def test_indices_method(self):
"""Tests the ``indices()`` method."""
wires = Wires([4, 0, 1])
# for Wires inputs
assert wires.indices(Wires([1, 4])) == [2, 0]
# for non-Wires inputs
assert wires.indices([1, 4]) == [2, 0]
def IQPEmbedding(features, wires, n_repeats=1, pattern=None):
r"""
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/pdf/1804.11326.pdf>`_.
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): array of features to encode
wires (Iterable or Wires): Wires that the template acts on. Accepts an iterable of numbers or strings, or
a Wires object.
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
.. UsageDetails::
A typical usage example of the template is the following:
.. code-block:: python
import pennylane as qml
from pennylane.templates import IQPEmbedding
dev = qml.device('default.qubit', wires=3)
@qml.qnode(dev)
def circuit(features=None):
IQPEmbedding(features=features, wires=range(3))
return [qml.expval(qml.PauliZ(w)) for w in range(3)]
circuit(features=[1., 2., 3.])
**Do not pass features as a positional argument to the qnode**
The ``features`` argument cannot be passed to the quantum node
as a positional argument. This is due to the fact that the embedding performs non-trivial calculations
on the features. As a consequence, the following code **will produce an error**:
.. code-block:: python
@qml.qnode(dev)
def circuit(features):
IQPEmbedding(features=features, wires=range(3), n_repeats=2)
return [qml.expval(qml.PauliZ(w)) for w in range(3)]
circuit([1., 2., 3.])
>>> ValueError: 'features' cannot be differentiable
**Repeating the embedding**
The embedding can be repeated by specifying the ``n_repeats`` argument:
.. code-block:: python
@qml.qnode(dev)
def circuit(features=None):
IQPEmbedding(features=features, wires=range(3), n_repeats=4)
return [qml.expval(qml.PauliZ(w)) for w in range(3)]
circuit(features=[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=None):
IQPEmbedding(features=features, wires=range(3), pattern=pattern)
return [qml.expval(qml.PauliZ(w)) for w in range(3)]
circuit(features=[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=None, pattern=None):
IQPEmbedding(features=features, wires=range(3), pattern=pattern, n_repeats=3)
return [qml.expval(qml.PauliZ(w)) for w in range(3)]
res1 = circuit(features=[1., 2., 3.], pattern=pattern1)
res2 = circuit(features=[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.
"""
wires = Wires(wires)
pattern = _preprocess(features, wires, pattern, n_repeats)
for i in range(n_repeats):
# first block of Hadamards
broadcast(unitary=Hadamard, pattern="single", wires=wires)
# encode features into block of RZ rotations
broadcast(unitary=RZ,
pattern="single",
wires=wires,
parameters=features)
# create new features for entangling block
products = []
for wire_pair in pattern:
# get the position of the wire indices in the array
idx1, idx2 = wires.indices(wire_pair)
# create products of parameters
products.append(features[idx1] * features[idx2])
broadcast(unitary=MultiRZ,
pattern=pattern,
wires=wires,
parameters=products)
