class_docstr: Applies the time-evolution operator for a Hamiltonian expressed as a linear combination
  of mutually commuting Pauli words.
  
  A commuting Hamiltonian is of the form
  
  .. math:: H \ = \ \displaystyle\sum_{j} c_j P_j,
  
  where :math:`P_j` are mutually commutative Pauli words and :math:`c_j` are real coefficients.
  The time-evolution under a commuting Hamiltonian is given by a unitary of the form
  
  .. math::
  
      U(t) \ = \ e^{-i H t} \ = \exp(-i t \displaystyle\sum_j c_j P_j) =
      \displaystyle\prod_j \exp(-i t c_j P_j).
  
  If the Hamiltonian has a small number of unique eigenvalues, partial derivatives of observable
  expectation values, i.e.
  
  .. math:: \langle 0 | W(t)^\dagger O W(t) | 0 \rangle,
  
  where :math:`W(t) = V U(t) Y` for some :math:`V` and :math:`Y`, taken with respect to
  :math:`t` may be efficiently computed through generalized parameter shift rules. When
  initialized, this template will automatically compute the parameter-shift rule if given the
  Hamiltonian's eigenvalue frequencies, i.e., the unique positive differences between
  eigenvalues.
  
  .. warning::
  
     This template uses the :class:`~.ApproxTimeEvolution` operation with ``n=1`` in order to
     implement the time evolution, as a single-step Trotterization is exact for a commuting
     Hamiltonian.
  
     - If the input Hamiltonian contains Pauli words which do not commute, the
       compilation of the time evolution operator to a sequence of gates will
       not equate to the exact propagation under the given Hamiltonian.
  
     - Furthermore, if the specified frequencies do not correspond to the
       true eigenvalue frequency spectrum of the commuting Hamiltonian,
       computed gradients will be incorrect in general.
  
  Args:
      hamiltonian (.Hamiltonian): The commuting Hamiltonian defining the time-evolution operator.
         The Hamiltonian must be explicitly written
         in terms of products of Pauli gates (:class:`~.PauliX`, :class:`~.PauliY`,
         :class:`~.PauliZ`, and :class:`~.Identity`).
      time (int or float): The time of evolution, namely the parameter :math:`t` in :math:`e^{- i H t}`.
  
  Keyword args:
      frequencies (tuple[int or float]): The unique positive differences between eigenvalues in
          the spectrum of the Hamiltonian. If the frequencies are not given, the cost function
          partial derivative will be computed using the standard two-term shift rule applied to
          the constituent Pauli words in the Hamiltonian individually.
  
      shifts (tuple[int or float]): The parameter shifts to use in obtaining the
          generalized parameter shift rules. If unspecified, equidistant shifts are used.
  
  .. details::
      :title: Usage Details
  
      The template is used inside a qnode:
  
      .. code-block:: python
  
          import pennylane as qml
  
          n_wires = 2
          dev = qml.device('default.qubit', wires=n_wires)
  
          coeffs = [1, -1]
          obs = [qml.PauliX(0) @ qml.PauliY(1), qml.PauliY(0) @ qml.PauliX(1)]
          hamiltonian = qml.Hamiltonian(coeffs, obs)
          frequencies = (2, 4)
  
          @qml.qnode(dev)
          def circuit(time):
              qml.PauliX(0)
              qml.CommutingEvolution(hamiltonian, time, frequencies)
              return qml.expval(qml.PauliZ(0))
  
      >>> circuit(1)
      0.6536436208636115
code: def _unflatten(cls, data, metadata) -> "CommutingEvolution":
      return cls(
          data[1], data[0], frequencies=metadata[0], shifts=metadata[1]
      )
  
file_path: pennylane/pennylane/templates/subroutines/commuting_evolution.py
imports: import pennylane
  from pennylane.operation import Operation, AnyWires
label_desc: Use image node_id 2 for calling the CommutingEvolution obj's underlying member method code with example usage: obj._unflatten(cls, data, metadata) and returns: cls