Qiskit / qiskit / 22056883703

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Fix HighLevelSynthesis qubit tracking mechanism (#15685) (#15687)

HighLevelSynthesis tracks qubit states throughout its execution, allowing the pass
to choose the best synthesis method for each operation, possibly requiring a certain
number of clean or dirty ancilla qubits. In particular, an operation with `k` qubits
can be synthesized using `m>k` qubits provided the remaining qubits are available in
the rest of the circuit.

As a concrete example, `MCXSynthesis2CleanKG24` is a plugin for synthesizing MCX gates
which applies when at least 2 clean ancilla qubits are available, and can synthesize
a 4-qubit MCX gate over qubits [2, 1, 3, 10] using a 6-qubit quantum circuit over qubits
[2, 1, 3, 10, 4, 12], where the first 4 qubits are the original qubits, and the last 2
qubits are the ancilla qubits.

We assume that each plugin is required to return the state of each ancilla qubit
to its original state. Thus, after we recursively synthesize an operation, the qubit
tracking mechanism returns the ancilla qubits to their previous state. In the example
above, this means restoring the values of qubits 4 and 12.

Previously this computation was done incorrectly, restoring qubits `k..m` instead of
`synthesized_qubits[k..m]`. In our example, this means restoring `4` and `5` instead
of `4` and `12`.

(cherry picked from commit 8f4e195fc)

Co-authored-by: Alexander Ivrii <alexi@il.ibm.com>

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