Source code for pennylane.templates.embeddings.iqp
# Copyright 2018-2021 Xanadu Quantum Technologies Inc.
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
# http://www.apache.org/licenses/LICENSE-2.0
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
r"""
Contains the IQPEmbedding template.
"""
# pylint: disable-msg=too-many-branches,too-many-arguments,protected-access
from itertools import combinations
import pennylane as qml
from pennylane.operation import Operation, AnyWires
[docs]class IQPEmbedding(Operation):
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/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);
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* 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.Z(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.Z(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.Z(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.Z(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.
"""
num_wires = AnyWires
grad_method = None
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)
@property
def num_params(self):
return 1
@property
def ndim_params(self):
return (1,)
[docs] @staticmethod
def compute_decomposition(
features, wires, n_repeats, pattern
): # pylint: disable=arguments-differ
r"""Representation of the operator as a product of other operators.
.. math:: O = O_1 O_2 \dots O_n.
.. seealso:: :meth:`~.IQPEmbedding.decomposition`.
Args:
features (tensor_like): tensor of features to encode
wires (Any or Iterable[Any]): wires that the template acts on
Returns:
list[.Operator]: decomposition of the operator
**Example**
>>> features = torch.tensor([1., 2., 3.])
>>> pattern = [(0, 1), (0, 2), (1, 2)]
>>> qml.IQPEmbedding.compute_decomposition(features, wires=[0, 1, 2], n_repeats=2, pattern=pattern)
[Hadamard(wires=[0]), RZ(tensor(1.), wires=[0]),
Hadamard(wires=[1]), RZ(tensor(2.), wires=[1]),
Hadamard(wires=[2]), RZ(tensor(3.), wires=[2]),
MultiRZ(tensor(2.), wires=[0, 1]), MultiRZ(tensor(3.), wires=[0, 2]), MultiRZ(tensor(6.), wires=[1, 2]),
Hadamard(wires=[0]), RZ(tensor(1.), wires=[0]),
Hadamard(wires=[1]), RZ(tensor(2.), wires=[1]),
Hadamard(wires=[2]), RZ(tensor(3.), wires=[2]),
MultiRZ(tensor(2.), wires=[0, 1]), MultiRZ(tensor(3.), wires=[0, 2]), MultiRZ(tensor(6.), wires=[1, 2])]
"""
wires = qml.wires.Wires(wires)
op_list = []
if qml.math.ndim(features) > 1:
# If broadcasting is used, we want to iterate over the wires axis of the features,
# not over the broadcasting dimension. The latter is passed on to the rotations.
features = qml.math.T(features)
for _ in range(n_repeats):
for i in range(len(wires)): # pylint: disable=consider-using-enumerate
op_list.append(qml.Hadamard(wires=wires[i]))
op_list.append(qml.RZ(features[i], wires=wires[i]))
for wire_pair in pattern:
# get the position of the wire indices in the array
idx1, idx2 = wires.indices(wire_pair)
# apply product of two features as entangler
op_list.append(qml.MultiRZ(features[idx1] * features[idx2], wires=wire_pair))
return op_list
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