code: def ctrl_decomp_bisect(
      target_operation: Operator,
      control_wires: Wires,
  ):
      """Decompose the controlled version of a target single-qubit operation
  
      Not backpropagation compatible (as currently implemented). Use only with numpy.
  
      Automatically selects the best algorithm based on the matrix (uses specialized more efficient
      algorithms if the matrix has a certain form, otherwise falls back to the general algorithm).
      These algorithms are defined in section 3.1 and 3.2 of
      `Vale et al. (2023) <https://arxiv.org/abs/2302.06377>`_.
  
      .. warning:: This method will add a global phase for target operations that do not
          belong to the SU(2) group.
  
      Args:
          target_operation (~.operation.Operator): the target operation to decompose
          control_wires (~.wires.Wires): the control wires of the operation
  
      Returns:
          list[Operation]: the decomposed operations
  
      Raises:
          ValueError: if ``target_operation`` is not a single-qubit operation
  
      **Example:**
  
      >>> op = qml.T(0) # uses OD algorithm
      >>> print(qml.draw(ctrl_decomp_bisect, wire_order=(0,1,2,3,4,5), show_matrices=False)(op, (1,2,3,4,5)))
      0: ─╭X──U(M0)─╭X──U(M0)†─╭X──U(M0)─╭X──U(M0)†─┤
      1: ─├●────────│──────────├●────────│──────────┤
      2: ─├●────────│──────────├●────────│──────────┤
      3: ─╰●────────│──────────╰●────────│──────────┤
      4: ───────────├●───────────────────├●─────────┤
      5: ───────────╰●───────────────────╰●─────────┤
      >>> op = qml.QubitUnitary([[0,1j],[1j,0]], 0) # uses MD algorithm
      >>> print(qml.draw(ctrl_decomp_bisect, wire_order=(0,1,2,3,4,5), show_matrices=False)(op, (1,2,3,4,5)))
      0: ──H─╭X──U(M0)─╭X──U(M0)†─╭X──U(M0)─╭X──U(M0)†──H─┤
      1: ────├●────────│──────────├●────────│─────────────┤
      2: ────├●────────│──────────├●────────│─────────────┤
      3: ────╰●────────│──────────╰●────────│─────────────┤
      4: ──────────────├●───────────────────├●────────────┤
      5: ──────────────╰●───────────────────╰●────────────┤
      >>> op = qml.Hadamard(0) # uses general algorithm
      >>> print(qml.draw(ctrl_decomp_bisect, wire_order=(0,1,2,3,4,5), show_matrices=False)(op, (1,2,3,4,5)))
      0: ──U(M0)─╭X──U(M1)†──U(M2)─╭X──U(M2)†─╭X──U(M2)─╭X──U(M2)†─╭X──U(M1)─╭X──U(M0)─┤
      1: ────────│─────────────────│──────────├●────────│──────────├●────────│─────────┤
      2: ────────│─────────────────│──────────├●────────│──────────├●────────│─────────┤
      3: ────────│─────────────────│──────────╰●────────│──────────╰●────────│─────────┤
      4: ────────├●────────────────├●───────────────────├●───────────────────├●────────┤
      5: ────────╰●────────────────╰●───────────────────╰●───────────────────╰●────────┤
  
      """
      if len(target_operation.wires) > 1:
          raise ValueError(
              "The target operation must be a single-qubit operation, instead "
              f"got {target_operation}."
          )
      target_matrix = target_operation.matrix()
      target_wire = target_operation.wires
  
      target_matrix = _convert_to_su2(target_matrix)
      target_matrix_imag = np.imag(target_matrix)
  
      if np.isclose(target_matrix_imag[1, 0], 0) and np.isclose(
          target_matrix_imag[0, 1], 0
      ):
          # Real off-diagonal specialized algorithm - 16n+O(1) CNOTs
          return _ctrl_decomp_bisect_od(
              target_matrix, target_wire, control_wires
          )
      if np.isclose(target_matrix_imag[0, 0], 0) and np.isclose(
          target_matrix_imag[1, 1], 0
      ):
          # Real main-diagonal specialized algorithm - 16n+O(1) CNOTs
          return _ctrl_decomp_bisect_md(
              target_matrix, target_wire, control_wires
          )
      # General algorithm - 20n+O(1) CNOTs
      return _ctrl_decomp_bisect_general(
          target_matrix, target_wire, control_wires
      )
  
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 10 for calling a global function with example usage: ctrl_decomp_bisect(target_operation, control_wires) and returns: _ctrl_decomp_bisect_general, _ctrl_decomp_bisect_od, _ctrl_decomp_bisect_md