code: def single_qubit_fusion(
      tape: QuantumTape, atol=1e-8, exclude_gates=None
  ) -> (Sequence[QuantumTape], Callable):
      r"""Quantum function transform to fuse together groups of single-qubit
      operations into a general single-qubit unitary operation (:class:`~.Rot`).
  
      Fusion is performed only between gates that implement the property
      ``single_qubit_rot_angles``. Any sequence of two or more single-qubit gates
      (on the same qubit) with that property defined will be fused into one ``Rot``.
  
      Args:
          tape (QNode or QuantumTape or Callable): A quantum circuit.
          atol (float): An absolute tolerance for which to apply a rotation after
              fusion. After fusion of gates, if the fused angles :math:`\theta` are such that
              :math:`|\theta|\leq \text{atol}`, no rotation gate will be applied.
          exclude_gates (None or list[str]): A list of gates that should be excluded
              from full fusion. If set to ``None``, all single-qubit gates that can
              be fused will be fused.
  
      Returns:
          qnode (QNode) or quantum function (Callable) or tuple[List[QuantumTape], function]: The transformed circuit as described in :func:`qml.transform <pennylane.transform>`.
  
      **Example**
  
      >>> dev = qml.device('default.qubit', wires=1)
  
      You can apply the transform directly on :class:`QNode`:
  
      .. code-block:: python
  
          @single_qubit_fusion
          @qml.qnode(device=dev)
          def qfunc(r1, r2):
              qml.Hadamard(wires=0)
              qml.Rot(*r1, wires=0)
              qml.Rot(*r2, wires=0)
              qml.RZ(r1[0], wires=0)
              qml.RZ(r2[0], wires=0)
              return qml.expval(qml.PauliX(0))
  
      The single qubit gates are fused before execution.
  
      .. details::
          :title: Usage Details
  
          Consider the following quantum function.
  
          .. code-block:: python
  
              def qfunc(r1, r2):
                  qml.Hadamard(wires=0)
                  qml.Rot(*r1, wires=0)
                  qml.Rot(*r2, wires=0)
                  qml.RZ(r1[0], wires=0)
                  qml.RZ(r2[0], wires=0)
                  return qml.expval(qml.PauliX(0))
  
          The circuit before optimization:
  
          >>> qnode = qml.QNode(qfunc, dev)
          >>> print(qml.draw(qnode)([0.1, 0.2, 0.3], [0.4, 0.5, 0.6]))
          0: ──H──Rot(0.1, 0.2, 0.3)──Rot(0.4, 0.5, 0.6)──RZ(0.1)──RZ(0.4)──┤ ⟨X⟩
  
          Full single-qubit gate fusion allows us to collapse this entire sequence into a
          single ``qml.Rot`` rotation gate.
  
          >>> optimized_qfunc = single_qubit_fusion(qfunc)
          >>> optimized_qnode = qml.QNode(optimized_qfunc, dev)
          >>> print(qml.draw(optimized_qnode)([0.1, 0.2, 0.3], [0.4, 0.5, 0.6]))
          0: ──Rot(3.57, 2.09, 2.05)──┤ ⟨X⟩
  
      """
      # Make a working copy of the list to traverse
      list_copy = tape.operations.copy()
      new_operations = []
      while len(list_copy) > 0:
          current_gate = list_copy[0]
  
          # If the gate should be excluded, queue it and move on regardless
          # of fusion potential
          if exclude_gates is not None:
              if current_gate.name in exclude_gates:
                  new_operations.append(current_gate)
                  list_copy.pop(0)
                  continue
  
          # Look for single_qubit_rot_angles; if not available, queue and move on.
          # If available, grab the angles and try to fuse.
          try:
              cumulative_angles = stack(
                  current_gate.single_qubit_rot_angles()
              )
          except (NotImplementedError, AttributeError):
              new_operations.append(current_gate)
              list_copy.pop(0)
              continue
  
          # Find the next gate that acts on the same wires
          next_gate_idx = find_next_gate(
              current_gate.wires, list_copy[1:]
          )
  
          if next_gate_idx is None:
              new_operations.append(current_gate)
              list_copy.pop(0)
              continue
  
          # Before entering the loop, we check to make sure the next gate is not in the
          # exclusion list. If it is, we should apply the original gate as-is, and not the
          # Rot version (example in test test_single_qubit_fusion_exclude_gates).
          if exclude_gates is not None:
              next_gate = list_copy[next_gate_idx + 1]
              if next_gate.name in exclude_gates:
                  new_operations.append(current_gate)
                  list_copy.pop(0)
                  continue
  
          # Loop as long as a valid next gate exists
          while next_gate_idx is not None:
              next_gate = list_copy[next_gate_idx + 1]
  
              # Check first if the next gate is in the exclusion list
              if exclude_gates is not None:
                  if next_gate.name in exclude_gates:
                      break
  
              # Try to extract the angles; since the Rot angles are implemented
              # solely for single-qubit gates, and we used find_next_gate to obtain
              # the gate in question, only valid single-qubit gates on the same
              # wire as the current gate will be fused.
              try:
                  next_gate_angles = stack(
                      next_gate.single_qubit_rot_angles()
                  )
              except (NotImplementedError, AttributeError):
                  break
  
              cumulative_angles = fuse_rot_angles(
                  cumulative_angles, stack(next_gate_angles)
              )
  
              list_copy.pop(next_gate_idx + 1)
              next_gate_idx = find_next_gate(
                  current_gate.wires, list_copy[1:]
              )
  
          # If we are tracing/jitting, don't perform any conditional checks and
          # apply the rotation regardless of the angles.
          if is_abstract(cumulative_angles):
              with QueuingManager.stop_recording():
                  new_operations.append(
                      Rot(*cumulative_angles, wires=current_gate.wires)
                  )
          # If not tracing, check whether all angles are 0 (or equivalently, if the RY
          # angle is close to 0, and so is the sum of the RZ angles
          else:
              if not allclose(
                  stack(
                      [
                          cumulative_angles[0] + cumulative_angles[2],
                          cumulative_angles[1],
                      ]
                  ),
                  [0.0, 0.0],
                  atol=atol,
                  rtol=0,
              ):
                  with QueuingManager.stop_recording():
                      new_operations.append(
                          Rot(
                              *cumulative_angles,
                              wires=current_gate.wires,
                          )
                      )
  
          # Remove the starting gate from the list
          list_copy.pop(0)
  
      new_tape = type(tape)(
          new_operations, tape.measurements, shots=tape.shots
      )
  
      def null_postprocessing(results):
          """A postprocesing function returned by a transform that only converts the batch of results
          into a result for a single ``QuantumTape``.
          """
          return results[0]
  
      return [new_tape], null_postprocessing
  
imports: from typing import Sequence, Callable
  from pennylane.tape import QuantumTape
  from pennylane.transforms import transform
  from pennylane.ops.qubit import Rot
  from pennylane.math import allclose, stack, is_abstract
  from pennylane.queuing import QueuingManager
  from .optimization_utils import find_next_gate, fuse_rot_angles
label_desc: Use image node_id 1 for calling a global function with example usage: single_qubit_fusion(tape, atol, exclude_gates) and returns: list,  null_postprocessing, results