code: def _register_jax_vjp():
      """
      Register the custom VJP for JAX
      """
      # pylint: disable=import-outside-toplevel
      import jax
  
      @jax.custom_vjp
      def _compute_fidelity_jax(dm0, dm1):
          return _compute_fidelity_vanilla(dm0, dm1)
  
      def _compute_fidelity_jax_fwd(dm0, dm1):
          fid = _compute_fidelity_jax(dm0, dm1)
          return fid, (dm0, dm1)
  
      def _compute_fidelity_jax_bwd(res, grad_out):
          dm0, dm1 = res
          return _compute_fidelity_grad(dm0, dm1, grad_out)
  
      _compute_fidelity_jax.defvjp(
          _compute_fidelity_jax_fwd, _compute_fidelity_jax_bwd
      )
      ar.register_function(
          "jax", "compute_fidelity", _compute_fidelity_jax
      )
  
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 11 for calling a global function with example usage: _register_jax_vjp() and returns: _compute_fidelity_vanilla, fid,  dm0,  dm1, _compute_fidelity_grad