code: def execute(
      tapes,
      device,
      execute_fn,
      gradient_fn,
      gradient_kwargs,
      _n=1,
      max_diff=2,
      grad_on_execution=None,
  ):
      """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.
          grad_on_execution (bool): Whether the gradients should be computed on execution or not.
  
      Returns:
          list[list[tf.Tensor]]: A nested list of tape results. Each element in
          the returned list corresponds in order to the provided tapes.
      """
  
      all_params = []
      parameters = []
      lens = []
      trainable = []
      output_types = []
  
      # assumes all tapes have the same shot vector
      has_partitioned_shots = tapes[0].shots.has_partitioned_shots
      num_shot_copies = tapes[0].shots.num_copies or 1
  
      for tape in 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
          ]
          all_params += params
          trainable += (
              np.array(list(tape.trainable_params)) + sum(lens)
          ).tolist()
  
          lens.append(len(params))
  
          o_types = []
          for m in tape.measurements:
              if isinstance(m, SampleMP):
                  o_types.append(tf.int64)
              elif isinstance(m, StateMP):
                  o_types.append(tf.complex128)
              else:
                  o_types.append(tf.float64)
  
          output_types.extend(o_types * num_shot_copies)
      total_measurements = sum(len(tape.measurements) for tape in tapes)
  
      if grad_on_execution:
          output_types += [tf.float64] * len(trainable)
  
      output_types += [tf.int32] * (
          total_measurements * num_shot_copies
      )
  
      def _nest_params(all_params):
          count = 0
          params_unwrapped = []
  
          for s in lens:
              params_unwrapped.append(all_params[count : count + s])
              count += s
  
          return params_unwrapped
  
      def _forward(*all_params):
          params_unwrapped = _nest_params(all_params)
          output_sizes = []
  
          new_tapes = set_parameters_on_copy_and_unwrap(
              tapes, params_unwrapped, unwrap=False
          )
          # Forward pass: execute the tapes
          res, jacs = execute_fn(new_tapes, **gradient_kwargs)
  
          # flatten the results
          res = _flatten_nested_list(res)
  
          for i, r in enumerate(res):
              # convert output to TensorFlow tensors
              res[i] = _to_tensors(r)
              output_sizes.append(tf.size(res[i]))
  
          # flatten the jacobians
          if jacs:
              jacs = _flatten_nested_list(jacs)
              for i, jac in enumerate(jacs):
                  jacs[i] = tf.convert_to_tensor(jac)
          else:
              jacs = []
  
          return res + jacs + output_sizes
  
      @tf.custom_gradient
      def _execute(*all_params):  # pylint:disable=unused-argument
          res = tf.numpy_function(
              func=_forward, inp=all_params, Tout=output_types
          )
          output_sizes = res[-total_measurements * num_shot_copies :]
  
          if grad_on_execution:
              jacs = res[
                  total_measurements
                  * num_shot_copies : -total_measurements
                  * num_shot_copies
              ]
  
          res = res[: total_measurements * num_shot_copies]
  
          # reconstruct the nested structure of res
          res = _res_restructured(res, tapes)
  
          def grad_fn(*dy, **tfkwargs):
              """Returns the vector-Jacobian product with given
              parameter values and output gradient dy"""
  
              # whether the tapes contain multiple measurements
              multi_measurements = [
                  len(tape.measurements) > 1 for tape in tapes
              ]
              dy = list(dy[: total_measurements * num_shot_copies])
  
              if grad_on_execution:
                  # Jacobians were computed on the forward pass (grad_on_execution=True)
                  # No additional quantum evaluations needed; simply compute the VJPs directly.
  
                  def _backward(*args):
                      for tape in tapes:
                          for m in tape.measurements:
                              if m.numeric_type == complex:
                                  raise NotImplementedError(
                                      f"Tensorflow autograph only supports real valued measurements. Got {m}"
                                  )
  
                      dy = args[: total_measurements * num_shot_copies]
                      jacs = args[
                          total_measurements
                          * num_shot_copies : -len(tapes)
                      ]
                      multi_measurements = args[-len(tapes) :]
  
                      dy = _res_restructured(dy, tapes)
                      jacs = _jac_restructured(jacs, tapes)
  
                      return _compute_vjp(
                          dy,
                          jacs,
                          multi_measurements,
                          has_partitioned_shots,
                      )
  
                  vjps = tf.numpy_function(
                      func=_backward,
                      inp=dy + list(jacs) + multi_measurements,
                      Tout=[tf.float64] * len(parameters),
                  )
  
              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:
                          len_all_params = len(all_params)
  
                          def _backward(*all_params):
                              dy = all_params[len_all_params:]
                              all_params = all_params[:len_all_params]
                              params_unwrapped = _nest_params(
                                  all_params
                              )
  
                              dy = _res_restructured(dy, tapes)
  
                              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,
                              )
  
                              return processing_fn(
                                  execute_fn(vjp_tapes)[0]
                              )
  
                          vjps = tf.py_function(
                              func=_backward,
                              inp=list(all_params) + dy,
                              Tout=[tf.float64] * len(parameters),
                          )
  
                      else:
                          dy = _res_restructured(dy, tapes)
  
                          (
                              vjp_tapes,
                              processing_fn,
                          ) = qml.gradients.batch_vjp(
                              tapes,
                              dy,
                              gradient_fn,
                              reduction="append",
                              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,
                                  grad_on_execution=grad_on_execution,
                              ),
                              nums=output_sizes,
                          )
  
                          vjps = tf.unstack(
                              tf.concat(vjps, 0), num=len(parameters)
                          )
  
                  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.
                      len_all_params = len(all_params)
  
                      def _backward(*all_params):
                          dy = all_params[len_all_params : -len(tapes)]
                          multi_measurements = all_params[-len(tapes) :]
                          all_params = all_params[:len_all_params]
                          params_unwrapped = _nest_params(all_params)
  
                          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,
                          )
                          return vjps
  
                      vjps = tf.numpy_function(
                          func=_backward,
                          inp=list(all_params)
                          + dy
                          + multi_measurements,
                          Tout=[tf.float64] * len(parameters),
                      )
  
              if not isinstance(vjps, (list, tuple)):
                  vjps = [vjps]
  
              vjps = iter(vjps)
              vjps = [
                  next(vjps) if x in trainable else None
                  for x in range(len(all_params))
              ]
  
              variables = tfkwargs.get("variables")
              return (
                  (vjps, variables) if variables is not None else vjps
              )
  
          return res, grad_fn
  
      return _execute(*all_params)
  
imports: from functools import reduce
  import numpy
  import tensorflow
  import pennylane
  from pennylane.measurements import SampleMP, StateMP
  from .tensorflow import _compute_vjp, _jac_restructured, _res_restructured, _to_tensors, set_parameters_on_copy_and_unwrap
label_desc: Use image node_id 2 for calling a global function with example usage: execute(tapes, device, execute_fn, gradient_fn, gradient_kwargs, _n, max_diff, grad_on_execution) and returns: _execute, params_unwrapped, unknown, res,  grad_fn, unknown, _compute_vjp, vjps, processing_fn