Fix Parameter.is_real()

qiskit/circuit/parameterexpression.py

@@ -535,11 +535,10 @@ def is_real(self):
             # expression's is_real attribute returns false that we have a
             # non-zero imaginary
             if _optionals.HAS_SYMENGINE:
-                if symbol_expr.imag != 0.0:
-                    return False
-            else:
-                return False
-        return True
+                if symbol_expr.imag == 0.0:
+                    return True
+            return False
+        return symbol_expr.is_real
 
     def sympify(self):
         """Return symbolic expression as a raw Sympy or Symengine object.

releasenotes/notes/fix-parameter-is_real-8b8f99811e58075e.yaml

@@ -0,0 +1,6 @@
+---
+fixes:
+  - |
+    Fixed a bug where :meth:`.Parameter.is_real` did not return ``None`` when
+    the parameter is not bound.
+    Fixed `#8619 <https://github.com/Qiskit/qiskit-terra/issues/8619>`.

test/python/circuit/test_parameters.py

@@ -1759,10 +1759,24 @@ def test_parameter_expression_grad(self):
     def test_bound_expression_is_real(self):
         """Test is_real on bound parameters."""
         x = Parameter("x")
+        self.assertEqual(x.is_real(), None)
+        self.assertEqual((1j * x).is_real(), None)
+
         expr = 1j * x
         bound = expr.bind({x: 2})
+        self.assertEqual(bound.is_real(), False)
+
+        bound = x.bind({x: 0 + 0j})
+        self.assertEqual(bound.is_real(), True)
+
+        bound = x.bind({x: 0 + 1j})
+        self.assertEqual(bound.is_real(), False)
+
+        bound = x.bind({x: 1 + 0j})
+        self.assertEqual(bound.is_real(), True)
 
-        self.assertFalse(bound.is_real())
+        bound = x.bind({x: 1 + 1j})
+        self.assertEqual(bound.is_real(), False)
 
 
 class TestParameterEquality(QiskitTestCase):