Handle pre-existing adjacent barriers

In the case when a label is set to trigger the removal of the labelled
barrier the merge step would lose the context around which barrier
instruction was transpiler inserted and which was user provided. To
address this issue this commit skips the MergeAdjacentBarrier step so
that the transpiler barrier is kept separate from any user inserted
barriers which need to be preserved.

qiskit/transpiler/passes/utils/barrier_before_final_measurements.py

@@ -87,6 +87,9 @@ def run(self, dag):
 
         dag.compose(barrier_layer)
 
-        # Merge the new barrier into any other barriers
-        adjacent_pass = MergeAdjacentBarriers()
-        return adjacent_pass.run(dag)
+        if self.label is None:
+            # Merge the new barrier into any other barriers
+            adjacent_pass = MergeAdjacentBarriers()
+            return adjacent_pass.run(dag)
+        else:
+            return dag

test/python/compiler/test_transpiler.py

@@ -1710,6 +1710,25 @@ def test_barrier_not_output(self, opt_level):
         )
         self.assertNotIn("barrier", tqc.count_ops())
 
+    @data(0, 1, 2, 3)
+    def test_barrier_not_output_input_preservered(self, opt_level):
+        """Test that barriers added as part internal transpiler operations do not leak out."""
+        qc = QuantumCircuit(2, 2)
+        qc.cx(0, 1)
+        qc.measure_all()
+        tqc = transpile(
+            qc,
+            initial_layout=[1, 4],
+            coupling_map=[[0, 1], [1, 2], [2, 3], [3, 4]],
+            optimization_level=opt_level,
+        )
+        op_counts = tqc.count_ops()
+        self.assertEqual(op_counts["barrier"], 1)
+        for inst in tqc.data:
+            if inst.operation.name == "barrier":
+                self.assertEqual(len(inst.qubits), 2)
+
+
     @combine(opt_level=[0, 1, 2, 3])
     def test_transpile_annotated_ops(self, opt_level):
         """Test transpilation of circuits with annotated operations."""

test/python/transpiler/test_sabre_layout.py

@@ -254,7 +254,7 @@ def test_layout_many_search_trials(self):
         self.assertIsInstance(res, QuantumCircuit)
         layout = res._layout.initial_layout
         self.assertEqual(
-            [layout[q] for q in qc.qubits], [22, 7, 2, 12, 1, 5, 14, 4, 11, 0, 16, 15, 3, 10]
+            [layout[q] for q in qc.qubits], [10, 16, 8, 4, 11, 20, 15, 19, 18, 7, 12, 1, 2, 0]
         )