code: def compile(
      tape: QuantumTape,
      pipeline=None,
      basis_set=None,
      num_passes=1,
      expand_depth=5,
  ) -> (Sequence[QuantumTape], Callable):
      """Compile a circuit by applying a series of transforms to a quantum function.
  
      The default set of transforms includes (in order):
  
      - pushing all commuting single-qubit gates as far right as possible
        (:func:`~pennylane.transforms.commute_controlled`)
      - cancellation of adjacent inverse gates
        (:func:`~pennylane.transforms.cancel_inverses`)
      - merging adjacent rotations of the same type
        (:func:`~pennylane.transforms.merge_rotations`)
  
      Args:
          tape (QNode or QuantumTape or Callable): A quantum circuit.
          pipeline (list[Callable]): A list of
              tape and/or quantum function transforms to apply.
          basis_set (list[str]): A list of basis gates. When expanding the tape,
              expansion will continue until gates in the specific set are
              reached. If no basis set is specified, a default of
              ``pennylane.ops.__all__`` will be used. This decomposes templates and
              operator arithmetic.
          num_passes (int): The number of times to apply the set of transforms in
              ``pipeline``. The default is to perform each transform once;
              however, doing so may produce a new circuit where applying the set
              of transforms again may yield further improvement, so the number of
              such passes can be adjusted.
          expand_depth (int): The depth to use for tape expansion into the basis gates.
  
      Returns:
          qnode (QNode) or quantum function (Callable) or tuple[List[QuantumTape], function]: The compiled circuit. The output type is explained in :func:`qml.transform <pennylane.transform>`.
  
      **Example**
  
      >>> dev = qml.device('default.qubit', wires=[0, 1, 2])
  
      You can apply the transform directly on a :class:`QNode`:
  
      .. code-block:: python
  
          @compile
          @qml.qnode(device=dev)
          def circuit(x, y, z):
              qml.Hadamard(wires=0)
              qml.Hadamard(wires=1)
              qml.Hadamard(wires=2)
              qml.RZ(z, wires=2)
              qml.CNOT(wires=[2, 1])
              qml.RX(z, wires=0)
              qml.CNOT(wires=[1, 0])
              qml.RX(x, wires=0)
              qml.CNOT(wires=[1, 0])
              qml.RZ(-z, wires=2)
              qml.RX(y, wires=2)
              qml.PauliY(wires=2)
              qml.CY(wires=[1, 2])
              return qml.expval(qml.PauliZ(wires=0))
  
      The default compilation pipeline is applied before execution.
  
      Consider the following quantum function:
  
      .. code-block:: python
  
          def qfunc(x, y, z):
              qml.Hadamard(wires=0)
              qml.Hadamard(wires=1)
              qml.Hadamard(wires=2)
              qml.RZ(z, wires=2)
              qml.CNOT(wires=[2, 1])
              qml.RX(z, wires=0)
              qml.CNOT(wires=[1, 0])
              qml.RX(x, wires=0)
              qml.CNOT(wires=[1, 0])
              qml.RZ(-z, wires=2)
              qml.RX(y, wires=2)
              qml.PauliY(wires=2)
              qml.CY(wires=[1, 2])
              return qml.expval(qml.PauliZ(wires=0))
  
      Visually, the original function looks like this:
  
      >>> qnode = qml.QNode(qfunc, dev)
      >>> print(qml.draw(qnode)(0.2, 0.3, 0.4))
      0: ──H──RX(0.40)────╭X──────────RX(0.20)─╭X────┤  <Z>
      1: ──H───────────╭X─╰●───────────────────╰●─╭●─┤
      2: ──H──RZ(0.40)─╰●──RZ(-0.40)──RX(0.30)──Y─╰Y─┤
  
      We can compile it down to a smaller set of gates using the ``qml.compile``
      transform.
  
      >>> compiled_qfunc = qml.compile(qfunc)
      >>> compiled_qnode = qml.QNode(compiled_qfunc, dev)
      >>> print(qml.draw(compiled_qnode)(0.2, 0.3, 0.4))
      0: ──H──RX(0.60)─────────────────┤  <Z>
      1: ──H─╭X──────────────────╭●────┤
      2: ──H─╰●─────────RX(0.30)─╰Y──Y─┤
  
      You can change up the set of transforms by passing a custom ``pipeline`` to
      ``qml.compile``. The pipeline is a list of transform functions. Furthermore,
      you can specify a number of passes (repetitions of the pipeline), and a list
      of gates into which the compiler will first attempt to decompose the
      existing operations prior to applying any optimization transforms.
  
      .. code-block:: python3
  
          compiled_qfunc = qml.compile(
              pipeline=[
                  partial(qml.transforms.commute_controlled, direction="left"),
                  partial(qml.transforms.merge_rotations, atol=1e-6),
                  qml.transforms.cancel_inverses
              ],
              basis_set=["CNOT", "RX", "RY", "RZ"],
              num_passes=2
          )(qfunc)
  
          compiled_qnode = qml.QNode(compiled_qfunc, dev)
  
          print(qml.draw(compiled_qnode)(0.2, 0.3, 0.4))
  
      .. code-block::
  
          0: ──RZ(1.57)──RX(1.57)──RZ(1.57)──RX(0.60)─────────────────────────────────────────────────────
          1: ──RZ(1.57)──RX(1.57)──RZ(1.57)─╭X─────────RZ(1.57)─────────────────────────────────────────╭●
          2: ──RZ(1.57)──RX(1.57)──RZ(1.57)─╰●─────────RX(0.30)──RZ(1.57)──RY(3.14)──RZ(1.57)──RY(1.57)─╰X
  
          ────────────────┤  <Z>
          ─────────────╭●─┤
          ───RY(-1.57)─╰X─┤
  
      """
      # Ensure that everything in the pipeline is a valid qfunc or tape transform
      if pipeline is None:
          pipeline = default_pipeline
      else:
          for p in pipeline:
              p_func = p.func if isinstance(p, partial) else p
              if not isinstance(p_func, TransformDispatcher):
                  raise ValueError(
                      "Invalid transform function {p} passed to compile."
                  )
  
      if num_passes < 1 or not isinstance(num_passes, int):
          raise ValueError(
              "Number of passes must be an integer with value at least 1."
          )
  
      # Expand the tape; this is done to unroll any templates that may be present,
      # as well as to decompose over a specified basis set
      # First, though, we have to stop whatever tape may be recording so that we
      # don't queue anything as a result of the expansion or transform pipeline
  
      with QueuingManager.stop_recording():
          basis_set = basis_set or all_ops
  
          def stop_at(obj):
              return obj.name in basis_set and (
                  not getattr(obj, "only_visual", False)
              )
  
          expanded_tape = tape.expand(
              depth=expand_depth, stop_at=stop_at
          )
  
          # Apply the full set of compilation transforms num_passes times
          for _ in range(num_passes):
              for transf in pipeline:
                  tapes, _ = transf(expanded_tape)
                  expanded_tape = tapes[0]
  
      new_tape = type(tape)(
          expanded_tape.operations,
          expanded_tape.measurements,
          shots=expanded_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 functools import partial
  from typing import Sequence, Callable
  from pennylane.queuing import QueuingManager
  from pennylane.ops import __all__
  from pennylane.tape import QuantumTape
  from pennylane.transforms.core import transform, TransformDispatcher
  from pennylane.transforms.optimization import cancel_inverses, commute_controlled, merge_rotations, remove_barrier
label_desc: Use image node_id 1 for calling a global function with example usage: compile(tape, pipeline, basis_set, num_passes, expand_depth) and returns: list,  null_postprocessing, results, unknown