text: # Copyright 2018-2021 Xanadu Quantum Technologies Inc.
  
  # Licensed under the Apache License, Version 2.0 (the "License");
  # you may not use this file except in compliance with the License.
  # You may obtain a copy of the License at
  
  #     http://www.apache.org/licenses/LICENSE-2.0
  
  # Unless required by applicable law or agreed to in writing, software
  # distributed under the License is distributed on an "AS IS" BASIS,
  # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  # See the License for the specific language governing permissions and
  # limitations under the License.
  """
  This module contains functions for adding the TensorFlow interface
  to a PennyLane Device class.
  """
  # pylint: disable=too-many-arguments,too-many-branches
  import numpy as np
  import tensorflow as tf
  from tensorflow.python.eager import context
  
  import pennylane as qml
  
  
  def _compute_vjp(dy, jacs):
      # compute the vector-Jacobian product dy @ jac
      # for a list of dy's and Jacobian matrices.
      vjps = []
  
      for d, jac in zip(dy, jacs):
          vjp = qml.gradients.compute_vjp(d, jac)
  
          if not context.executing_eagerly():
              vjp = qml.math.unstack(vjp)
  
          vjps.extend(vjp)
  
      return vjps
  
  
  def execute(tapes, device, execute_fn, gradient_fn, gradient_kwargs, _n=1, max_diff=2, mode=None):
      """Execute a batch of tapes with TensorFlow parameters on a device.
  
      Args:
          tapes (Sequence[.QuantumTape]): batch of tapes to execute
          device (.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.
          mode (str): Whether the gradients should be computed on the forward
              pass (``forward``) or the backward pass (``backward``).
  
      Returns:
          list[list[tf.Tensor]]: A nested list of tape results. Each element in
          the returned list corresponds in order to the provided tapes.
      """
      # pylint: disable=unused-argument
  
      parameters = []
      params_unwrapped = []
  
      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]
          )
  
      with qml.tape.Unwrap(*tapes):
          # Forward pass: execute the tapes
          res, jacs = execute_fn(tapes, **gradient_kwargs)
  
      for i, tape in enumerate(tapes):
          # convert output to TensorFlow tensors
  
          if isinstance(res[i], np.ndarray):
              # For backwards compatibility, we flatten ragged tape outputs
              # when there is no sampling
              r = np.hstack(res[i]) if res[i].dtype == np.dtype("object") else res[i]
              res[i] = tf.convert_to_tensor(r)
  
          elif isinstance(res[i], tuple):
              res[i] = tuple(tf.convert_to_tensor(r) for r in res[i])
  
          else:
              res[i] = tf.convert_to_tensor(qml.math.toarray(res[i]))
  
      @tf.custom_gradient
      def _execute(*parameters):  # pylint:disable=unused-argument
          def grad_fn(*dy, **tfkwargs):
              """Returns the vector-Jacobian product with given
              parameter values and output gradient dy"""
  
              dy = [qml.math.T(d) for d in dy]
  
              if jacs:
                  # Jacobians were computed on the forward pass (mode="forward")
                  # No additional quantum evaluations needed; simply compute the VJPs directly.
                  vjps = _compute_vjp(dy, jacs)
  
              else:
                  # Need to compute the Jacobians on the backward pass (accumulation="backward")
  
                  if isinstance(gradient_fn, qml.gradients.gradient_transform):
                      # Gradient function is a gradient transform.
  
                      # Generate and execute the required gradient tapes
                      if _n == max_diff or not context.executing_eagerly():
  
                          with qml.tape.Unwrap(*tapes, params=params_unwrapped):
                              vjp_tapes, processing_fn = qml.gradients.batch_vjp(
                                  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.
                      with qml.tape.Unwrap(*tapes, params=params_unwrapped):
                          vjps = _compute_vjp(dy, gradient_fn(tapes, **gradient_kwargs))
  
              variables = tfkwargs.get("variables", None)
              return (vjps, variables) if variables is not None else vjps
  
          return res, grad_fn
  
      return _execute(*parameters)
  