class_docstr: Test the torch interface execute function
  integrates well for both forward and backward execution
class_docstr_tok: ["Test","the","torch","interface","execute","function","integrates","well","for","both","forward","and","backward","execution"]
docstr: Test that operation and nested tapes expansion
  is differentiable
docstr_tok: ["Test","that","operation","and","nested","tapes","expansion","is","differentiable"]
code: def test_differentiable_expand(self, execute_kwargs, device, shots):
      """Test that operation and nested tapes expansion
      is differentiable"""
  
      class U3(qml.U3):
          """Dummy operator."""
  
          def decomposition(self):
              theta, phi, lam = self.data
              wires = self.wires
              return [
                  qml.Rot(lam, theta, -lam, wires=wires),
                  qml.PhaseShift(phi + lam, wires=wires),
              ]
  
      def cost_fn(a, p):
          tape = qml.tape.QuantumScript(
              [qml.RX(a, wires=0), U3(*p, wires=0)],
              [qml.expval(qml.PauliX(0))],
          )
          gradient_fn = execute_kwargs["gradient_fn"]
          if gradient_fn is None:
              _gradient_method = None
          elif isinstance(gradient_fn, str):
              _gradient_method = gradient_fn
          else:
              _gradient_method = "gradient-transform"
          config = qml.devices.ExecutionConfig(
              interface="autograd",
              gradient_method=_gradient_method,
              grad_on_execution=execute_kwargs.get(
                  "grad_on_execution", None
              ),
          )
          program, _ = device.preprocess(execution_config=config)
          return execute(
              [tape],
              device,
              **execute_kwargs,
              transform_program=program,
          )[0]
  
      a = torch.tensor(0.1, requires_grad=False)
      p = torch.tensor([0.1, 0.2, 0.3], requires_grad=True)
  
      res = cost_fn(a, p)
      expected = torch.cos(a) * torch.cos(p[1]) * torch.sin(
          p[0]
      ) + torch.sin(a) * (
          torch.cos(p[2]) * torch.sin(p[1])
          + torch.cos(p[0]) * torch.cos(p[1]) * torch.sin(p[2])
      )
      assert torch.allclose(
          res, expected, atol=atol_for_shots(shots), rtol=0
      )
  
      res = torch.autograd.functional.jacobian(
          lambda _p: cost_fn(a, _p), p
      )
      expected = torch.tensor(
          [
              torch.cos(p[1])
              * (
                  torch.cos(a) * torch.cos(p[0])
                  - torch.sin(a) * torch.sin(p[0]) * torch.sin(p[2])
              ),
              torch.cos(p[1]) * torch.cos(p[2]) * torch.sin(a)
              - torch.sin(p[1])
              * (
                  torch.cos(a) * torch.sin(p[0])
                  + torch.cos(p[0]) * torch.sin(a) * torch.sin(p[2])
              ),
              torch.sin(a)
              * (
                  torch.cos(p[0]) * torch.cos(p[1]) * torch.cos(p[2])
                  - torch.sin(p[1]) * torch.sin(p[2])
              ),
          ]
      )
      assert torch.allclose(
          res, expected, atol=atol_for_shots(shots), rtol=0
      )
  
imports: import numpy
  import pytest
  from param_shift_dev import ParamShiftDerivativesDevice
  import pennylane
  from pennylane.devices import DefaultQubit
  from pennylane.gradients import param_shift
  from pennylane import execute
  from pennylane.measurements import Shots
label_desc: Use image node_id 10 for calling the TestTorchExecuteIntegration obj's underlying member method code with example usage: obj.test_differentiable_expand(execute_kwargs, device, shots) and returns: execute, list