code: def _ctrl_decomp_bisect_md(
      u: np.ndarray,
      target_wire: Wires,
      control_wires: Wires,
  ):
      """Decompose the controlled version of a target single-qubit operation
  
      Not backpropagation compatible (as currently implemented). Use only with numpy.
  
      This function decomposes a controlled single-qubit target operation using the
      decomposition defined in section 3.1, Theorem 2 of
      `Vale et al. (2023) <https://arxiv.org/abs/2302.06377>`_.
  
      The target operation's matrix must have a real main-diagonal for this specialized method to work.
  
      .. warning:: This method will add a global phase for target operations that do not
          belong to the SU(2) group.
  
      Args:
          u (np.ndarray): the target operation's matrix
          target_wire (~.wires.Wires): the target wire of the controlled operation
          control_wires (~.wires.Wires): the control wires of the operation
  
      Returns:
          list[Operation]: the decomposed operations
  
      Raises:
          ValueError: if ``u`` does not have a real main-diagonal
  
      """
      ui = np.imag(u)
      if not np.isclose(ui[0, 0], 0) or not np.isclose(ui[1, 1], 0):
          raise ValueError(
              f"Target operation's matrix must have real main-diagonal, but it is {u}"
          )
  
      h_matrix = qml.Hadamard.compute_matrix()
      mod_u = h_matrix @ u @ h_matrix
  
      decomposition = [qml.Hadamard(target_wire)]
      decomposition += _ctrl_decomp_bisect_od(
          mod_u, target_wire, control_wires
      )
      decomposition.append(qml.Hadamard(target_wire))
  
      return decomposition
  
file_path: pennylane/pennylane/ops/op_math/controlled_decompositions.py
imports: from copy import copy
  import numpy
  import numpy.linalg
  import pennylane
  from pennylane.operation import Operator
  from pennylane.wires import Wires
  from pennylane import math
label_desc: Use image node_id 8 for calling a global function with example usage: _ctrl_decomp_bisect_md(u, target_wire, control_wires) and returns: decomposition