qubit synthesis code from qiskit/quantum_info/synthesis to qiskit/synthesis/two_qubits

* update qsd docs

* minor

* add release notes

* updates following review

* add disable cyclic import to rv.py

* add deprecation warning in qiskit/quantum_info/__init__.py

* fix links

* improve qsd docs following review

* update qsd after review

* change pending deprecatrion to deprecation in ion_decompose

* update release notes following review

* update pending deprecation to deprecation

* add test for a deprecation

* add more tests for deprecations

* add another test for deprecation

* handle lint errors

* minor fix following review

* remove test for _cnot_rxx_decompose() private method

(cherry picked from commit 8887f4436)

# Conflicts:
#	qiskit/synthesis/__init__.py
#	qiskit/transpiler/synthesis/qsd.py
#	test/benchmarks/random_circuit_hex.py

* fix merge conflicts

* fix merge c... (continued)

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