Update MCX recursive synthesis method to reduce number of CX gates

[ShellyGarion]

Summary

Close #9743.
This PR replaces #8710 in order to get it merged on time for qiskit 1.2 release.

Details and comments

[qiskit-bot]

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

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

[ShellyGarion]

Comparison of the old vs. new code:

        from qiskit import transpile
        from qiskit.circuit.library import MCXRecursive
        for n in range(5, 20):
            qc_rec = MCXRecursive(n).definition
            tqc_rec = transpile(qc_rec, basis_gates=['u', 'cx'])
            print("num_qubits=", n, "cx count=", tqc_rec.count_ops()["cx"])

Current code:

num_qubits= 5 cx count= 56
num_qubits= 6 cx count= 100
num_qubits= 7 cx count= 144
num_qubits= 8 cx count= 184
num_qubits= 9 cx count= 224
num_qubits= 10 cx count= 312
num_qubits= 11 cx count= 400
num_qubits= 12 cx count= 488
num_qubits= 13 cx count= 576
num_qubits= 14 cx count= 656
num_qubits= 15 cx count= 736
num_qubits= 16 cx count= 816
num_qubits= 17 cx count= 896
num_qubits= 18 cx count= 1072
num_qubits= 19 cx count= 1248

New code:

num_qubits= 5 cx count= 56
num_qubits= 6 cx count= 80
num_qubits= 7 cx count= 104
num_qubits= 8 cx count= 120
num_qubits= 9 cx count= 136
num_qubits= 10 cx count= 152
num_qubits= 11 cx count= 168
num_qubits= 12 cx count= 184
num_qubits= 13 cx count= 200
num_qubits= 14 cx count= 216
num_qubits= 15 cx count= 232
num_qubits= 16 cx count= 248
num_qubits= 17 cx count= 264
num_qubits= 18 cx count= 280
num_qubits= 19 cx count= 296

[ShellyGarion]

For n>=7 the number of CX gates is 16*n-8

[coveralls]

Pull Request Test Coverage Report for Build 9973712807

Details

• 11 of 11 (100.0%) changed or added relevant lines in 1 file are covered.
• 12 unchanged lines in 3 files lost coverage.
• Overall coverage decreased (-0.004%) to 89.897%

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Files with Coverage Reduction	New Missed Lines	%
crates/qasm2/src/expr.rs	1	94.02%
crates/qasm2/src/lex.rs	5	92.37%
crates/qasm2/src/parse.rs	6	96.69%

Totals
Change from base Build 9958403825:	-0.004%
Covered Lines:	65790
Relevant Lines:	73184

---

💛 - Coveralls

[ShellyGarion]

Some further experiments with more qubits:

num_qubits= 50 cx count current code= 9536 cx count new code= 792
num_qubits= 100 cx count current code= 38784 cx count new code=1592