code: def test_trainable_hamiltonian(dev_name, diff_method):
      """Test that the ApproxTimeEvolution template
      can be differentiated if the Hamiltonian coefficients are trainable
      """
      dev = qml.device(dev_name, wires=2)
  
      obs = [
          qml.PauliX(0) @ qml.PauliY(1),
          qml.PauliY(0) @ qml.PauliX(1),
      ]
  
      def create_tape(coeffs, t):
          H = qml.Hamiltonian(coeffs, obs)
  
          with qml.queuing.AnnotatedQueue() as q:
              qml.templates.ApproxTimeEvolution(H, t, 2)
              qml.expval(qml.PauliZ(0))
  
          tape = qml.tape.QuantumScript.from_queue(q)
          return tape
  
      def cost(coeffs, t):
          tape = create_tape(coeffs, t)
  
          if (
              diff_method is qml.gradients.param_shift
              and dev_name != "default.qubit"
          ):
              tape = dev.expand_fn(tape)
              return qml.execute([tape], dev, diff_method)[0]
          program, _ = dev.preprocess()
          return qml.execute(
              [tape],
              dev,
              gradient_fn=diff_method,
              transform_program=program,
          )[0]
  
      t = pnp.array(0.54, requires_grad=True)
      coeffs = pnp.array([-0.6, 2.0], requires_grad=True)
  
      cost(coeffs, t)
      grad = qml.grad(cost)(coeffs, t)
  
      assert len(grad) == 2
  
      assert isinstance(grad[0], np.ndarray)
      assert grad[0].shape == (2,)
  
      assert isinstance(grad[1], np.ndarray)
      assert grad[1].shape == tuple()
  
      # compare to finite-differences
  
      @qml.qnode(dev, diff_method="finite-diff")
      def circuit(coeffs, t):
          H = qml.Hamiltonian(coeffs, obs)
          qml.ApproxTimeEvolution(H, t, 2)
          return qml.expval(qml.PauliZ(0))
  
      expected = qml.grad(circuit)(coeffs, t)
      assert np.allclose(
          qml.math.hstack(grad), qml.math.hstack(expected)
      )
  
imports: import pytest
  import numpy
  from pennylane import numpy
  import pennylane
label_desc: Use image node_id 5 for calling a global function with example usage: test_trainable_hamiltonian(dev_name, diff_method) and returns: tape, qml, qml, qml