code: def pauli_decompose(
      H,
      hide_identity=False,
      wire_order=None,
      pauli=False,
      check_hermitian=True,
  ) -> Union[Hamiltonian, PauliSentence]:
      r"""Decomposes a Hermitian matrix into a linear combination of Pauli operators.
  
      Args:
          H (tensor_like[complex]): a Hermitian matrix of dimension :math:`2^n\times 2^n`.
          hide_identity (bool): does not include the Identity observable within
              the tensor products of the decomposition if ``True``.
          wire_order (list[Union[int, str]]): the ordered list of wires with respect
              to which the operator is represented as a matrix.
          pauli (bool): return a :class:`~.PauliSentence` instance if ``True``.
          check_hermitian (bool): check if the provided matrix is Hermitian if ``True``.
  
      Returns:
          Union[~.Hamiltonian, ~.PauliSentence]: the matrix decomposed as a linear combination
          of Pauli operators, returned either as a :class:`~.Hamiltonian` or :class:`~.PauliSentence`
          instance.
  
      **Example:**
  
      We can use this function to compute the Pauli operator decomposition of an arbitrary Hermitian
      matrix:
  
      >>> A = np.array(
      ... [[-2, -2+1j, -2, -2], [-2-1j,  0,  0, -1], [-2,  0, -2, -1], [-2, -1, -1,  0]])
      >>> H = qml.pauli_decompose(A)
      >>> print(H)
      (-1.5) [I0 X1]
      + (-1.5) [X0 I1]
      + (-1.0) [I0 I1]
      + (-1.0) [I0 Z1]
      + (-1.0) [X0 X1]
      + (-0.5) [I0 Y1]
      + (-0.5) [X0 Z1]
      + (-0.5) [Z0 X1]
      + (-0.5) [Z0 Y1]
      + (1.0) [Y0 Y1]
  
      We can return a :class:`~.PauliSentence` instance by using the keyword argument ``pauli=True``:
  
      >>> ps = qml.pauli_decompose(A, pauli=True)
      >>> print(ps)
      -1.0 * I
      + -1.5 * X(1)
      + -0.5 * Y(1)
      + -1.0 * Z(1)
      + -1.5 * X(0)
      + -1.0 * X(0) @ X(1)
      + -0.5 * X(0) @ Z(1)
      + 1.0 * Y(0) @ Y(1)
      + -0.5 * Z(0) @ X(1)
      + -0.5 * Z(0) @ Y(1)
  
      By default the wires are numbered [0, 1, ..., n], but we can also set custom wires using the
      ``wire_order`` argument:
  
      >>> ps = qml.pauli_decompose(A, pauli=True, wire_order=['a', 'b'])
      >>> print(ps)
      -1.0 * I
      + -1.5 * X(b)
      + -0.5 * Y(b)
      + -1.0 * Z(b)
      + -1.5 * X(a)
      + -1.0 * X(a) @ X(b)
      + -0.5 * X(a) @ Z(b)
      + 1.0 * Y(a) @ Y(b)
      + -0.5 * Z(a) @ X(b)
      + -0.5 * Z(a) @ Y(b)
  
      .. details::
          :title: Theory
          :href: theory
  
          This method internally uses a generalized decomposition routine to convert the matrix to a
          weighted sum of Pauli words acting on :math:`n` qubits in time :math:`O(n 4^n)`. The input
          matrix is written as a quantum state in the computational basis following the
          `channel-state duality <https://en.wikipedia.org/wiki/Channel-state_duality>`_.
          A Bell basis transformation is then performed using the
          `Walsh-Hadamard transform <https://en.wikipedia.org/wiki/Hadamard_transform>`_, after which
          coefficients for each of the :math:`4^n` Pauli words are computed while accounting for the
          phase from each ``PauliY`` term occurring in the word.
  
      """
      shape = qml.math.shape(H)
      n = int(qml.math.log2(shape[0]))
      N = 2**n
  
      if check_hermitian:
          if shape != (N, N):
              raise ValueError(
                  "The matrix should have shape (2**n, 2**n), for any qubit number n>=1"
              )
  
          if not qml.math.allclose(
              H, qml.math.conj(qml.math.transpose(H))
          ):
              raise ValueError("The matrix is not Hermitian")
  
      coeffs, obs = _generalized_pauli_decompose(
          H,
          hide_identity=hide_identity,
          wire_order=wire_order,
          pauli=pauli,
          padding=True,
      )
  
      if check_hermitian:
          coeffs = qml.math.real(coeffs)
  
      if pauli:
          return PauliSentence(
              {
                  PauliWord({w: o for o, w in obs_n_wires}): coeff
                  for coeff, obs_n_wires in zip(coeffs, obs)
              }
          )
  
      return Hamiltonian(coeffs, obs)
  
imports: from functools import reduce, singledispatch
  from itertools import product
  from operator import matmul
  from typing import Union, Tuple
  import pennylane
  from pennylane.operation import Tensor
  from pennylane.ops import Hamiltonian, Identity, PauliX, PauliY, PauliZ, Prod, SProd, Sum
  from pennylane.ops.qubit.matrix_ops import _walsh_hadamard_transform
  from .pauli_arithmetic import I, PauliSentence, PauliWord, X, Y, Z, op_map
  from .utils import is_pauli_word
label_desc: Use image node_id 2 for calling a global function with example usage: pauli_decompose(H, hide_identity, wire_order, pauli, check_hermitian) and returns: Hamiltonian, PauliSentence