Fix global-phase of copied BlueprintCircuits

Using `BlueprintCircuit.copy()` or `.copy_empty_like()` would previously
erase the global phase as part of the rebuild operation.  This overrides
`BlueprintCircuit.copy_empty_like()` to ensure that it is always
propagated through.

qiskit/circuit/library/blueprintcircuit.py

@@ -178,6 +178,16 @@ def num_connected_components(self, unitary_only=False):
             self._build()
         return super().num_connected_components(unitary_only=unitary_only)
 
+    def copy_empty_like(self, name=None):
+        if not self._is_built:
+            self._build()
+        cpy = super().copy_empty_like(name=name)
+        # The base `copy_empty_like` will typically trigger code that `BlueprintCircuit` treats as
+        # an "invalidation", so we have to manually restore properties deleted by that that
+        # `copy_empty_like` is supposed to propagate.
+        cpy.global_phase = self.global_phase
+        return cpy
+
     def copy(self, name=None):
         if not self._is_built:
             self._build()

releasenotes/notes/fix-blueprintcircuit-phase-7102043cf2e47e33.yaml

@@ -0,0 +1,6 @@
+---
+fixes:
+  - |
+    Calling :meth:`~.QuantumCircuit.copy` or :meth:`~.QuantumCircuit.copy_empty_like` on a
+    :class:¬.BlueprintCircuit` will now correctly propagate the
+    :attr:`~.QuantumCircuit.global_phase` to the copy.  Previously, the global phase would always be zero after the copy.

test/python/circuit/library/test_blueprintcircuit.py

@@ -12,6 +12,7 @@
 
 """Test the blueprint circuit."""
 
+import math
 import unittest
 from ddt import ddt, data
 
@@ -174,6 +175,40 @@ def _build(self):
         mock._append(CircuitInstruction(XGate(), (qr[0],), ()))
         self.assertEqual(expected, mock)
 
+    def test_global_phase_copied(self):
+        """Test that a global-phase parameter is correctly propagated through."""
+
+        class DummyBlueprint(BlueprintCircuit):
+            """Dummy circuit."""
+
+            def _check_configuration(self, raise_on_failure=True):
+                return True
+
+            def _build(self):
+                # We don't need to do anything, we just need `_build` to be non-abstract.
+                # pylint: disable=useless-parent-delegation
+                return super()._build()
+
+        base = DummyBlueprint()
+        base.global_phase = math.pi / 2
+
+        self.assertEqual(base.copy_empty_like().global_phase, math.pi / 2)
+        self.assertEqual(base.copy().global_phase, math.pi / 2)
+
+        # Verify that a parametric global phase can be assigned after the copy.
+        a = Parameter("a")
+        parametric = DummyBlueprint()
+        parametric.global_phase = a
+
+        self.assertEqual(
+            parametric.copy_empty_like().assign_parameters({a: math.pi / 2}).global_phase,
+            math.pi / 2,
+        )
+        self.assertEqual(
+            parametric.copy().assign_parameters({a: math.pi / 2}).global_phase,
+            math.pi / 2,
+        )
+
 
 if __name__ == "__main__":
     unittest.main()