code: def _reduced_row_echelon(binary_matrix):
      r"""Returns the reduced row echelon form (RREF) of a matrix in a binary finite field :math:`\mathbb{Z}_2`.
  
      Args:
          binary_matrix (array[int]): binary matrix representation of the Hamiltonian
      Returns:
          array[int]: reduced row-echelon form of the given `binary_matrix`
  
      **Example**
  
      >>> binary_matrix = np.array([[1, 0, 0, 0, 0, 1, 0, 0],
      ...                           [1, 0, 1, 0, 0, 0, 1, 0],
      ...                           [0, 0, 0, 1, 1, 0, 0, 1]])
      >>> _reduced_row_echelon(binary_matrix)
      array([[1, 0, 0, 0, 0, 1, 0, 0],
             [0, 0, 1, 0, 0, 1, 1, 0],
             [0, 0, 0, 1, 1, 0, 0, 1]])
      """
      rref_mat = binary_matrix.copy()
      shape = rref_mat.shape
      icol = 0
  
      for irow in range(shape[0]):
          while icol < shape[1] and not rref_mat[irow][icol]:
              # get the nonzero indices in the remainder of column icol
              non_zero_idx = rref_mat[irow:, icol].nonzero()[0]
  
              if (
                  len(non_zero_idx) == 0
              ):  # if remainder of column icol is all zero
                  icol += 1
              else:
                  # find value and index of largest element in remainder of column icol
                  krow = irow + non_zero_idx[0]
  
                  # swap rows krow and irow
                  rref_mat[irow, icol:], rref_mat[krow, icol:] = (
                      rref_mat[krow, icol:].copy(),
                      rref_mat[irow, icol:].copy(),
                  )
          if icol < shape[1] and rref_mat[irow][icol]:
              # store remainder right hand side columns of the pivot row irow
              rpvt_cols = rref_mat[irow, icol:].copy()
  
              # get the column icol and set its irow element to 0 to avoid XORing pivot row with itself
              currcol = rref_mat[:, icol].copy()
              currcol[irow] = 0
  
              # XOR the right hand side of the pivot row irow with all of the other rows
              rref_mat[:, icol:] ^= np.outer(currcol, rpvt_cols)
              icol += 1
  
      return rref_mat.astype(int)
  
imports: import functools
  import itertools
  import numpy
  import scipy
  import pennylane
  from pennylane.operation import active_new_opmath
  from pennylane.pauli import PauliSentence, PauliWord, pauli_sentence, simplify
  from pennylane.pauli.utils import _binary_matrix_from_pws
  from pennylane.wires import Wires
label_desc: Use image node_id 1 for calling a global function with example usage: _reduced_row_echelon(binary_matrix) and returns: rref_mat