code: def optimal_sector(qubit_op, generators, active_electrons):
      r"""Get the optimal sector which contains the ground state.
  
      To obtain the optimal sector, we need to choose the right eigenvalues for the symmetry generators :math:`\bm{\tau}`.
      We can do so by using the following relation between the Pauli-Z qubit operator and the occupation number under a
      Jordan-Wigner transform.
  
      .. math::
  
          \sigma_{i}^{z} = I - 2a_{i}^{\dagger}a_{i}
  
      According to this relation, the occupied and unoccupied fermionic modes correspond to the -1 and +1 eigenvalues of
      the Pauli-Z operator, respectively. Since all of the generators :math:`\bm{\tau}` consist only of :math:`I` and
      Pauli-Z operators, the correct eigenvalue for each :math:`\tau` operator can be simply obtained by applying it on
      the reference Hartree-Fock (HF) state, and looking at the overlap between the wires on which the Pauli-Z operators
      act and the wires that correspond to occupied orbitals in the HF state.
  
      Args:
          qubit_op (Operator): Hamiltonian for which symmetries are being generated
          generators (list[Operator]): list of symmetry generators for the Hamiltonian
          active_electrons (int): The number of active electrons in the system
  
      Returns:
          list[int]: eigenvalues corresponding to the optimal sector which contains the ground state
  
      **Example**
  
      >>> symbols = ["H", "H"]
      >>> geometry = np.array([[0.0, 0.0, -0.69440367], [0.0, 0.0, 0.69440367]])
      >>> H, qubits = qml.qchem.molecular_hamiltonian(symbols, geometry)
      >>> generators = qml.qchem.symmetry_generators(H)
      >>> qml.qchem.optimal_sector(H, generators, 2)
          [1, -1, -1]
      """
  
      if active_electrons < 1:
          raise ValueError(
              f"The number of active electrons must be greater than zero;"
              f"got 'electrons'={active_electrons}"
          )
  
      num_orbitals = len(qubit_op.wires)
  
      if active_electrons > num_orbitals:
          raise ValueError(
              f"Number of active orbitals cannot be smaller than number of active electrons;"
              f" got 'orbitals'={num_orbitals} < 'electrons'={active_electrons}."
          )
  
      hf_str = np.where(
          np.arange(num_orbitals) < active_electrons, 1, 0
      )
  
      perm = []
      for tau in generators:
          symmstr = np.array(
              [1 if wire in tau.wires else 0 for wire in qubit_op.wires]
          )
          coeff = (
              -1
              if np.logical_xor.reduce(np.logical_and(symmstr, hf_str))
              else 1
          )
          perm.append(coeff)
  
      return perm
  
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 9 for calling a global function with example usage: optimal_sector(qubit_op, generators, active_electrons) and returns: perm