code: def execute(
      tapes,
      device,
      execute_fn,
      gradient_fn,
      gradient_kwargs,
      _n=1,
      max_diff=2,
  ):
      """Execute a batch of tapes with TensorFlow parameters on a device.
  
      Args:
          tapes (Sequence[.QuantumTape]): batch of tapes to execute
          device (pennylane.Device): Device to use to execute the batch of tapes.
              If the device does not provide a ``batch_execute`` method,
              by default the tapes will be executed in serial.
          execute_fn (callable): The execution function used to execute the tapes
              during the forward pass. This function must return a tuple ``(results, jacobians)``.
              If ``jacobians`` is an empty list, then ``gradient_fn`` is used to
              compute the gradients during the backwards pass.
          gradient_kwargs (dict): dictionary of keyword arguments to pass when
              determining the gradients of tapes
          gradient_fn (callable): the gradient function to use to compute quantum gradients
          _n (int): a positive integer used to track nesting of derivatives, for example
              if the nth-order derivative is requested.
          max_diff (int): If ``gradient_fn`` is a gradient transform, this option specifies
              the maximum number of derivatives to support. Increasing this value allows
              for higher order derivatives to be extracted, at the cost of additional
              (classical) computational overhead during the backwards pass.
  
      Returns:
          list[list[tf.Tensor]]: A nested list of tape results. Each element in
          the returned list corresponds in order to the provided tapes.
      """
      if logger.isEnabledFor(logging.DEBUG):
          logger.debug(
              "Entry with args=(tapes=%s, jacs=%s, execute_fn=%s, gradient_fn=%s, gradient_kwargs=%s, _n=%s, max_diff=%s) called by=%s",
              tapes,
              repr(device),
              execute_fn
              if not (
                  logger.isEnabledFor(qml.logging.TRACE)
                  and inspect.isfunction(execute_fn)
              )
              else "\n" + inspect.getsource(execute_fn) + "\n",
              gradient_fn
              if not (
                  logger.isEnabledFor(qml.logging.TRACE)
                  and inspect.isfunction(gradient_fn)
              )
              else "\n" + inspect.getsource(gradient_fn) + "\n",
              gradient_kwargs,
              _n,
              max_diff,
              "::L".join(
                  str(i)
                  for i in inspect.getouterframes(
                      inspect.currentframe(), 2
                  )[1][1:3]
              ),
          )
  
      # pylint: disable=unused-argument
  
      parameters = []
      params_unwrapped = []
  
      # assumes all tapes have the same shot vector
      has_partitioned_shots = tapes[0].shots.has_partitioned_shots
  
      for i, tape in enumerate(tapes):
          # store the trainable parameters
          params = tape.get_parameters(trainable_only=False)
          tape.trainable_params = qml.math.get_trainable_indices(params)
  
          parameters += [
              p
              for i, p in enumerate(params)
              if i in tape.trainable_params
          ]
  
          # store all unwrapped parameters
          params_unwrapped.append(
              [
                  i.numpy()
                  if isinstance(i, (tf.Variable, tf.Tensor))
                  else i
                  for i in params
              ]
          )
      res, jacs = execute_fn(tapes, **gradient_kwargs)
      res = tuple(
          _to_tensors(r) for r in res
      )  # convert output to TensorFlow tensors
  
      @tf.custom_gradient
      def _execute(*parameters):  # pylint:disable=unused-argument
          if logger.isEnabledFor(logging.DEBUG):
              logger.debug(
                  "Entry with args=(parameters=%s) called by=%s",
                  parameters,
                  "::L".join(
                      str(i)
                      for i in inspect.getouterframes(
                          inspect.currentframe(), 2
                      )[1][1:3]
                  ),
              )
  
          def grad_fn(*dy, **tfkwargs):
              """Returns the vector-Jacobian product with given
              parameter values and output gradient dy"""
              if logger.isEnabledFor(logging.DEBUG):
                  logger.debug(
                      "Entry with args=(dy=%s, tfkwargs=%s) called by=%s",
                      dy,
                      tfkwargs,
                      "::L".join(
                          str(i)
                          for i in inspect.getouterframes(
                              inspect.currentframe(), 2
                          )[1][1:3]
                      ),
                  )
  
              # whether the tapes contain multiple measurements
              multi_measurements = [
                  len(tape.measurements) > 1 for tape in tapes
              ]
  
              # TF obeys the dL/dz_conj convention instead of the
              # dL/dz convention of PennyLane, autograd and jax. This converts between the formats
              dy = _recursive_conj(dy)
  
              # reconstruct the nested structure of dy
              dy = _res_restructured(dy, tapes)
  
              if jacs:
                  # Jacobians were computed on execution
                  # No additional quantum evaluations needed; simply compute the VJPs directly.
                  vjps = _compute_vjp(
                      dy,
                      jacs,
                      multi_measurements,
                      has_partitioned_shots,
                  )
  
              else:
                  # Need to compute the Jacobians on the backward pass (accumulation="backward")
  
                  if isinstance(
                      gradient_fn,
                      qml.transforms.core.TransformDispatcher,
                  ):
                      # Gradient function is a gradient transform.
  
                      # Generate and execute the required gradient tapes
                      if (
                          _n == max_diff
                          or not context.executing_eagerly()
                      ):
                          new_tapes = set_parameters_on_copy_and_unwrap(
                              tapes, params_unwrapped, unwrap=False
                          )
                          (
                              vjp_tapes,
                              processing_fn,
                          ) = qml.gradients.batch_vjp(
                              new_tapes,
                              dy,
                              gradient_fn,
                              reduction=lambda vjps, x: vjps.extend(
                                  qml.math.unstack(x)
                              ),
                              gradient_kwargs=gradient_kwargs,
                          )
  
                          vjps = processing_fn(execute_fn(vjp_tapes)[0])
  
                      else:
                          (
                              vjp_tapes,
                              processing_fn,
                          ) = qml.gradients.batch_vjp(
                              tapes,
                              dy,
                              gradient_fn,
                              reduction="extend",
                              gradient_kwargs=gradient_kwargs,
                          )
  
                          # This is where the magic happens. Note that we call ``execute``.
                          # This recursion, coupled with the fact that the gradient transforms
                          # are differentiable, allows for arbitrary order differentiation.
                          vjps = processing_fn(
                              execute(
                                  vjp_tapes,
                                  device,
                                  execute_fn,
                                  gradient_fn,
                                  gradient_kwargs,
                                  _n=_n + 1,
                                  max_diff=max_diff,
                              )
                          )
  
                  else:
                      # Gradient function is not a gradient transform
                      # (e.g., it might be a device method).
                      # Note that unlike the previous branch:
                      #
                      # - there is no recursion here
                      # - gradient_fn is not differentiable
                      #
                      # so we cannot support higher-order derivatives.
                      new_tapes = set_parameters_on_copy_and_unwrap(
                          tapes, params_unwrapped, unwrap=False
                      )
                      jac = gradient_fn(new_tapes, **gradient_kwargs)
  
                      vjps = _compute_vjp(
                          dy,
                          jac,
                          multi_measurements,
                          has_partitioned_shots,
                      )
  
              # filter out untrainable parameters if they happen to appear in the vjp
              vjps = [
                  vjp for vjp in vjps if 0 not in qml.math.shape(vjp)
              ]
  
              variables = tfkwargs.get("variables")
              return (
                  (vjps, variables) if variables is not None else vjps
              )
  
          return res, grad_fn
  
      return _execute(*parameters)
  
file_path: pennylane/pennylane/workflow/interfaces/tensorflow.py
imports: import inspect
  import logging
  import tensorflow
  from tensorflow.python.eager import context
  import pennylane
  from pennylane.measurements import Shots
  from pennylane.transforms import convert_to_numpy_parameters
label_desc: Use image node_id 8 for calling a global function with example usage: execute(tapes, device, execute_fn, gradient_fn, gradient_kwargs, _n, max_diff) and returns: _execute, res,  grad_fn, unknown