class_docstr: Encodes :math:`n` features into :math:`n` qubits using diagonal gates of an IQP circuit.
  
  The embedding has been proposed by `Havlicek et al. (2018) <https://arxiv.org/abs/1804.11326>`_.
  
  The basic IQP circuit can be repeated by specifying ``n_repeats``. Repetitions can make the
  embedding "richer" through interference.
  
  .. warning::
  
      ``IQPEmbedding`` calls a circuit that involves non-trivial classical processing of the
      features. The ``features`` argument is therefore **not differentiable** when using the template, and
      gradients with respect to the features cannot be computed by PennyLane.
  
  An IQP circuit is a quantum circuit of a block of Hadamards, followed by a block of gates that are
  diagonal in the computational basis. Here, the diagonal gates are single-qubit ``RZ`` rotations, applied to each
  qubit and encoding the :math:`n` features, followed by two-qubit ZZ entanglers,
  :math:`e^{-i x_i x_j \sigma_z \otimes \sigma_z}`. The entangler applied to wires ``(wires[i], wires[j])``
  encodes the product of features ``features[i]*features[j]``. The pattern in which the entanglers are
  applied is either the default, or a custom pattern:
  
  * If ``pattern`` is not specified, the default pattern will be used, in which the entangling gates connect all
    pairs of neighbours:
  
    |
  
    .. figure:: ../../_static/templates/embeddings/iqp.png
        :align: center
        :width: 50%
        :target: javascript:void(0);
  
    |
  
  * Else, ``pattern`` is a list of wire pairs ``[[a, b], [c, d],...]``, applying the entangler
    on wires ``[a, b]``, ``[c, d]``, etc. For example, ``pattern = [[0, 1], [1, 2]]`` produces
    the following entangler pattern:
  
    |
  
    .. figure:: ../../_static/templates/embeddings/iqp_custom.png
        :align: center
        :width: 50%
        :target: javascript:void(0);
  
    |
  
    Since diagonal gates commute, the order of the entanglers does not change the result.
  
  Args:
      features (tensor_like): tensor of features to encode
      wires (Any or Iterable[Any]): wires that the template acts on
      n_repeats (int): number of times the basic embedding is repeated
      pattern (list[int]): specifies the wires and features of the entanglers
  
  Raises:
      ValueError: if inputs do not have the correct format
  
  .. details::
      :title: Usage Details
  
      A typical usage example of the template is the following:
  
      .. code-block:: python
  
          import pennylane as qml
  
          dev = qml.device('default.qubit', wires=3)
  
          @qml.qnode(dev)
          def circuit(features):
              qml.IQPEmbedding(features, wires=range(3))
              return [qml.expval(qml.PauliZ(w)) for w in range(3)]
  
          circuit([1., 2., 3.])
  
      **Repeating the embedding**
  
      The embedding can be repeated by specifying the ``n_repeats`` argument:
  
      .. code-block:: python
  
          @qml.qnode(dev)
          def circuit(features):
              qml.IQPEmbedding(features, wires=range(3), n_repeats=4)
              return [qml.expval(qml.PauliZ(w)) for w in range(3)]
  
          circuit([1., 2., 3.])
  
      Every repetition uses exactly the same quantum circuit.
  
      **Using a custom entangler pattern**
  
      A custom entangler pattern can be used by specifying the ``pattern`` argument. A pattern has to be
      a nested list of dimension ``(K, 2)``, where ``K`` is the number of entanglers to apply.
  
      .. code-block:: python
  
          pattern = [[1, 2], [0, 2], [1, 0]]
  
          @qml.qnode(dev)
          def circuit(features):
              qml.IQPEmbedding(features, wires=range(3), pattern=pattern)
              return [qml.expval(qml.PauliZ(w)) for w in range(3)]
  
          circuit([1., 2., 3.])
  
      Since diagonal gates commute, the order of the wire pairs has no effect on the result.
  
      .. code-block:: python
  
          from pennylane import numpy as np
  
          pattern1 = [[1, 2], [0, 2], [1, 0]]
          pattern2 = [[1, 0], [0, 2], [1, 2]]  # a reshuffling of pattern1
  
          @qml.qnode(dev)
          def circuit(features, pattern):
              qml.IQPEmbedding(features, wires=range(3), pattern=pattern, n_repeats=3)
              return [qml.expval(qml.PauliZ(w)) for w in range(3)]
  
          res1 = circuit([1., 2., 3.], pattern=pattern1)
          res2 = circuit([1., 2., 3.], pattern=pattern2)
  
          assert np.allclose(res1, res2)
  
      **Non-consecutive wires**
  
      In principle, the user can also pass a non-consecutive wire list to the template.
      For single qubit gates, the i'th feature is applied to the i'th wire index (which may not be the i'th wire).
      For the entanglers, the product of i'th and j'th features is applied to the wire indices at the i'th and j'th
      position in ``wires``.
  
      For example, for ``wires=[2, 0, 1]`` the ``RZ`` block applies the first feature to wire 2,
      the second feature to wire 0, and the third feature to wire 1.
  
      Likewise, using the default pattern, the entangler block applies the product of the first and second
      feature to the wire pair ``[2, 0]``, the product of the second and third feature to ``[2, 1]``, and so
      forth.
code: def __init__(
      self, features, wires, n_repeats=1, pattern=None, id=None
  ):
      shape = qml.math.shape(features)
  
      if len(shape) not in {1, 2}:
          raise ValueError(
              "Features must be a one-dimensional tensor, or two-dimensional "
              f"when broadcasting; got shape {shape}."
          )
  
      n_features = shape[-1]
      if n_features != len(wires):
          raise ValueError(
              f"Features must be of length {len(wires)}; got length {n_features}."
          )
  
      if pattern is None:
          # default is an all-to-all pattern
          pattern = tuple(combinations(wires, 2))
      self._hyperparameters = {
          "pattern": pattern,
          "n_repeats": n_repeats,
      }
  
      super().__init__(features, wires=wires, id=id)
  
file_path: pennylane/pennylane/templates/embeddings/iqp.py
imports: from itertools import combinations
  import pennylane
  from pennylane.operation import Operation, AnyWires
label_desc: Use image node_id 1 to create a new IQPEmbedding object from inherited base classes: Operation with example: obj = IQPEmbedding(features, wires, n_repeats, pattern, id)