Fix PauliOp.adjoint() (#9434)

* bug fix

* reno mod

* reno mod

* Update releasenotes/notes/fix-PauliOp-adjoint-a275876185df989f.yaml

Co-authored-by: Julien Gacon <gaconju@gmail.com>

Co-authored-by: Julien Gacon <gaconju@gmail.com>
(cherry picked from commit 85c30a2)

qiskit/opflow/primitive_ops/pauli_op.py

@@ -84,7 +84,7 @@ def add(self, other: OperatorBase) -> OperatorBase:
         return SummedOp([self, other])
 
     def adjoint(self) -> "PauliOp":
-        return PauliOp(self.primitive, coeff=self.coeff.conjugate())
+        return PauliOp(self.primitive.adjoint(), coeff=self.coeff.conjugate())
 
     def equals(self, other: OperatorBase) -> bool:
         if isinstance(other, PauliOp) and self.coeff == other.coeff:

releasenotes/notes/fix-PauliOp-adjoint-a275876185df989f.yaml

@@ -0,0 +1,6 @@
+---
+fixes:
+  - |
+    Fixed a bug where :meth:`.PauliOp.adjoint` did not return a correct value for Paulis
+    with complex coefficients, like ``PauliOp(Pauli("iX"))``. 
+    Fixed `#9433 <https://github.com/Qiskit/qiskit-terra/issues/9433>`.

test/python/opflow/test_op_construction.py

@@ -1288,6 +1288,10 @@ def test_adjoint(self):
         expected = PauliOp(Pauli("XYZX"), coeff=2 - 3j)
         self.assertEqual(~pauli_op, expected)
 
+        pauli_op = PauliOp(Pauli("iXYZX"), coeff=2 + 3j)
+        expected = PauliOp(Pauli("-iXYZX"), coeff=2 - 3j)
+        self.assertEqual(~pauli_op, expected)
+
     @data(*itertools.product(pauli_group_labels(2, full_group=True), repeat=2))
     @unpack
     def test_compose(self, label1, label2):