Fix TrotterProduct differentiability with parameter-shift

doc/releases/changelog-dev.md

@@ -616,6 +616,9 @@ same information.
 
 <h3>Bug fixes 🐛</h3>
 
+* Fixes incorrect differentiation of `TrotterProduct` when using `diff_method="parameter-shift"`.
+  [(#6432)](https://github.com/PennyLaneAI/pennylane/pull/6432)
+
 * `qml.ControlledQubitUnitary` has consistent behaviour with program capture enabled. 
   [(#6719)](https://github.com/PennyLaneAI/pennylane/pull/6719)
 

tests/ops/functions/conftest.py

@@ -64,7 +64,10 @@ def _trotterize_qfunc_dummy(time, theta, phi, wires, flip=False):
     (qml.s_prod(1.1, qml.RX(1.1, 0)), {}),
     (qml.prod(qml.PauliX(0), qml.PauliY(1), qml.PauliZ(0)), {}),
     (qml.ctrl(qml.RX(1.1, 0), 1), {}),
-    (qml.exp(qml.PauliX(0), 1.1), {}),
+    (qml.exp(qml.PauliX(0), 1.1), {"skip_differentiation": True}),
+    # FIXME: Generator of Exp is incorrect when coefficient is imaginary
+    # (qml.exp(qml.PauliX(0), 2.9j), {}),
+    (qml.evolve(qml.PauliX(0), -0.5), {}),
     (qml.pow(qml.IsingXX(1.1, [0, 1]), 2.5), {}),
     (qml.ops.Evolution(qml.PauliX(0), 5.2), {}),
     (qml.QutritBasisState([1, 2, 0], wires=[0, 1, 2]), {"skip_differentiation": True}),

tests/ops/op_math/test_exp.py

@@ -870,7 +870,6 @@ def circuit(phi):
         grad = qml.grad(circuit)(phi)
         assert qml.math.allclose(grad, -qml.numpy.sin(phi))
 
-    @pytest.mark.xfail  # related to #6333
     @pytest.mark.autograd
     def test_autograd_param_shift_qnode(self):
         """Test execution and gradient with pennylane numpy array."""

tests/templates/test_subroutines/test_trotter.py

@@ -452,13 +452,57 @@ def test_copy(self, hamiltonian, time, n, order):
         assert op.hyperparameters == new_op.hyperparameters
         assert op is not new_op
 
-    @pytest.mark.xfail(reason="https://github.com/PennyLaneAI/pennylane/issues/6333", strict=False)
     @pytest.mark.parametrize("hamiltonian", test_hamiltonians)
     def test_standard_validity(self, hamiltonian):
         """Test standard validity criteria using assert_valid."""
         time, n, order = (4.2, 10, 4)
         op = qml.TrotterProduct(hamiltonian, time, n=n, order=order)
-        qml.ops.functions.assert_valid(op)
+        qml.ops.functions.assert_valid(op, skip_differentiation=True)
+
+    @pytest.mark.parametrize("hamiltonian", test_hamiltonians)
+    def test_differentiation(self, hamiltonian):
+        """Tests the differentiation of the TrotterProduct with parameter-shift"""
+
+        time, n, order = (4.2, 10, 4)
+
+        dev = qml.device("default.qubit")
+        coeffs, ops = hamiltonian.terms()
+
+        @qml.qnode(dev, diff_method="backprop")
+        def circ_bp(coeffs, time):
+            with qml.queuing.QueuingManager.stop_recording():
+                hamiltonian = qml.dot(coeffs, ops)
+
+            qml.TrotterProduct(hamiltonian, time, n, order)
+            return qml.probs()
+
+        @qml.qnode(dev, diff_method="parameter-shift")
+        def circ_ps(coeffs, time):
+            with qml.queuing.QueuingManager.stop_recording():
+                hamiltonian = qml.dot(coeffs, ops)
+
+            qml.TrotterProduct(hamiltonian, time, n, order)
+            return qml.probs()
+
+        coeffs = qml.numpy.array(coeffs)
+        time = qml.numpy.array(time)
+
+        expected_bp = qml.jacobian(circ_bp)(coeffs, time)
+        assert expected_bp[0].shape == (2**hamiltonian.num_wires, len(coeffs))
+        assert expected_bp[1].shape == (2**hamiltonian.num_wires,)
+
+        ps = qml.jacobian(circ_ps)(coeffs, time)
+        assert ps[0].shape == (2**hamiltonian.num_wires, len(coeffs))
+        assert ps[1].shape == (2**hamiltonian.num_wires,)
+
+        error_msg = (
+            "Parameter-shift does not produce the same Jacobian as with backpropagation. "
+            "This might be a bug, or it might be expected due to the mathematical nature "
+            "of backpropagation, in which case, this test can be skipped for this operator."
+        )
+
+        for actual, expected in zip(ps, expected_bp):
+            assert qml.math.allclose(actual, expected, atol=1e-6), error_msg
 
     # TODO: Remove test when we deprecate ApproxTimeEvolution
     @pytest.mark.parametrize("n", (1, 2, 5, 10))