code: def _compute_fidelity_vanilla(density_matrix0, density_matrix1):
      r"""Compute the fidelity for two density matrices with the same number of wires.
  
      .. math::
              F( \rho , \sigma ) = -\text{Tr}( \sqrt{\sqrt{\rho} \sigma \sqrt{\rho}})^2
      """
      # Implementation in single dispatches (sqrt(rho))
      sqrt_mat = qml.math.sqrt_matrix(density_matrix0)
  
      # sqrt(rho) * sigma * sqrt(rho)
      sqrt_mat_sqrt = sqrt_mat @ density_matrix1 @ sqrt_mat
  
      # extract eigenvalues
      evs = qml.math.eigvalsh(sqrt_mat_sqrt)
      evs = qml.math.real(evs)
      evs = qml.math.where(evs > 0.0, evs, 0)
  
      trace = (qml.math.sum(qml.math.sqrt(evs), -1)) ** 2
  
      return trace
  
file_path: pennylane/pennylane/math/fidelity.py
imports: from functools import lru_cache
  import autograd
  import autoray
  import pennylane
  from .utils import cast
  from .quantum import _check_density_matrix, _check_state_vector
label_desc: Use image node_id 4 for calling a global function with example usage: _compute_fidelity_vanilla(density_matrix0, density_matrix1) and returns: trace