fix(transpiler): RemoveFinalMeasurements incorrectly removes measurements feeding control-flow conditions

[adcorcol]

Summary

RemoveFinalMeasurements was incorrectly removing measurements whose classical output feeds a control-flow condition (while_loop, if_else, switch_case). The pass only checked quantum wire successors to determine if a measurement was "final", completely ignoring classical wire successors. Removing such measurements left the condition register at its default value 0, causing while_loop circuits to run indefinitely.

Fixes #14319.

Root cause

In calc_final_ops, the reverse DAG traversal walks backwards through quantum wire predecessors. A measure node's classical wire successors were never inspected, so a measurement whose clbit feeds a while_loop condition was indistinguishable from a truly final one.

Fix

Before marking a node as final, check whether any classical successor is a DAGOpNode that is not itself a measure. A measure successor merely overwrites the clbit (safe to remove); any other op means the clbit value is being read and the measurement must be preserved. For all other classical successors we err on the side of preservation (conservative but correct).

if any(
    isinstance(s, DAGOpNode) and s.name != "measure"
    for s in dag.classical_successors(node)
):
    continue

Test plan

• test_measure_feeding_while_loop_condition_not_removed
• test_measure_feeding_if_else_condition_not_removed
• test_measure_feeding_switch_case_condition_not_removed
• test_chained_measures_first_is_removed_second_feeds_condition — exercises the != "measure" branch: first measure is overwritten and correctly removed, second feeds the condition and is preserved
• All 9 existing tests continue to pass
• LightCone pass (which also uses calc_final_ops) tested and unaffected

🤖 Generated with Claude Code

[qiskit-bot]

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

• @Qiskit/terra-core