code: def estimate_error(coeffs, variances=None, shots=1000):
      r"""Estimate the error in computing an expectation value with a given number of measurements.
  
      See also :func:`estimate_shots`.
  
      Args:
          coeffs (list[tensor_like]): list of coefficient groups
          variances (list[float]): variances of the Pauli word groups
          shots (int): the number of measurements
  
      Returns:
          float: target error in computing the expectation value
  
      **Example**
  
      >>> coeffs = [np.array([-0.32707061, 0.7896887]), np.array([0.18121046])]
      >>> qml.resource.estimate_error(coeffs, shots=100000)
      0.00327597
  
      .. details::
          :title: Theory
  
          An estimation for the error :math:`\epsilon` in predicting the expectation
          value of an observable :math:`H = \sum_i A_i` with :math:`A = \sum_j c_j O_j` representing a
          linear combination of Pauli words can be obtained following Eq. (34) of
          [`PRX Quantum 2, 040320 (2021) <https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.2.040320>`_]
          as
  
          .. math::
  
              \epsilon = \frac{\sum_i \sqrt{\text{Var}(A_i)}}{\sqrt{M}},
  
          with :math:`M` and :math:`\text{Var}(A)` denoting the number of measurements and the
          variance in computing :math:`\left \langle A \right \rangle`, respectively. It has been
          shown in Eq. (10) of
          [`arXiv:2201.01471v3 <https://arxiv.org/abs/2201.01471v3>`_] that the variances can be
          computed from the covariances between the Pauli words as
  
          .. math::
  
              \text{Var}(A_i) = \sum_{jk} c_j c_k \text{Cov}(O_j, O_k),
  
          where
  
          .. math::
  
              \text{Cov}(O_j, O_k) = \left \langle O_j O_k \right \rangle - \left \langle O_j \right \rangle \left \langle O_k \right \rangle.
  
          The values of :math:`\text{Cov}(O_j, O_k)` are not known a priori and should be either
          computed from affordable classical methods, such as the configuration interaction with
          singles and doubles (CISD), or approximated with other methods. If the variances are not
          provided to the function as input, they will be approximated following Eqs. (6-7) of
          [`Phys. Rev. Research 4, 033154, 2022 <https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.4.033154>`_]
          by assuming
          :math:`\text{Cov}(O_j, O_k) =0` for :math:`j \neq k` and using :math:`\text{Var}(O_i) \leq 1`
          from
  
          .. math::
  
              \text{Var}(O_i) = \left \langle O_i^2 \right \rangle - \left \langle O_i \right \rangle^2 = 1 - \left \langle O_i \right \rangle^2.
  
          This approximation gives
  
          .. math::
  
              \epsilon \approx \frac{\sum_i \sqrt{\sum_j c_{ij}^2}}{\sqrt{M}},
  
          where :math:`i` and :math:`j` run over the observable groups and the Pauli words inside the
          group, respectively.
      """
      if variances:
          return np.sum(np.sqrt(variances)) / np.sqrt(shots)
  
      group_sum = [np.sum(coeff**2) for coeff in coeffs]
      return np.sum(np.sqrt(group_sum)) / np.sqrt(shots)
  
label_desc: Use image node_id 2 for calling a global function with example usage: estimate_error(coeffs, variances, shots) and returns: unknown, unknown