def cv_neural_net_layer(theta_1, phi_1, varphi_1, r, phi_r, theta_2, phi_2, varphi_2, a, phi_a, k, wires):
r"""A single continuous-variable neural network layer.
The layer acts on the :math:`M` wires modes specified in ``wires``, and includes interferometers
of :math:`K=M(M-1)/2` beamsplitters.
Args:
theta_1 (array[float]): length :math:`(K, )` array of transmittivity angles for first interferometer
phi_1 (array[float]): length :math:`(K, )` array of phase angles for first interferometer
varphi_1 (array[float]): length :math:`(M, )` array of rotation angles to apply after first interferometer
r (array[float]): length :math:`(M, )` array of squeezing amounts for
:class:`~pennylane.ops.Squeezing` operations
phi_r (array[float]): length :math:`(M, )` array of squeezing angles for
:class:`~pennylane.ops.Squeezing` operations
theta_2 (array[float]): length :math:`(K, )` array of transmittivity angles for second interferometer
phi_2 (array[float]): length :math:`(K, )` array of phase angles for second interferometer
varphi_2 (array[float]): length :math:`(M, )` array of rotation angles to apply after second interferometer
a (array[float]): length :math:`(M, )` array of displacement magnitudes for
:class:`~pennylane.ops.Displacement` operations
phi_a (array[float]): length :math:`(M, )` array of displacement angles for
:class:`~pennylane.ops.Displacement` operations
k (array[float]): length :math:`(M, )` array of kerr parameters for :class:`~pennylane.ops.Kerr` operations
wires (Sequence[int]): sequence of mode indices that the template acts on
"""
Interferometer(theta=theta_1, phi=phi_1, varphi=varphi_1, wires=wires)
for i, wire in enumerate(wires):
Squeezing(r[i], phi_r[i], wires=wire)
Interferometer(theta=theta_2, phi=phi_2, varphi=varphi_2, wires=wires)
for i, wire in enumerate(wires):
Displacement(a[i], phi_a[i], wires=wire)
for i, wire in enumerate(wires):
Kerr(k[i], wires=wire)
def test_three_mode(self, tol):
"""Test that a three mode interferometer using either mesh gives the correct gates"""
N = 3
wires = range(N)
theta = [0.321, 0.4523, 0.21321]
phi = [0.234, 0.324, 0.234]
varphi = [0.42342, 0.234, 0.1121]
with qml.utils.OperationRecorder() as rec_rect:
Interferometer(theta, phi, varphi, wires=wires)
with qml.utils.OperationRecorder() as rec_tria:
Interferometer(theta, phi, varphi, wires=wires)
for rec in [rec_rect, rec_tria]:
# test both meshes (both give identical results for the 3 mode case).
assert len(rec.queue) == 6
expected_bs_wires = [[0, 1], [1, 2], [0, 1]]
for idx, op in enumerate(rec_rect.queue[:3]):
assert isinstance(op, qml.Beamsplitter)
assert op.parameters == [theta[idx], phi[idx]]
assert op.wires == expected_bs_wires[idx]
for idx, op in enumerate(rec.queue[3:]):
assert isinstance(op, qml.Rotation)
assert op.parameters == [varphi[idx]]
assert op.wires == [idx]
def cv_neural_net_layer(
theta_1,
phi_1,
varphi_1,
r,
phi_r,
theta_2,
phi_2,
varphi_2,
a,
phi_a,
k,
wires):
# unitary transformation
Interferometer(theta=theta_1, phi=phi_1, varphi=varphi_1, wires=wires)
# scaling
broadcast(unitary=Squeezing, pattern="single", wires=wires, parameters=list(zip(r, phi_r)))
# unitary transformation
Interferometer(theta=theta_2, phi=phi_2, varphi=varphi_2, wires=wires)
# bias
broadcast(unitary=Displacement, pattern="single", wires=wires, parameters=list(zip(a, phi_a)))
# non-linearity
broadcast(unitary=Kerr, pattern="single", wires=wires, parameters=k)
def test_clements_beamsplitter_convention(self, tol):
"""test the beamsplitter convention"""
N = 2
wires = range(N)
theta = [0.321]
phi = [0.234]
varphi = [0.42342, 0.1121]
with qml.utils.OperationRecorder() as rec_rect:
Interferometer(theta, phi, varphi, mesh='rectangular', beamsplitter='clements', wires=wires)
with qml.utils.OperationRecorder() as rec_tria:
Interferometer(theta, phi, varphi, mesh='triangular', beamsplitter='clements', wires=wires)
for rec in [rec_rect, rec_tria]:
assert len(rec.queue) == 4
assert isinstance(rec.queue[0], qml.Rotation)
assert rec.queue[0].parameters == phi
assert isinstance(rec.queue[1], qml.Beamsplitter)
assert rec.queue[1].parameters == [theta[0], 0]
assert isinstance(rec.queue[2], qml.Rotation)
assert rec.queue[2].parameters == [varphi[0]]
assert isinstance(rec.queue[3], qml.Rotation)
assert rec.queue[3].parameters == [varphi[1]]
def CVNeuralNetLayer(theta_1, phi_1, varphi_1, r, phi_r, theta_2, phi_2,
varphi_2, a, phi_a, k, wires):
r"""A layer of interferometers, displacement and squeezing gates mimicking a neural network,
as well as a Kerr gate nonlinearity.
The layer acts on the :math:`M` wires modes specified in ``wires``, and includes interferometers
of :math:`K=M(M-1)/2` beamsplitters.
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:`(K, )` array of transmittivity angles for first interferometer
phi_1 (array[float]): length :math:`(K, )` array of phase angles for first interferometer
varphi_1 (array[float]): length :math:`(M, )` array of rotation angles to apply after first interferometer
r (array[float]): length :math:`(M, )` array of squeezing amounts for :class:`~pennylane.ops.Squeezing` operations
phi_r (array[float]): length :math:`(M, )` array of squeezing angles for :class:`~pennylane.ops.Squeezing` operations
theta_2 (array[float]): length :math:`(K, )` array of transmittivity angles for second interferometer
phi_2 (array[float]): length :math:`(K, )` array of phase angles for second interferometer
varphi_2 (array[float]): length :math:`(M, )` array of rotation angles to apply after second interferometer
a (array[float]): length :math:`(M, )` array of displacement magnitudes for :class:`~pennylane.ops.Displacement` operations
phi_a (array[float]): length :math:`(M, )` array of displacement angles for :class:`~pennylane.ops.Displacement` operations
k (array[float]): length :math:`(M, )` array of kerr parameters for :class:`~pennylane.ops.Kerr` operations
wires (Sequence[int]): sequence of mode indices that the template acts on
"""
Interferometer(theta=theta_1, phi=phi_1, varphi=varphi_1, wires=wires)
for i, wire in enumerate(wires):
Squeezing(r[i], phi_r[i], wires=wire)
Interferometer(theta=theta_2, phi=phi_2, varphi=varphi_2, wires=wires)
for i, wire in enumerate(wires):
Displacement(a[i], phi_a[i], wires=wire)
for i, wire in enumerate(wires):
Kerr(k[i], wires=wire)
def circuit(varphi, bs=None):
Interferometer(theta=[],
phi=[],
varphi=varphi,
beamsplitter=bs,
wires=0)
return qml.expval(qml.NumberOperator(0))
def test_four_mode_triangular(self, tol):
"""Test that a 4 mode interferometer using triangular mesh gives the correct gates"""
N = 4
wires = range(N)
theta = [0.321, 0.4523, 0.21321, 0.123, 0.5234, 1.23]
phi = [0.234, 0.324, 0.234, 1.453, 1.42341, -0.534]
varphi = [0.42342, 0.234, 0.4523, 0.1121]
with qml.utils.OperationRecorder() as rec:
Interferometer(theta, phi, varphi, mesh='triangular', wires=wires)
assert len(rec.queue) == 10
expected_bs_wires = [[2, 3], [1, 2], [0, 1], [2, 3], [1, 2], [2, 3]]
for idx, op in enumerate(rec.queue[:6]):
assert isinstance(op, qml.Beamsplitter)
assert op.parameters == [theta[idx], phi[idx]]
assert op.wires == expected_bs_wires[idx]
for idx, op in enumerate(rec.queue[6:]):
assert isinstance(op, qml.Rotation)
assert op.parameters == [varphi[idx]]
assert op.wires == [idx]
def cv_neural_net_layer(theta_1, phi_1, varphi_1, r, phi_r, theta_2, phi_2,
varphi_2, a, phi_a, k, wires):
Interferometer(theta=theta_1, phi=phi_1, varphi=varphi_1, wires=wires)
broadcast(unitary=Squeezing,
pattern="single",
wires=wires,
parameters=list(zip(r, phi_r)))
Interferometer(theta=theta_2, phi=phi_2, varphi=varphi_2, wires=wires)
broadcast(unitary=Displacement,
pattern="single",
wires=wires,
parameters=list(zip(a, phi_a)))
broadcast(unitary=Kerr, pattern="single", wires=wires, parameters=k)
def test_one_mode(self, tol):
"""Test that a one mode interferometer correctly gives a rotation gate"""
varphi = [0.42342]
with qml.utils.OperationRecorder() as rec:
Interferometer(theta=[], phi=[], varphi=varphi, wires=0)
assert len(rec.queue) == 1
assert isinstance(rec.queue[0], qml.Rotation)
assert np.allclose(rec.queue[0].parameters, varphi, atol=tol)
def cv_neural_net_layer(theta_1, phi_1, varphi_1, r, phi_r, theta_2, phi_2,
varphi_2, a, phi_a, k, wires):
r"""A single continuous-variable neural network layer.
The layer acts on the :math:`M` wires modes specified in ``wires``, and includes interferometers
of :math:`K=M(M-1)/2` beamsplitters.
Args:
theta_1 (tensor_like): shape :math:`(K, )` tensor of transmittivity angles for first interferometer
phi_1 (tensor_like): shape :math:`(K, )` tensor of phase angles for first interferometer
varphi_1 (tensor_like): shape :math:`(M, )` tensor of rotation angles to apply after first interferometer
r (tensor_like): shape :math:`(M, )` tensor of squeezing amounts for
:class:`~pennylane.ops.Squeezing` operations
phi_r (tensor_like): shape :math:`(M, )` tensor of squeezing angles for
:class:`~pennylane.ops.Squeezing` operations
theta_2 (tensor_like): shape :math:`(K, )` tensor of transmittivity angles for second interferometer
phi_2 (tensor_like): shape :math:`(K, )` tensor of phase angles for second interferometer
varphi_2 (tensor_like): shape :math:`(M, )` tensor of rotation angles to apply after second interferometer
a (tensor_like): shape :math:`(M, )` tensor of displacement magnitudes for
:class:`~pennylane.ops.Displacement` operations
phi_a (tensor_like): shape :math:`(M, )` tensor of displacement angles for
:class:`~pennylane.ops.Displacement` operations
k (tensor_like): shape :math:`(M, )` tensor of kerr parameters for :class:`~pennylane.ops.Kerr` operations
wires (Wires): wires that the template acts on
"""
Interferometer(theta=theta_1, phi=phi_1, varphi=varphi_1, wires=wires)
broadcast(unitary=Squeezing,
pattern="single",
wires=wires,
parameters=list(zip(r, phi_r)))
Interferometer(theta=theta_2, phi=phi_2, varphi=varphi_2, wires=wires)
broadcast(unitary=Displacement,
pattern="single",
wires=wires,
parameters=list(zip(a, phi_a)))
broadcast(unitary=Kerr, pattern="single", wires=wires, parameters=k)
def test_two_mode_rect(self, tol):
"""Test that a two mode interferometer using the rectangular mesh
correctly gives a beamsplitter+rotation gate"""
N = 2
wires = range(N)
theta = [0.321]
phi = [0.234]
varphi = [0.42342, 0.1121]
with qml.utils.OperationRecorder() as rec:
Interferometer(theta, phi, varphi, wires=wires)
isinstance(rec.queue[0], qml.Beamsplitter)
assert rec.queue[0].parameters == theta + phi
assert isinstance(rec.queue[1], qml.Rotation)
assert rec.queue[1].parameters == [varphi[0]]
assert isinstance(rec.queue[2], qml.Rotation)
assert rec.queue[2].parameters == [varphi[1]]
def circuit(varphi, mesh=None):
Interferometer(theta=[], phi=[], varphi=varphi, mesh=mesh, wires=0)
return qml.expval(qml.NumberOperator(0))
def circuit(theta, phi, varphi):
for w in wires:
qml.Squeezing(sq[w][0], sq[w][1], wires=w)
Interferometer(theta=theta, phi=phi, varphi=varphi, wires=wires)
return [qml.expval(qml.NumberOperator(w)) for w in wires]
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 (tensor_like): shape :math:`(L, K)` tensor of transmittivity angles for first interferometer
phi_1 (tensor_like): shape :math:`(L, K)` tensor of phase angles for first interferometer
varphi_1 (tensor_like): shape :math:`(L, M)` tensor of rotation angles to apply after first interferometer
r (tensor_like): shape :math:`(L, M)` tensor of squeezing amounts for :class:`~pennylane.ops.Squeezing` operations
phi_r (tensor_like): shape :math:`(L, M)` tensor of squeezing angles for :class:`~pennylane.ops.Squeezing` operations
theta_2 (tensor_like): shape :math:`(L, K)` tensor of transmittivity angles for second interferometer
phi_2 (tensor_like): shape :math:`(L, K)` tensor of phase angles for second interferometer
varphi_2 (tensor_like): shape :math:`(L, M)` tensor of rotation angles to apply after second interferometer
a (tensor_like): shape :math:`(L, M)` tensor of displacement magnitudes for :class:`~pennylane.ops.Displacement` operations
phi_a (tensor_like): shape :math:`(L, M)` tensor of displacement angles for :class:`~pennylane.ops.Displacement` operations
k (tensor_like): shape :math:`(L, M)` tensor of kerr parameters for :class:`~pennylane.ops.Kerr` operations
wires (Iterable or Wires): Wires that the template acts on. Accepts an iterable of numbers or strings, or
a Wires object.
Raises:
ValueError: if inputs do not have the correct format
"""
wires = Wires(wires)
repeat = _preprocess(
theta_1, phi_1, varphi_1, r, phi_r, theta_2, phi_2, varphi_2, a, phi_a, k, wires
)
for l in range(repeat):
Interferometer(theta=theta_1[l], phi=phi_1[l], varphi=varphi_1[l], wires=wires)
r_and_phi_r = qml.math.stack([r[l], phi_r[l]], axis=1)
broadcast(unitary=Squeezing, pattern="single", wires=wires, parameters=r_and_phi_r)
Interferometer(theta=theta_2[l], phi=phi_2[l], varphi=varphi_2[l], wires=wires)
a_and_phi_a = qml.math.stack([a[l], phi_a[l]], axis=1)
broadcast(unitary=Displacement, pattern="single", wires=wires, parameters=a_and_phi_a)
broadcast(unitary=Kerr, pattern="single", wires=wires, parameters=k[l])
