Fix build ordering of BlueprintCircuit._append

`QuantumCircuit._append` is the actual append primitive and is allowed
in inner-loop appends (and for `QuantumCircuit` to assume that it's
callable from other methods), so it's important that the "ensure built"
check happens there, not in `append`.

qiskit/circuit/library/blueprintcircuit.py

@@ -119,10 +119,10 @@ def qasm(self, formatted=False, filename=None, encoding=None):
             self._build()
         return super().qasm(formatted, filename, encoding)
 
-    def append(self, instruction, qargs=None, cargs=None):
+    def _append(self, instruction, _qargs=None, _cargs=None):
         if not self._is_built:
             self._build()
-        return super().append(instruction, qargs, cargs)
+        return super()._append(instruction, _qargs, _cargs)
 
     def compose(self, other, qubits=None, clbits=None, front=False, inplace=False, wrap=False):
         if not self._is_built:

releasenotes/notes/fix-blueprint-circuit-_append-b4d6c9c41db860f5.yaml

@@ -0,0 +1,6 @@
+---
+fixes:
+  - |
+    :class:`.BlueprintCircuit` subclasses will now behave correctly when the semi-public method
+    :meth:`.QuantumCircuit._append` is used with the blueprint in an unbuilt state, *i.e.* the
+    circuit will be built before attempting the append.

test/python/circuit/library/test_blueprintcircuit.py

@@ -16,8 +16,15 @@
 from ddt import ddt, data
 
 from qiskit.test.base import QiskitTestCase
-from qiskit.circuit import QuantumRegister, Parameter, QuantumCircuit, Gate, Instruction
-from qiskit.circuit.library import BlueprintCircuit
+from qiskit.circuit import (
+    QuantumRegister,
+    Parameter,
+    QuantumCircuit,
+    Gate,
+    Instruction,
+    CircuitInstruction,
+)
+from qiskit.circuit.library import BlueprintCircuit, XGate
 
 
 class MockBlueprint(BlueprintCircuit):
@@ -139,6 +146,34 @@ def test_to_gate_and_instruction(self, method):
             gate = circuit.to_instruction()
             self.assertIsInstance(gate, Instruction)
 
+    def test_build_before_appends(self):
+        """Test that both forms of direct append (public and semi-public) function correctly."""
+
+        class DummyBlueprint(BlueprintCircuit):
+            """Dummy circuit."""
+
+            def _check_configuration(self, raise_on_failure=True):
+                return True
+
+            def _build(self):
+                super()._build()
+                self.z(0)
+
+        expected = QuantumCircuit(2)
+        expected.z(0)
+        expected.x(0)
+
+        qr = QuantumRegister(2, "q")
+        mock = DummyBlueprint()
+        mock.add_register(qr)
+        mock.append(XGate(), [qr[0]], [])
+        self.assertEqual(expected, mock)
+
+        mock = DummyBlueprint()
+        mock.add_register(qr)
+        mock._append(CircuitInstruction(XGate(), (qr[0],), ()))
+        self.assertEqual(expected, mock)
+
 
 if __name__ == "__main__":
     unittest.main()