def AmplitudeEmbedding(features, wires):
r"""Encodes :math:`2^n` features into the amplitude vector of :math:`n` qubits.
The absolute square of all elements in ``features`` has to add up to one.
.. note::
AmplitudeEmbedding uses PennyLane's :class:`~pennylane.ops.QubitStateVector` and only works in conjunction with
devices that implement this function.
Args:
features (array): Input array of shape ``(2**n,)``
wires (Sequence[int]): sequence of qubit indices that the template acts on
"""
if not isinstance(wires, Iterable):
raise ValueError(
"Wires needs to be a list of wires that the embedding uses; got {}."
.format(wires))
if 2**len(wires) != len(features):
raise ValueError(
"AmplitudeEmbedding requires a feature vector of size 2**len(wires), which is {}; "
"got {}.".format(2**len(wires), len(features)))
QubitStateVector(features, wires=wires)
def AmplitudeEmbedding(features, wires, pad=False, normalize=False):
r"""Encodes :math:`2^n` features into the amplitude vector of :math:`n` qubits.
If the total number of features to embed are less than the :math:`2^n` available amplitudes,
non-informative constants (zeros) can be padded to ``features``. To enable this, the argument
``pad`` should be set to ``True``.
The L2-norm of ``features`` must be one. By default, AmplitudeEmbedding expects a normalized
feature vector. The argument ``normalize`` can be set to ``True`` to automatically normalize it.
.. note::
AmplitudeEmbedding uses PennyLane's :class:`~pennylane.ops.QubitStateVector` and only works in conjunction with
devices that implement this function.
Args:
features (array): input array of shape ``(2**n,)``
wires (Sequence[int]): sequence of qubit indices that the template acts on
pad (Boolean): controls the activation of the padding option
normalize (Boolean): controls the activation of automatic normalization
"""
if not isinstance(wires, Iterable):
raise ValueError(
"Wires needs to be a list of wires that the embedding uses; got {}."
.format(wires))
n_features = len(features)
n_amplitudes = 2**len(wires)
if n_amplitudes < n_features:
raise ValueError(
"AmplitudeEmbedding requires the size of feature vector to be smaller than or equal to 2**len(wires), which is {}; "
"got {}.".format(n_amplitudes, n_features))
if pad and n_amplitudes >= n_features:
features = np.pad(features, (0, n_amplitudes - n_features), 'constant')
if not pad and n_amplitudes != n_features:
raise ValueError(
"AmplitudeEmbedding with no padding requires a feature vector of size 2**len(wires), which is {}; "
"got {}.".format(n_amplitudes, n_features))
if normalize and np.linalg.norm(features, 2) != 1:
features = features * (1 / np.linalg.norm(features, 2))
if not normalize and np.linalg.norm(features, 2) != 1:
raise ValueError(
"AmplitudeEmbedding requires a normalized feature vector. The argument normalize can be set to True to automatically normalize it."
)
QubitStateVector(features, wires=wires)
def AmplitudeEmbedding(features, wires, pad=None, normalize=False):
r"""Encodes :math:`2^n` features into the amplitude vector of :math:`n` qubits.
By setting ``pad`` 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 node.
.. note::
``AmplitudeEmbedding`` 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.
.. warning::
``AmplitudeEmbedding`` 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 argument cannot be computed by PennyLane.
Args:
features (array): input array of shape ``(2^n,)``
wires (Sequence[int] or int): :math:`n` qubit indices that the template acts on
pad (float or complex): if not None, the input is padded with this constant to size :math:`2^n`
normalize (Boolean): controls the activation of automatic normalization
Raises:
ValueError: if inputs do not have the correct format
.. UsageDetails::
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
from pennylane.templates import AmplitudeEmbedding
dev = qml.device('default.qubit', wires=2)
@qml.qnode(dev)
def circuit(f=None):
AmplitudeEmbedding(features=f, wires=range(2))
return qml.expval(qml.PauliZ(0))
circuit(f=[1/2, 1/2, 1/2, 1/2])
Checking the final state of the device, we find that it is 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]
**Passing features as positional arguments to a quantum node**
The ``features`` argument of ``AmplitudeEmbedding`` can in principle also be passed to the quantum node
as a positional argument:
.. code-block:: python
@qml.qnode(dev)
def circuit(f):
AmplitudeEmbedding(features=f, wires=range(2))
return qml.expval(qml.PauliZ(0))
However, due to non-trivial classical processing to construct the state preparation circuit,
the features argument is **not differentiable**.
>>> g = qml.grad(circuit, argnum=0)
>>> g([1,1,1,1])
ValueError: Cannot differentiate wrt parameter(s) {0, 1, 2, 3}.
**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):
AmplitudeEmbedding(features=f, wires=range(2), normalize=True)
return qml.expval(qml.PauliZ(0))
circuit(f=[15, 15, 15, 15])
The re-normalized feature vector is encoded into the quantum state vector:
>>> 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`` option:
.. code-block:: python
from math import sqrt
@qml.qnode(dev)
def circuit(f=None):
AmplitudeEmbedding(features=f, wires=range(2), pad=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]
**Operations before the embedding**
On some devices, ``AmplitudeEmbedding`` must be the first operation in the quantum node.
For example, ``'default.qubit'`` complains when running the following circuit:
.. code-block:: python
dev = qml.device('default.qubit', wires=2)
@qml.qnode(dev)
def circuit(f=None):
qml.Hadamard(wires=0)
AmplitudeEmbedding(features=f, wires=range(2))
return qml.expval(qml.PauliZ(0))
>>> circuit(f=[1/2, 1/2, 1/2, 1/2])
pennylane._device.DeviceError: Operation QubitStateVector cannot be used
after other Operations have already been applied on a default.qubit device.
"""
#############
# Input checks
_check_no_variable(pad, msg="'pad' cannot be differentiable")
_check_no_variable(normalize, msg="'normalize' cannot be differentiable")
wires = _check_wires(wires)
n_amplitudes = 2**len(wires)
expected_shape = (n_amplitudes,)
if pad is None:
shape = _check_shape(features, expected_shape, msg="'features' must be of shape {}; got {}. Use the 'pad' "
"argument for automated padding."
"".format(expected_shape, _get_shape(features)))
else:
shape = _check_shape(features, expected_shape, bound='max', msg="'features' must be of shape {} or smaller "
"to be padded; got {}"
"".format(expected_shape, _get_shape(features)))
_check_type(pad, [float, complex, type(None)], msg="'pad' must be a float or complex; got {}".format(pad))
_check_type(normalize, [bool], msg="'normalize' must be a boolean; got {}".format(normalize))
###############
#############
# Preprocessing
# pad
n_features = shape[0]
if pad is not None and n_amplitudes > n_features:
features = np.pad(features, (0, n_amplitudes-n_features), mode='constant', constant_values=pad)
# normalize
if isinstance(features[0], Variable):
feature_values = [s.val for s in features]
norm = np.sum(np.abs(feature_values)**2)
else:
norm = np.sum(np.abs(features)**2)
if not np.isclose(norm, 1.0, atol=TOLERANCE, rtol=0):
if normalize or pad:
features = features/np.sqrt(norm)
else:
raise ValueError("'features' must be a vector of length 1.0; got length {}."
"Use 'normalization=True' to automatically normalize.".format(norm))
###############
features = np.array(features)
QubitStateVector(features, wires=wires)
def expand(self):
with qml.tape.QuantumTape() as tape:
QubitStateVector(self.parameters[0], wires=self.wires)
return tape
def AmplitudeEmbedding(features, wires, pad=False, normalize=False):
r"""Encodes :math:`2^n` features into the amplitude vector of :math:`n` qubits.
If the total number of features to embed are less than the :math:`2^n` available amplitudes,
non-informative constants (zeros) can be padded to ``features``. To enable this, the argument
``pad`` should be set to ``True``.
The L2-norm of ``features`` must be one. By default, AmplitudeEmbedding expects a normalized
feature vector. The argument ``normalize`` can be set to ``True`` to automatically normalize it.
.. note::
AmplitudeEmbedding uses PennyLane's :class:`~pennylane.ops.QubitStateVector` and only works in conjunction with
devices that implement this function.
Args:
features (array): input array of shape ``(2**n,)``
wires (Sequence[int]): sequence of qubit indices that the template acts on
pad (Boolean): controls the activation of the padding option
normalize (Boolean): controls the activation of automatic normalization
Raises:
ValueError: if ``features`` or ``wires`` is invalid
"""
if isinstance(wires, int):
wires = [wires]
features = np.array(features)
n_features = len(features)
n_amplitudes = 2**len(wires)
if n_amplitudes < n_features:
raise ValueError(
"AmplitudeEmbedding requires the size of feature vector to be "
"smaller than or equal to 2**len(wires), which is {}; "
"got {}.".format(n_amplitudes, n_features))
if pad and n_amplitudes >= n_features:
features = np.pad(features, (0, n_amplitudes - n_features), 'constant')
if not pad and n_amplitudes != n_features:
raise ValueError(
"AmplitudeEmbedding must get a feature vector of size 2**len(wires), "
"which is {}; got {}. Use ``pad=True`` to automatically pad the "
"features with zeros.".format(n_amplitudes, n_features))
# Get normalization
norm = 0
for f in features:
if isinstance(f, Variable):
norm += np.conj(f.val) * f.val
else:
norm += np.conj(f) * f
if not np.isclose(norm, 1):
if normalize:
features = features / np.sqrt(norm)
else:
raise ValueError(
"AmplitudeEmbedding requires a normalized feature vector. "
"Set ``normalize=True`` to automatically normalize it.")
QubitStateVector(features, wires=wires)
def AmplitudeEmbedding(features, wires, pad=None, normalize=False):
r"""Encodes :math:`2^n` features into the amplitude vector of :math:`n` qubits.
If the total number of features to embed is less than the :math:`2^n` available amplitudes,
non-informative constants (zeros) can be padded to ``features``. To enable this, the argument
``pad`` should be set to ``True``.
The L2-norm of ``features`` must be one. By default, ``AmplitudeEmbedding`` expects a normalized
feature vector. The argument ``normalize`` can be set to ``True`` to automatically normalize it.
.. warning::
``AmplitudeEmbedding`` 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 argument cannot be computed by PennyLane.
Args:
features (array): input array of shape ``(2^n,)``
wires (Sequence[int] or int): qubit indices that the template acts on
pad (float or complex): if not None, the input is padded with this constant to size :math:`2^n`
normalize (Boolean): controls the activation of automatic normalization
Raises:
ValueError: if inputs do not have the correct format
"""
#############
# Input checks
_check_no_variable([pad, normalize], ['pad', 'normalize'])
wires, n_wires = _check_wires(wires)
n_ampl = 2**n_wires
if pad is None:
msg = "AmplitudeEmbedding must get a feature vector of size 2**len(wires), which is {}. Use 'pad' " \
"argument for automated padding.".format(n_ampl)
shp = _check_shape(features, (n_ampl,), msg=msg)
else:
msg = "AmplitudeEmbedding must get a feature vector of at least size 2**len(wires) = {}.".format(n_ampl)
shp = _check_shape(features, (n_ampl,), msg=msg, bound='max')
_check_type(pad, [float, complex, type(None)])
_check_type(normalize, [bool])
###############
# Pad
n_feats = shp[0]
if pad is not None and n_ampl > n_feats:
features = np.pad(features, (0, n_ampl-n_feats), mode='constant', constant_values=pad)
# Normalize
if isinstance(features[0], Variable):
feature_values = [s.val for s in features]
norm = np.sum(np.abs(feature_values)**2)
else:
norm = np.sum(np.abs(features)**2)
if not np.isclose(norm, 1.0, atol=TOLERANCE, rtol=0):
if normalize or pad:
features = features/np.sqrt(norm)
else:
raise ValueError("Vector of features has to be normalized to 1.0, got {}."
"Use 'normalization=True' to automatically normalize.".format(norm))
features = np.array(features)
QubitStateVector(features, wires=wires)
def AmplitudeEmbedding(features,
wires,
pad_with=None,
normalize=False,
pad=None):
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 vector of length ``2^n``, or less if `pad_with` is specified
wires (Iterable or :class:`.wires.Wires`): Wires that the template acts on.
Accepts an iterable of numbers or strings, or a Wires object.
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
pad (float or complex): same as `pad`, to be deprecated
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
from pennylane.templates import AmplitudeEmbedding
dev = qml.device('default.qubit', wires=2)
@qml.qnode(dev)
def circuit(f=None):
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 **not always differentiable**.
.. code-block:: python
from pennylane import numpy as np
@qml.qnode(dev)
def circuit(f):
AmplitudeEmbedding(features=f, wires=range(2))
return qml.expval(qml.PauliZ(0))
>>> g = qml.grad(circuit, argnum=0)
>>> f = np.array([1, 1, 1, 1], requires_grad=True)
>>> g(f)
ValueError: Cannot differentiate wrt parameter(s) {0, 1, 2, 3}.
**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):
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):
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]
**Operations before the embedding**
On some devices, ``AmplitudeEmbedding`` must be the first operation in the quantum node.
For example, ``'default.qubit'`` complains when running the following circuit:
.. code-block:: python
dev = qml.device('default.qubit', wires=2)
@qml.qnode(dev)
def circuit(f=None):
qml.Hadamard(wires=0)
AmplitudeEmbedding(features=f, wires=range(2))
return qml.expval(qml.PauliZ(0))
>>> circuit(f=[1/2, 1/2, 1/2, 1/2])
pennylane._device.DeviceError: Operation QubitStateVector cannot be used
after other Operations have already been applied on a default.qubit device.
"""
wires = Wires(wires)
# pad is replaced with the more verbose pad_with
if pad is not None:
warnings.warn(
"The pad argument will be replaced by the pad_with option in future versions of PennyLane.",
PendingDeprecationWarning,
)
if pad_with is None:
pad_with = pad
features = _preprocess(features, wires, pad_with, normalize)
QubitStateVector(features, wires=wires)