fix bugs

pennylane/ops/functions/assert_valid.py

@@ -316,12 +316,20 @@ def circuit(*args):
         circuit, device=qml.device("reference.qubit"), diff_method="parameter-shift"
     )
 
-    ps = qml.jacobian(qnode_ps)(*(qml.numpy.array(x) for x in data))
-    expected_ps = qml.jacobian(qnode_ref)(*(qml.numpy.array(x) for x in data))
+    params = [x if isinstance(x, int) else qml.numpy.array(x) for x in data]
 
-    assert qml.math.allclose(
-        ps, expected_ps
-    ), "Parameter shift does not produce the expected Jacobian with this operator."
+    ps = qml.jacobian(qnode_ps)(*params)
+    expected_ps = qml.jacobian(qnode_ref)(*params)
+
+    if isinstance(ps, tuple):
+        for actual, expected in zip(ps, expected_ps):
+            assert qml.math.allclose(
+                actual, expected
+            ), "Backpropagation does not produce the expected Jacobian with this operator."
+    else:
+        assert qml.math.allclose(
+            ps, expected_ps
+        ), "Parameter shift does not produce the expected Jacobian with this operator."
 
 
 def _check_wires(op, skip_wire_mapping):

pennylane/ops/op_math/prod.py

@@ -231,6 +231,7 @@ def circuit(weights):
 
     _op_symbol = "@"
     _math_op = math.prod
+    grad_method = None
 
     @property
     def is_hermitian(self):
@@ -359,7 +360,7 @@ def arithmetic_depth(self) -> int:
     def _build_pauli_rep(self):
         """PauliSentence representation of the Product of operations."""
         if all(operand_pauli_reps := [op.pauli_rep for op in self.operands]):
-            return reduce(lambda a, b: a @ b, operand_pauli_reps)
+            return reduce(lambda a, b: a @ b, operand_pauli_reps) if operand_pauli_reps else None
         return None
 
     def _simplify_factors(self, factors: tuple[Operator]) -> tuple[complex, Operator]: