Source code for pennylane.templates.embeddings.amplitude
# 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 AmplitudeEmbedding template.
"""
# pylint: disable-msg=too-many-branches,too-many-arguments,protected-access
import numpy as np
import pennylane as qml
from pennylane.operation import Operation, AnyWires
from pennylane.ops import QubitStateVector
from pennylane.wires import Wires
# tolerance for normalization
TOLERANCE = 1e-10
[docs]class AmplitudeEmbedding(Operation):
r"""Encodes :math:`2^n` features into the amplitude vector of :math:`n` qubits.
By setting ``pad_with`` to a real or complex number, ``features`` is automatically padded to dimension
:math:`2^n` where :math:`n` is the number of qubits used in the embedding.
To represent a valid quantum state vector, the L2-norm of ``features`` must be one.
The argument ``normalize`` can be set to ``True`` to automatically normalize the features.
If both automatic padding and normalization are used, padding is executed *before* normalizing.
.. note::
On some devices, ``AmplitudeEmbedding`` must be the first operation of a quantum circuit.
.. warning::
At the moment, the ``features`` argument is **not differentiable** when using the template, and
gradients with respect to the features cannot be computed by PennyLane.
Args:
features (tensor_like): input tensor of dimension ``(2^len(wires),)``, or less if `pad_with` is specified
wires (Any or Iterable[Any]): wires that the template acts on
pad_with (float or complex): if not None, the input is padded with this constant to size :math:`2^n`
normalize (bool): whether to automatically normalize the features
Example:
Amplitude embedding encodes a normalized :math:`2^n`-dimensional feature vector into the state
of :math:`n` qubits:
.. code-block:: python
import pennylane as qml
dev = qml.device('default.qubit', wires=2)
@qml.qnode(dev)
def circuit(f=None):
qml.AmplitudeEmbedding(features=f, wires=range(2))
return qml.expval(qml.PauliZ(0))
circuit(f=[1/2, 1/2, 1/2, 1/2])
The final state of the device is - up to a global phase - equivalent to the input passed to the circuit:
>>> dev.state
[0.5+0.j 0.5+0.j 0.5+0.j 0.5+0.j]
**Differentiating with respect to the features**
Due to non-trivial classical processing to construct the state preparation circuit,
the features argument is in general **not differentiable**.
**Normalization**
The template will raise an error if the feature input is not normalized.
One can set ``normalize=True`` to automatically normalize it:
.. code-block:: python
@qml.qnode(dev)
def circuit(f=None):
qml.AmplitudeEmbedding(features=f, wires=range(2), normalize=True)
return qml.expval(qml.PauliZ(0))
circuit(f=[15, 15, 15, 15])
>>> dev.state
[0.5 + 0.j, 0.5 + 0.j, 0.5 + 0.j, 0.5 + 0.j]
**Padding**
If the dimension of the feature vector is smaller than the number of amplitudes,
one can automatically pad it with a constant for the missing dimensions using the ``pad_with`` option:
.. code-block:: python
from math import sqrt
@qml.qnode(dev)
def circuit(f=None):
qml.AmplitudeEmbedding(features=f, wires=range(2), pad_with=0.)
return qml.expval(qml.PauliZ(0))
circuit(f=[1/sqrt(2), 1/sqrt(2)])
>>> dev.state
[0.70710678 + 0.j, 0.70710678 + 0.j, 0.0 + 0.j, 0.0 + 0.j]
"""
num_wires = AnyWires
grad_method = None
def __init__(self, features, wires, pad_with=None, normalize=False, do_queue=True, id=None):
wires = Wires(wires)
self.pad_with = pad_with
self.normalize = normalize
features = self._preprocess(features, wires, pad_with, normalize)
super().__init__(features, wires=wires, do_queue=do_queue, id=id)
@property
def num_params(self):
return 1
@property
def ndim_params(self):
return (1,)
[docs] @staticmethod
def compute_decomposition(features, wires): # 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:`~.AmplitudeEmbedding.decomposition`.
Args:
features (tensor_like): input tensor of dimension ``(2^len(wires),)``
wires (Any or Iterable[Any]): wires that the operator acts on
Returns:
list[.Operator]: decomposition of the operator
**Example**
>>> features = torch.tensor([1., 0., 0., 0.])
>>> qml.AmplitudeEmbedding.compute_decomposition(features, wires=["a", "b"])
[QubitStateVector(tensor([1., 0., 0., 0.]), wires=['a', 'b'])]
"""
return [QubitStateVector(features, wires=wires)]
@staticmethod
def _preprocess(features, wires, pad_with, normalize):
"""Validate and pre-process inputs as follows:
* If features is batched, the processing that follows is applied to each feature set in the batch.
* Check that the features tensor is one-dimensional.
* If pad_with is None, check that the last dimension of the features tensor
has length :math:`2^n` where :math:`n` is the number of qubits. Else check that the
last dimension of the features tensor is not larger than :math:`2^n` and pad features
with value if necessary.
* If normalize is false, check that last dimension of features is normalised to one. Else, normalise the
features tensor.
"""
# check if features is batched
batched = qml.math.ndim(features) > 1
if batched and qml.math.get_interface(features) == "tensorflow":
raise ValueError("AmplitudeEmbedding does not support batched Tensorflow features.")
features_batch = features if batched else [features]
new_features_batch = []
# apply pre-processing to each features tensor in the batch
for feature_set in features_batch:
shape = qml.math.shape(feature_set)
# check shape
if len(shape) != 1:
raise ValueError(f"Features must be a one-dimensional tensor; got shape {shape}.")
n_features = shape[0]
dim = 2 ** len(wires)
if pad_with is None and n_features != dim:
raise ValueError(
f"Features must be of length {dim}; got length {n_features}. "
f"Use the 'pad_with' argument for automated padding."
)
if pad_with is not None:
if n_features > dim:
raise ValueError(
f"Features must be of length {dim} or "
f"smaller to be padded; got length {n_features}."
)
# pad
if n_features < dim:
padding = [pad_with] * (dim - n_features)
padding = qml.math.convert_like(padding, feature_set)
feature_set = qml.math.hstack([feature_set, padding])
# normalize
norm = qml.math.sum(qml.math.abs(feature_set) ** 2)
if qml.math.is_abstract(norm):
if normalize or pad_with:
feature_set = feature_set / qml.math.sqrt(norm)
elif not qml.math.allclose(norm, 1.0, atol=TOLERANCE):
if normalize or pad_with:
feature_set = feature_set / qml.math.sqrt(norm)
else:
raise ValueError(
f"Features must be a vector of norm 1.0; got norm {norm}. "
"Use 'normalize=True' to automatically normalize."
)
new_features_batch.append(feature_set)
return qml.math.cast(
qml.math.stack(new_features_batch) if batched else new_features_batch[0], np.complex128
)
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