Add __iadd__ method to PauliSentence

pennylane/pauli/pauli_arithmetic.py

@@ -342,6 +342,15 @@
             larger_ps[key] += smaller_ps[key]
 
         return larger_ps
+
+    def __iadd__(self, other):
+        """Inplace addition of two Pauli sentence together by adding terms of other to self"""
+        for key in other:
+            if key in self:
+                self[key] += other[key]
+            else:
+                self[key] = other[key]
+        return self
 
     def __copy__(self):
         """Copy the PauliSentence instance."""

tests/pauli/test_pauli_arithmetic.py

@@ -409,6 +409,16 @@ def test_add(self, string1, string2, result):
         (ps5, "Can't get the matrix of an empty PauliSentence."),
     )
 
+    @pytest.mark.parametrize("string1, string2, result", tup_ps_add)
+    def test_iadd(self, string1, string2, result):
+        """Test that the correct result of inplace addition is produced and other object is not changed."""
+        original_string2=copy(string2)
+        string1 += string2
+        string1.simplify()
+
+        assert string1 == result # Check if the modified object matches the expected result
+        assert original_string2 == string2  # Ensure the original object is not modified
+
     @pytest.mark.parametrize("ps, match", ps_match)
     def test_to_mat_error_empty(self, ps, match):
         """Test that an appropriate error is raised when an empty