def test_check_shape_list_of_inputs_exception(self, inpt, target_shape,
bound):
"""Tests that list version of shape check succeeds for valid arguments."""
with pytest.raises(ValueError, match="XXX"):
_check_shapes(inpt,
target_shape,
bounds=[bound] * len(inpt),
msg="XXX")
def CVNeuralNetLayers(theta_1, phi_1, varphi_1, r, phi_r, theta_2, phi_2,
varphi_2, a, phi_a, k, wires):
r"""A sequence of layers of a continuous-variable quantum neural network,
as specified in `arXiv:1806.06871 <https://arxiv.org/abs/1806.06871>`_.
The layer consists
of interferometers, displacement and squeezing gates mimicking the linear transformation of
a neural network in the x-basis of the quantum system, and uses a Kerr gate
to introduce a 'quantum' nonlinearity.
The layers act on the :math:`M` modes given in ``wires``,
and include interferometers of :math:`K=M(M-1)/2` beamsplitters. The different weight parameters
contain the weights for each layer. The number of layers :math:`L` is therefore derived
from the first dimension of ``weights``.
This example shows a 4-mode CVNeuralNet layer with squeezing gates :math:`S`, displacement gates :math:`D` and
Kerr gates :math:`K`. The two big blocks are interferometers of type
:mod:`pennylane.templates.layers.Interferometer`:
.. figure:: ../../_static/layer_cvqnn.png
:align: center
:width: 60%
:target: javascript:void(0);
.. note::
The CV neural network architecture includes :class:`~pennylane.ops.Kerr` operations.
Make sure to use a suitable device, such as the :code:`strawberryfields.fock`
device of the `PennyLane-SF <https://github.com/XanaduAI/pennylane-sf>`_ plugin.
Args:
theta_1 (array[float]): length :math:`(L, K)` array of transmittivity angles for first interferometer
phi_1 (array[float]): length :math:`(L, K)` array of phase angles for first interferometer
varphi_1 (array[float]): length :math:`(L, M)` array of rotation angles to apply after first interferometer
r (array[float]): length :math:`(L, M)` array of squeezing amounts for :class:`~pennylane.ops.Squeezing` operations
phi_r (array[float]): length :math:`(L, M)` array of squeezing angles for :class:`~pennylane.ops.Squeezing` operations
theta_2 (array[float]): length :math:`(L, K)` array of transmittivity angles for second interferometer
phi_2 (array[float]): length :math:`(L, K)` array of phase angles for second interferometer
varphi_2 (array[float]): length :math:`(L, M)` array of rotation angles to apply after second interferometer
a (array[float]): length :math:`(L, M)` array of displacement magnitudes for :class:`~pennylane.ops.Displacement` operations
phi_a (array[float]): length :math:`(L, M)` array of displacement angles for :class:`~pennylane.ops.Displacement` operations
k (array[float]): length :math:`(L, M)` array of kerr parameters for :class:`~pennylane.ops.Kerr` operations
wires (Sequence[int]): sequence of mode indices that the template acts on
Raises:
ValueError: if inputs do not have the correct format
"""
#############
# Input checks
wires, n_wires = _check_wires(wires)
n_if = n_wires * (n_wires - 1) // 2
weights_list = [
theta_1, phi_1, varphi_1, r, phi_r, theta_2, phi_2, varphi_2, a, phi_a,
k
]
repeat = _check_number_of_layers(weights_list)
shapes_list = [(repeat, n_if), (repeat, n_if), (repeat, n_wires),
(repeat, n_wires), (repeat, n_wires), (repeat, n_if),
(repeat, n_if), (repeat, n_wires), (repeat, n_wires),
(repeat, n_wires), (repeat, n_wires)]
_check_shapes(weights_list, shapes_list)
_check_type(repeat, [int])
###############
for l in range(repeat):
_cv_neural_net_layer(theta_1=theta_1[l],
phi_1=phi_1[l],
varphi_1=varphi_1[l],
r=r[l],
phi_r=phi_r[l],
theta_2=theta_2[l],
phi_2=phi_2[l],
varphi_2=varphi_2[l],
a=a[l],
phi_a=phi_a[l],
k=k[l],
wires=wires)
def Interferometer(theta,
phi,
varphi,
wires,
mesh="rectangular",
beamsplitter="pennylane"):
r"""General linear interferometer, an array of beamsplitters and phase shifters.
For :math:`M` wires, the general interferometer is specified by
providing :math:`M(M-1)/2` transmittivity angles :math:`\theta` and the same number of
phase angles :math:`\phi`, as well as :math:`M-1` additional rotation
parameters :math:`\varphi`.
By specifying the keyword argument ``mesh``, the scheme used to implement the interferometer
may be adjusted:
* ``mesh='rectangular'`` (default): uses the scheme described in
`Clements et al. <https://dx.doi.org/10.1364/OPTICA.3.001460>`__, resulting in a *rectangular* array of
:math:`M(M-1)/2` beamsplitters arranged in :math:`M` slices and ordered from left
to right and top to bottom in each slice. The first beamsplitter acts on
wires :math:`0` and :math:`1`:
.. figure:: ../../_static/clements.png
:align: center
:width: 30%
:target: javascript:void(0);
* ``mesh='triangular'``: uses the scheme described in `Reck et al. <https://dx.doi.org/10.1103/PhysRevLett.73.58>`__,
resulting in a *triangular* array of :math:`M(M-1)/2` beamsplitters arranged in
:math:`2M-3` slices and ordered from left to right and top to bottom. The
first and fourth beamsplitters act on wires :math:`M-1` and :math:`M`, the second
on :math:`M-2` and :math:`M-1`, and the third on :math:`M-3` and :math:`M-2`, and
so on.
.. figure:: ../../_static/reck.png
:align: center
:width: 30%
:target: javascript:void(0);
In both schemes, the network of :class:`~pennylane.ops.Beamsplitter` operations is followed by
:math:`M` local :class:`~pennylane.ops.Rotation` Operations.
The rectangular decomposition is generally advantageous, as it has a lower
circuit depth (:math:`M` vs :math:`2M-3`) and optical depth than the triangular
decomposition, resulting in reduced optical loss.
This is an example of a 4-mode interferometer with beamsplitters :math:`B` and rotations :math:`R`,
using ``mesh='rectangular'``:
.. figure:: ../../_static/layer_interferometer.png
:align: center
:width: 60%
:target: javascript:void(0);
.. note::
The decomposition as formulated in `Clements et al. <https://dx.doi.org/10.1364/OPTICA.3.001460>`__ uses a different
convention for a beamsplitter :math:`T(\theta, \phi)` than PennyLane, namely:
.. math:: T(\theta, \phi) = BS(\theta, 0) R(\phi)
For the universality of the decomposition, the used convention is irrelevant, but
for a given set of angles the resulting interferometers will be different.
If an interferometer consistent with the convention from `Clements et al. <https://dx.doi.org/10.1364/OPTICA.3.001460>`__
is needed, the optional keyword argument ``beamsplitter='clements'`` can be specified. This
will result in each :class:`~pennylane.ops.Beamsplitter` being preceded by a :class:`~pennylane.ops.Rotation` and
thus increase the number of elementary operations in the circuit.
Args:
theta (array): length :math:`M(M-1)/2` array of transmittivity angles :math:`\theta`
phi (array): length :math:`M(M-1)/2` array of phase angles :math:`\phi`
varphi (array): length :math:`M` array of rotation angles :math:`\varphi`
wires (Sequence[int]): wires the interferometer should act on
mesh (string): the type of mesh to use
beamsplitter (str): if ``clements``, the beamsplitter convention from
Clements et al. 2016 (https://dx.doi.org/10.1364/OPTICA.3.001460) is used; if ``pennylane``, the
beamsplitter is implemented via PennyLane's ``Beamsplitter`` operation.
Raises:
ValueError: if inputs do not have the correct format
"""
#############
# Input checks
_check_no_variable(beamsplitter,
msg="'beamsplitter' cannot be differentiable")
_check_no_variable(mesh, msg="'mesh' cannot be differentiable")
wires = _check_wires(wires)
weights_list = [theta, phi, varphi]
n_wires = len(wires)
n_if = n_wires * (n_wires - 1) // 2
expected_shapes = [(n_if, ), (n_if, ), (n_wires, )]
_check_shapes(weights_list,
expected_shapes,
msg="wrong shape of weight input(s) detected")
_check_is_in_options(
beamsplitter,
["clements", "pennylane"],
msg="did not recognize option {} for 'beamsplitter'"
"".format(beamsplitter),
)
_check_is_in_options(
mesh,
["triangular", "rectangular"],
msg="did not recognize option {} for 'mesh'"
"".format(mesh),
)
###############
M = len(wires)
if M == 1:
# the interferometer is a single rotation
Rotation(varphi[0], wires=wires[0])
return
n = 0 # keep track of free parameters
if mesh == "rectangular":
# Apply the Clements beamsplitter array
# The array depth is N
for l in range(M):
for k, (w1, w2) in enumerate(zip(wires[:-1], wires[1:])):
# skip even or odd pairs depending on layer
if (l + k) % 2 != 1:
if beamsplitter == "clements":
Rotation(phi[n], wires=[w1])
Beamsplitter(theta[n], 0, wires=[w1, w2])
else:
Beamsplitter(theta[n], phi[n], wires=[w1, w2])
n += 1
elif mesh == "triangular":
# apply the Reck beamsplitter array
# The array depth is 2*N-3
for l in range(2 * M - 3):
for k in range(abs(l + 1 - (M - 1)), M - 1, 2):
if beamsplitter == "clements":
Rotation(phi[n], wires=[wires[k]])
Beamsplitter(theta[n], 0, wires=[wires[k], wires[k + 1]])
else:
Beamsplitter(theta[n],
phi[n],
wires=[wires[k], wires[k + 1]])
n += 1
# apply the final local phase shifts to all modes
for i, p in enumerate(varphi):
Rotation(p, wires=[wires[i]])
def test_check_shape_list_of_inputs(self, inpt, target_shape, bound):
"""Tests that list version of shape check succeeds for valid arguments."""
_check_shapes(inpt, target_shape, bounds=[bound]*len(inpt), msg="XXX")