code: def expval_hessian_param_shift(
      tape, argnum, method_map, diagonal_shifts, off_diagonal_shifts, f0
  ):
      r"""Generate the Hessian tapes that are used in the computation of the second derivative of a
      quantum tape, using analytical parameter-shift rules to do so exactly. Also define a
      post-processing function to combine the results of evaluating the tapes into the Hessian.
  
      Args:
          tape (.QuantumTape): quantum tape to differentiate
          argnum (array_like[bool]): Parameter indices to differentiate
              with respect to, in form of a two-dimensional boolean ``array_like`` mask.
          method_map (dict[int, string]): The differentiation method to use for each trainable
              parameter. Can be "A" or "0", where "A" is the analytical parameter shift rule
              and "0" indicates a 0 derivative (the parameter does not affect the tape's output).
          diagonal_shifts (list[tuple[int or float]]): List containing tuples of shift values
              for the Hessian diagonal.
              If provided, one tuple of shifts should be given per trainable parameter
              and the tuple length should match the number of frequencies for that parameter.
              If unspecified, equidistant shifts are used.
          off_diagonal_shifts (list[tuple[int or float]]): List containing tuples of shift
              values for the off-diagonal entries of the Hessian.
              If provided, one tuple of shifts should be given per trainable parameter
              and the tuple should match the number of frequencies for that parameter.
              The combination of shifts into bivariate shifts is performed automatically.
              If unspecified, equidistant shifts are used.
          f0 (tensor_like[float] or None): Output of the evaluated input tape. If provided,
              and the Hessian tapes include the original input tape, the 'f0' value is used
              instead of evaluating the input tape, reducing the number of device invocations.
  
      Returns:
          tuple[list[QuantumTape], function]: A tuple containing a
          list of generated tapes, together with a post-processing
          function to be applied to the results of the evaluated tapes
          in order to obtain the Hessian matrix.
      """
      # pylint: disable=too-many-arguments, too-many-statements
      h_dim = tape.num_params
  
      unshifted_coeffs = {}
      # Marks whether we will need to add the unshifted tape to all Hessian tapes.
      add_unshifted = f0 is None
  
      # Assemble all univariate recipes for the diagonal and as partial components for the
      # off-diagonal entries.
      diag_recipes, partial_offdiag_recipes = _collect_recipes(
          tape, argnum, method_map, diagonal_shifts, off_diagonal_shifts
      )
  
      hessian_tapes = []
      hessian_coeffs = []
      for i, j in it.combinations_with_replacement(range(h_dim), r=2):
          if not argnum[i, j]:
              # The (i, j) entry of the Hessian is not to be computed
              hessian_coeffs.append(None)
              continue
  
          if i == j:
              (
                  add_unshifted,
                  unshifted_coeffs[(i, i)],
              ) = _generate_diag_tapes(
                  tape,
                  i,
                  diag_recipes,
                  add_unshifted,
                  hessian_tapes,
                  hessian_coeffs,
              )
          else:
              # Create tapes and coefficients for the off-diagonal entry by combining
              # the two univariate first-order derivative recipes.
              (
                  add_unshifted,
                  unshifted_coeffs[(i, j)],
              ) = _generate_offdiag_tapes(
                  tape,
                  (i, j),
                  partial_offdiag_recipes,
                  add_unshifted,
                  hessian_tapes,
                  hessian_coeffs,
              )
      unshifted_coeffs = {
          key: val
          for key, val in unshifted_coeffs.items()
          if val is not None
      }
  
      def processing_fn(results):
          num_measurements = len(tape.measurements)
          if num_measurements == 1:
              results = tuple((r,) for r in results)
  
          # the hessian should have a nested tuple structure with shape
          #     (num_measurements, num_params, num_params, *output_dims)
          # first accumulate all elements of the hessian into a list
          hessians = []
  
          # Keep track of tape results already consumed. Start with 1 if the unshifted tape was
          # included in the tapes for the Hessian.
          start = 1 if unshifted_coeffs and f0 is None else 0
  
          # Results of the unshifted tape.
          r0 = results[0] if start == 1 else f0
  
          for i, j in it.product(range(h_dim), repeat=2):
              if j < i:
                  hessians.append(hessians[j * h_dim + i])
                  continue
  
              k = i * h_dim + j - i * (i + 1) // 2
              coeffs = hessian_coeffs[k]
  
              if coeffs is None or len(coeffs) == 0:
                  hessian = []
                  for m in range(num_measurements):
                      hessian.append(qml.math.zeros_like(results[0][m]))
  
                  hessians.append(tuple(hessian))
                  continue
  
              res = results[start : start + len(coeffs)]
              start = start + len(coeffs)
  
              unshifted_coeff = unshifted_coeffs.get((i, j), None)
              hessian = []
              for m in range(num_measurements):
                  # the res array has shape (num_tapes, num_measurements, *output_dims)
  
                  # first collect all tape results for the individual measurements
                  measure_res = qml.math.stack([r[m] for r in res])
  
                  # then compute the hessian via parameter-shift
                  coeffs = qml.math.convert_like(coeffs, measure_res)
                  hess = qml.math.tensordot(
                      measure_res, coeffs, [[0], [0]]
                  )
  
                  if unshifted_coeff is not None:
                      hess = hess + unshifted_coeff * r0[m]
  
                  hess = qml.math.array(hess, like=measure_res)
                  hessian.append(hess)
  
              hessians.append(tuple(hessian))
  
          # at this point, the hessian has shape (num_params ** 2, num_measurements, *output_dims)
  
          # swap the first two axes, so that the hessian now has
          # shape (num_measurements, num_params ** 2, *output_dims)
          hessians = tuple(
              tuple(h[i] for h in hessians)
              for i in range(num_measurements)
          )
  
          # replace the axis of size num_params ** 2 with two axes of size num_params;
          # that is, reshape the hessian to have shape (num_measurements, num_params, num_params, *output_dims)
          hessians = tuple(
              tuple(
                  tuple(hess[i * h_dim + j] for j in range(h_dim))
                  for i in range(h_dim)
              )
              for hess in hessians
          )
  
          # squeeze every axis with size 1
          if h_dim == 1:
              hessians = tuple(hess[0][0] for hess in hessians)
  
          if num_measurements == 1:
              hessians = hessians[0]
  
          return hessians
  
      return hessian_tapes, processing_fn
  
imports: import itertools
  import warnings
  from functools import partial
  from typing import Sequence, Callable
  import numpy
  import pennylane
  from pennylane.measurements import ProbabilityMP, StateMP, VarianceMP
  from pennylane.transforms import transform
  from .general_shift_rules import _combine_shift_rules, generate_multishifted_tapes, generate_shifted_tapes
  from .gradient_transform import find_and_validate_gradient_methods
  from .parameter_shift import _get_operation_recipe
  from .hessian_transform import _process_jacs
label_desc: Use image node_id 7 for calling a global function with example usage: expval_hessian_param_shift(tape, argnum, method_map, diagonal_shifts, off_diagonal_shifts, f0) and returns: hessian_tapes,  processing_fn, hessians