Give IGate a no-op definition

qiskit/circuit/library/standard_gates/i.py

@@ -44,6 +44,11 @@ def __init__(self, label: Optional[str] = None):
         """Create new Identity gate."""
         super().__init__("id", 1, [], label=label)
 
+    def _define(self) -> None:
+        from qiskit.circuit import QuantumCircuit  # pylint: disable=cyclic-import
+
+        self.definition = QuantumCircuit(1, name=self.name)
+
     def inverse(self):
         """Invert this gate."""
         return IGate()  # self-inverse

releasenotes/notes/fix-igate-definition-7385cff02e663867.yaml

@@ -0,0 +1,13 @@
+fixes:
+  - |
+    Fixed a bug where certain operations, such as
+    :meth:`.QuantumCircuit.control`, would crash if an identity operation
+    represented by an :class:`.IGate` was present in a :class:`.QuantumCircuit`.
+    For example, the following code was previously an error, but will now function
+    correctly::
+
+        from qiskit import QuantumCircuit
+
+        qc = QuantumCircuit(1)
+        qc.i(0)
+        controlled = qc.control()

test/python/circuit/test_circuit_operations.py

@@ -803,6 +803,27 @@ def test_control_implementation(self):
 
         self.assertEqual(ref, c_qc)
 
+    def test_control_primitive_gates(self):
+        """Test that circuits containing primitive gates (with no definition) can be controlled
+        during `QuantumCircuit.control`.
+
+        Regression test of gh-7399."""
+        qc = QuantumCircuit(2)
+        qc.u(0.2, 0.3, 0.4, 0)
+        qc.i(1)
+        controlled = qc.control()
+
+        # The identity gate should have no effect.
+        expected = QuantumCircuit(
+            QuantumRegister(1, name="control"), QuantumRegister(2, name="target")
+        )
+        expected.cu(0.2, 0.3, 0.4, 0, 0, 1)
+
+        self.assertIsInstance(controlled, QuantumCircuit)
+        self.assertEqual(len(controlled.data), 1)
+        instruction, _, _ = controlled.data[0]
+        self.assertEqual(instruction.definition, expected)
+
     @data("gate", "instruction")
     def test_repeat_appended_type(self, subtype):
         """Test repeat appends Gate if circuit contains only gates and Instructions otherwise."""