code: def find_and_place_cuts(
      graph: MultiDiGraph,
      cut_method: Callable = kahypar_cut,
      cut_strategy: CutStrategy = None,
      replace_wire_cuts=False,
      local_measurement=False,
      **kwargs,
  ) -> MultiDiGraph:
      """Automatically finds and places optimal :class:`~.WireCut` nodes into a given tape-converted graph
      using a customizable graph partitioning function. Preserves existing placed cuts.
  
      Args:
          graph (MultiDiGraph): The original (tape-converted) graph to be cut.
          cut_method (Callable): A graph partitioning function that takes an input graph and returns
              a list of edges to be cut based on a given set of constraints and objective. Defaults
              to :func:`kahypar_cut` which requires KaHyPar to be installed using
              ``pip install kahypar`` for Linux and Mac users or visiting the
              instructions `here <https://kahypar.org>`__ to compile from
              source for Windows users.
          cut_strategy (CutStrategy): Strategy for optimizing cutting parameters based on device
              constraints. Defaults to ``None`` in which case ``kwargs`` must be fully specified
              for passing to the ``cut_method``.
          replace_wire_cuts (bool): Whether to replace :class:`~.WireCut` nodes with
              :class:`~.MeasureNode` and :class:`~.PrepareNode` pairs. Defaults to ``False``.
          local_measurement (bool): Whether to use the local-measurement circuit-cutting objective,
              i.e. the maximum node-degree of the communication graph, for cut evaluation. Defaults
              to ``False`` which assumes global measurement and uses the total number of cuts as the
              cutting objective.
          kwargs: Additional keyword arguments to be passed to the callable ``cut_method``.
  
      Returns:
          nx.MultiDiGraph: Copy of the input graph with :class:`~.WireCut` nodes inserted.
  
      **Example**
  
      Consider the following 4-wire circuit with a single CNOT gate connecting the top (wires
      ``[0, 1]``) and bottom (wires ``["a", "b"]``) halves of the circuit. Note there's a
      :class:`~.WireCut` manually placed into the circuit already.
  
      .. code-block:: python
  
          ops = [
              qml.RX(0.1, wires=0),
              qml.RY(0.2, wires=1),
              qml.RX(0.3, wires="a"),
              qml.RY(0.4, wires="b"),
              qml.CNOT(wires=[0, 1]),
              qml.WireCut(wires=1),
              qml.CNOT(wires=["a", "b"]),
              qml.CNOT(wires=[1, "a"]),
              qml.CNOT(wires=[0, 1]),
              qml.CNOT(wires=["a", "b"]),
              qml.RX(0.5, wires="a"),
              qml.RY(0.6, wires="b"),
          ]
          measurements = [qml.expval(qml.PauliX(wires=[0]) @ qml.PauliY(wires=["a"]) @ qml.PauliZ(wires=["b"]))]
          tape = qml.tape.QuantumTape(ops, measurements)
  
      >>> print(qml.drawer.tape.text(tape))
       0: ──RX(0.1)──╭●──────────╭●───────────╭┤ ⟨X ⊗ Y ⊗ Z⟩
       1: ──RY(0.2)──╰X──//──╭●──╰X───────────│┤
       a: ──RX(0.3)──╭●──────╰X──╭●──RX(0.5)──├┤ ⟨X ⊗ Y ⊗ Z⟩
       b: ──RY(0.4)──╰X──────────╰X──RY(0.6)──╰┤ ⟨X ⊗ Y ⊗ Z⟩
  
      Since the existing :class:`~.WireCut` doesn't sufficiently fragment the circuit, we can find the
      remaining cuts using the default KaHyPar partitioner:
  
      >>> graph = qml.qcut.tape_to_graph(tape)
      >>> cut_graph = qml.qcut.find_and_place_cuts(
              graph=graph,
              num_fragments=2,
              imbalance=0.5,
          )
  
      Visualizing the newly-placed cut:
  
      >>> print(qml.qcut.graph_to_tape(cut_graph).draw())
       0: ──RX(0.1)──╭●───────────────╭●────────╭┤ ⟨X ⊗ Y ⊗ Z⟩
       1: ──RY(0.2)──╰X──//──╭●───//──╰X────────│┤
       a: ──RX(0.3)──╭●──────╰X──╭●────RX(0.5)──├┤ ⟨X ⊗ Y ⊗ Z⟩
       b: ──RY(0.4)──╰X──────────╰X────RY(0.6)──╰┤ ⟨X ⊗ Y ⊗ Z⟩
  
      We can then proceed with the usual process of replacing :class:`~.WireCut` nodes with
      pairs of :class:`~.MeasureNode` and :class:`~.PrepareNode`, and then break the graph
      into fragments. Or, alternatively, we can directly get such processed graph by passing
      ``replace_wire_cuts=True``:
  
      >>> cut_graph = qml.qcut.find_and_place_cuts(
              graph=graph,
              num_fragments=2,
              imbalance=0.5,
              replace_wire_cuts=True,
          )
      >>> frags, comm_graph = qml.qcut.fragment_graph(cut_graph)
      >>> for t in frags:
      ...     print(qml.qcut.graph_to_tape(t).draw())
  
      .. code-block::
  
           0: ──RX(0.1)──────╭●───────────────╭●──┤ ⟨X⟩
           1: ──RY(0.2)──────╰X──MeasureNode──│───┤
           2: ──PrepareNode───────────────────╰X──┤
  
           a: ──RX(0.3)──────╭●──╭X──╭●────────────RX(0.5)──╭┤ ⟨Y ⊗ Z⟩
           b: ──RY(0.4)──────╰X──│───╰X────────────RY(0.6)──╰┤ ⟨Y ⊗ Z⟩
           1: ──PrepareNode──────╰●───MeasureNode────────────┤
  
      Alternatively, if all we want to do is to find the optimal way to fit a circuit onto a smaller
      device, a :class:`~.CutStrategy` can be used to populate the necessary explorations of cutting
      parameters. As an extreme example, if the only device at our disposal is a 2-qubit device, a
      simple cut strategy is to simply specify the the ``max_free_wires`` argument (or equivalently
      directly passing a :class:`pennylane.Device` to the ``device`` argument):
  
      >>> cut_strategy = qml.qcut.CutStrategy(max_free_wires=2)
      >>> print(cut_strategy.get_cut_kwargs(graph))
       [{'num_fragments': 2, 'imbalance': 0.5714285714285714},
        {'num_fragments': 3, 'imbalance': 1.4},
        {'num_fragments': 4, 'imbalance': 1.75},
        {'num_fragments': 5, 'imbalance': 2.3333333333333335},
        {'num_fragments': 6, 'imbalance': 2.0},
        {'num_fragments': 7, 'imbalance': 3.0},
        {'num_fragments': 8, 'imbalance': 2.5},
        {'num_fragments': 9, 'imbalance': 2.0},
        {'num_fragments': 10, 'imbalance': 1.5},
        {'num_fragments': 11, 'imbalance': 1.0},
        {'num_fragments': 12, 'imbalance': 0.5},
        {'num_fragments': 13, 'imbalance': 0.05},
        {'num_fragments': 14, 'imbalance': 0.1}]
  
      The printed list above shows all the possible cutting configurations one can attempt to perform
      in order to search for the optimal cut. This is done by directly passing a
      :class:`~.CutStrategy` to :func:`~.find_and_place_cuts`:
  
      >>> cut_graph = qml.qcut.find_and_place_cuts(
              graph=graph,
              cut_strategy=cut_strategy,
          )
      >>> print(qml.qcut.graph_to_tape(cut_graph).draw())
       0: ──RX──//─╭●──//────────╭●──//─────────┤ ╭<X@Y@Z>
       1: ──RY──//─╰X──//─╭●──//─╰X─────────────┤ │
       a: ──RX──//─╭●──//─╰X──//─╭●──//──RX──//─┤ ├<X@Y@Z>
       b: ──RY──//─╰X──//────────╰X──//──RY─────┤ ╰<X@Y@Z>
  
      As one can tell, quite a few cuts have to be made in order to execute the circuit on solely
      2-qubit devices. To verify, let's print the fragments:
  
      >>> qml.qcut.replace_wire_cut_nodes(cut_graph)
      >>> frags, comm_graph = qml.qcut.fragment_graph(cut_graph)
      >>> for t in frags:
      ...     print(qml.qcut.graph_to_tape(t).draw())
  
      .. code-block::
  
           0: ──RX──MeasureNode─┤
  
           1: ──RY──MeasureNode─┤
  
           a: ──RX──MeasureNode─┤
  
           b: ──RY──MeasureNode─┤
  
           0: ──PrepareNode─╭●──MeasureNode─┤
           1: ──PrepareNode─╰X──MeasureNode─┤
  
           a: ──PrepareNode─╭●──MeasureNode─┤
           b: ──PrepareNode─╰X──MeasureNode─┤
  
           1: ──PrepareNode─╭●──MeasureNode─┤
           a: ──PrepareNode─╰X──MeasureNode─┤
  
           0: ──PrepareNode─╭●──MeasureNode─┤
           1: ──PrepareNode─╰X──────────────┤
  
           b: ──PrepareNode─╭X──MeasureNode─┤
           a: ──PrepareNode─╰●──MeasureNode─┤
  
           a: ──PrepareNode──RX──MeasureNode─┤
  
           b: ──PrepareNode──RY─┤  <Z>
  
           0: ──PrepareNode─┤  <X>
  
           a: ──PrepareNode─┤  <Y>
  
      """
  
      cut_graph = _remove_existing_cuts(graph)
  
      if isinstance(cut_strategy, CutStrategy):
          cut_kwargs_probed = cut_strategy.get_cut_kwargs(cut_graph)
  
          # Need to reseed if a seed is passed:
          seed = kwargs.pop("seed", None)
          seeds = (
              np.random.default_rng(seed)
              .choice(2**15, cut_strategy.trials_per_probe)
              .tolist()
          )
  
          cut_edges_probed = {
              (cut_kwargs["num_fragments"], trial_id): cut_method(
                  cut_graph,
                  **{
                      **cut_kwargs,
                      **kwargs,
                      "seed": seed,
                  },  # kwargs has higher precedence for colliding keys
              )
              for cut_kwargs in cut_kwargs_probed
              for trial_id, seed in zip(
                  range(cut_strategy.trials_per_probe), seeds
              )
          }
  
          valid_cut_edges = {}
          for (
              num_partitions,
              _,
          ), cut_edges in cut_edges_probed.items():
              # The easiest way to tell if a cut is valid is to just do the fragment graph.
  
              cut_graph = place_wire_cuts(
                  graph=graph, cut_edges=cut_edges
              )
              num_cuts = sum(
                  isinstance(n.obj, WireCut) for n in cut_graph.nodes
              )
  
              replace_wire_cut_nodes(cut_graph)
              frags, comm = fragment_graph(cut_graph)
  
              max_frag_degree = max(dict(comm.degree()).values())
  
              if _is_valid_cut(
                  fragments=frags,
                  num_cuts=num_cuts,
                  max_frag_degree=max_frag_degree,
                  num_fragments_requested=num_partitions,
                  cut_candidates=valid_cut_edges,
                  max_free_wires=cut_strategy.max_free_wires,
              ):
                  key = (len(frags), max_frag_degree)
                  valid_cut_edges[key] = cut_edges
  
          if len(valid_cut_edges) < 1:
              raise ValueError(
                  "Unable to find a circuit cutting that satisfies all constraints. "
                  "Are the constraints too strict?"
              )
  
          cut_edges = _get_optim_cut(
              valid_cut_edges, local_measurement=local_measurement
          )
  
      else:
          cut_edges = cut_method(cut_graph, **kwargs)
  
      cut_graph = place_wire_cuts(graph=graph, cut_edges=cut_edges)
  
      if replace_wire_cuts:
          replace_wire_cut_nodes(cut_graph)
  
      return cut_graph
  
imports: import uuid
  from typing import Any, Callable, Sequence, Tuple
  import warnings
  import numpy
  from networkx import MultiDiGraph, has_path, weakly_connected_components
  import pennylane
  from pennylane.measurements import MeasurementProcess
  from pennylane.ops.meta import WireCut
  from pennylane.queuing import WrappedObj
  from pennylane.operation import Operation
  from .kahypar import kahypar_cut
  from .cutstrategy import CutStrategy
label_desc: Use image node_id 7 for calling a global function with example usage: find_and_place_cuts(graph, cut_method, cut_strategy, replace_wire_cuts, local_measurement) and returns: cut_graph