From 206fbee391a0b394052716ffd890e94dbfc686c4 Mon Sep 17 00:00:00 2001
From: "mergify[bot]" <37929162+mergify[bot]@users.noreply.github.com>
Date: Fri, 5 Aug 2022 11:41:49 +0000
Subject: [PATCH] Fix ``ParameterExpression.is_real`` if ``symengine`` is
 installed (#8456) (#8462)

* Fix is_real on ParameterExpression

* typo in reno

Co-authored-by: mergify[bot] <37929162+mergify[bot]@users.noreply.github.com>
(cherry picked from commit 2bab09c1aae84e5bf38ba52fa3a272667c1887cc)

Co-authored-by: Julien Gacon <gaconju@gmail.com>
---
 qiskit/circuit/parameterexpression.py              | 11 +++++++++--
 .../fix-paramexpr-isreal-8d20348b4ce6cbe7.yaml     | 14 ++++++++++++++
 test/python/circuit/test_parameters.py             |  8 ++++++++
 3 files changed, 31 insertions(+), 2 deletions(-)
 create mode 100644 releasenotes/notes/fix-paramexpr-isreal-8d20348b4ce6cbe7.yaml

diff --git a/qiskit/circuit/parameterexpression.py b/qiskit/circuit/parameterexpression.py
index 641a7404c553..30bc46922197 100644
--- a/qiskit/circuit/parameterexpression.py
+++ b/qiskit/circuit/parameterexpression.py
@@ -508,14 +508,21 @@ def __eq__(self, other):
     def is_real(self):
         """Return whether the expression is real"""
 
-        if not self._symbol_expr.is_real and self._symbol_expr.is_real is not None:
+        # workaround for symengine behavior that const * (0 + 1 * I) is not real
+        # see https://github.com/symengine/symengine.py/issues/414
+        if _optionals.HAS_SYMENGINE and self._symbol_expr.is_real is None:
+            symbol_expr = self._symbol_expr.evalf()
+        else:
+            symbol_expr = self._symbol_expr
+
+        if not symbol_expr.is_real and symbol_expr.is_real is not None:
             # Symengine returns false for is_real on the expression if
             # there is a imaginary component (even if that component is 0),
             # but the parameter will evaluate as real. Check that if the
             # expression's is_real attribute returns false that we have a
             # non-zero imaginary
             if _optionals.HAS_SYMENGINE:
-                if self._symbol_expr.imag != 0.0:
+                if symbol_expr.imag != 0.0:
                     return False
             else:
                 return False
diff --git a/releasenotes/notes/fix-paramexpr-isreal-8d20348b4ce6cbe7.yaml b/releasenotes/notes/fix-paramexpr-isreal-8d20348b4ce6cbe7.yaml
new file mode 100644
index 000000000000..f9219b813169
--- /dev/null
+++ b/releasenotes/notes/fix-paramexpr-isreal-8d20348b4ce6cbe7.yaml
@@ -0,0 +1,14 @@
+---
+fixes:
+  - |
+    Fix a bug where a bound :class:`.ParameterExpression` was not identified as real 
+    if ``symengine`` was installed and the bound expression was not a plain ``1j``.
+    For example::
+  
+        from qiskit.circuit import Parameter
+
+        x = Parameter("x")
+        expr = 1j * x
+        bound = expr.bind({x: 2})
+        print(bound.is_real())  # used to be True, but is now False
+
diff --git a/test/python/circuit/test_parameters.py b/test/python/circuit/test_parameters.py
index ed25350bf227..3a96963b7f86 100644
--- a/test/python/circuit/test_parameters.py
+++ b/test/python/circuit/test_parameters.py
@@ -1718,6 +1718,14 @@ def test_parameter_expression_grad(self):
             self.assertEqual(expr.gradient(x), 2 * x)
             self.assertEqual(expr.gradient(x).gradient(x), 2)
 
+    def test_bound_expression_is_real(self):
+        """Test is_real on bound parameters."""
+        x = Parameter("x")
+        expr = 1j * x
+        bound = expr.bind({x: 2})
+
+        self.assertFalse(bound.is_real())
+
 
 class TestParameterEquality(QiskitTestCase):
     """Test equality of Parameters and ParameterExpressions."""