Fix decomposition for a single qubit and clbit (#8614)

Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>
(cherry picked from commit c008008)

qiskit/transpiler/passes/basis/decompose.py

@@ -91,7 +91,11 @@ def run(self, dag: DAGCircuit) -> DAGCircuit:
                     continue
                 # TODO: allow choosing among multiple decomposition rules
                 rule = node.op.definition.data
-                if len(rule) == 1 and len(node.qargs) == len(rule[0].qubits) == 1:
+                if (
+                    len(rule) == 1
+                    and len(node.qargs) == len(rule[0].qubits) == 1  # to preserve gate order
+                    and len(node.cargs) == len(rule[0].clbits) == 0
+                ):
                     if node.op.definition.global_phase:
                         dag.global_phase += node.op.definition.global_phase
                     dag.substitute_node(node, rule[0].operation, inplace=True)

releasenotes/notes/fix-decomp-1q-1c-84f369f9a897a5b7.yaml

@@ -0,0 +1,13 @@
+---
+fixes:
+  - |
+    Fixed a bug where decomposing an instruction with one qubit and one classical bit 
+    containing a single quantum gate failed. Now the following decomposes as expected::
+
+        block = QuantumCircuit(1, 1)
+        block.h(0)
+
+        circuit = QuantumCircuit(1, 1)
+        circuit.append(block, [0], [0])
+
+        decomposed = circuit.decompose()

test/python/transpiler/test_decompose.py

@@ -300,3 +300,18 @@ def test_decompose_reps(self):
         decom_circ = self.complex_circuit.decompose(reps=2)
         decomposed = self.complex_circuit.decompose().decompose()
         self.assertEqual(decom_circ, decomposed)
+
+    def test_decompose_single_qubit_clbit(self):
+        """Test the decomposition of a block with a single qubit and clbit works.
+
+        Regression test of Qiskit/qiskit-terra#8591.
+        """
+        block = QuantumCircuit(1, 1)
+        block.h(0)
+
+        circuit = QuantumCircuit(1, 1)
+        circuit.append(block, [0], [0])
+
+        decomposed = circuit.decompose()
+
+        self.assertEqual(decomposed, block)