# Source code for pennylane.templates.layers.random

```
# 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 RandomLayers 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
[docs]class RandomLayers(Operation):
r"""Layers of randomly chosen single qubit rotations and 2-qubit entangling gates, acting
on randomly chosen qubits.
.. warning::
This template uses random number generation inside qnodes. Find more
details about how to invoke the desired random behaviour in the "Usage Details" section below.
The argument ``weights`` contains the weights for each layer. The number of layers :math:`L` is therefore derived
from the first dimension of ``weights``.
The two-qubit gates of type ``imprimitive`` and the rotations are distributed randomly in the circuit.
The number of random rotations is derived from the second dimension of ``weights``. The number of
two-qubit gates is determined by ``ratio_imprim``. For example, a ratio of ``0.3`` with ``30`` rotations
will lead to the use of ``10`` two-qubit gates.
.. note::
If applied to one qubit only, this template will use no imprimitive gates.
This is an example of two 4-qubit random layers with four Pauli-Y/Pauli-Z rotations :math:`R_y, R_z`,
controlled-Z gates as imprimitives, as well as ``ratio_imprim=0.3``:
.. figure:: ../../_static/layer_rnd.png
:align: center
:width: 60%
:target: javascript:void(0);
Args:
weights (tensor_like): weight tensor of shape ``(L, k)``,
wires (Iterable): wires that the template acts on
ratio_imprim (float): value between 0 and 1 that determines the ratio of imprimitive to rotation gates
imprimitive (pennylane.ops.Operation): two-qubit gate to use, defaults to :class:`~pennylane.ops.CNOT`
rotations (tuple[pennylane.ops.Operation]): List of Pauli-X, Pauli-Y and/or Pauli-Z gates. The frequency
determines how often a particular rotation type is used. Defaults to the use of all three
rotations with equal frequency.
seed (int): seed to generate random architecture, defaults to 42
.. details::
:title: Usage Details
**Default seed**
``RandomLayers`` always uses a seed to initialize the construction of a random circuit. This means
that the template creates the same circuit every time it is called. If no seed is provided, the default
seed of ``42`` is used.
.. code-block:: python
import pennylane as qml
from pennylane import numpy as np
dev = qml.device("default.qubit", wires=2)
weights = np.array([[0.1, -2.1, 1.4]])
@qml.qnode(dev)
def circuit1(weights):
qml.RandomLayers(weights=weights, wires=range(2))
return qml.expval(qml.PauliZ(0))
@qml.qnode(dev)
def circuit2(weights):
qml.RandomLayers(weights=weights, wires=range(2))
return qml.expval(qml.PauliZ(0))
>>> np.allclose(circuit1(weights), circuit2(weights))
True
You can verify this by drawing the circuits.
>>> print(qml.draw(circuit1, expansion_strategy="device")(weights))
0: ──────────────────────╭X─╭X──RZ(1.40)─┤ <Z>
1: ──RX(0.10)──RX(-2.10)─╰●─╰●───────────┤
>>> print(qml.draw(circuit2, expansion_strategy="device")(weights))
0: ──────────────────────╭X─╭X──RZ(1.40)─┤ <Z>
1: ──RX(0.10)──RX(-2.10)─╰●─╰●───────────┤
**Changing the seed**
To change the randomly generated circuit architecture, you have to change the seed passed to the template.
For example, these two calls of ``RandomLayers`` *do not* create the same circuit:
>>> @qml.qnode(dev)
... def circuit(weights, seed=None):
... qml.RandomLayers(weights=weights, wires=range(2), seed=seed)
... return qml.expval(qml.PauliZ(0))
>>> np.allclose(circuit(weights, seed=9), circuit(weights, seed=12))
False
>>> print(qml.draw(circuit, expansion_strategy="device")(weights, seed=9))
0: ─╭X──RX(0.10)────────────┤ <Z>
1: ─╰●──RY(-2.10)──RX(1.40)─┤
>>> print(qml.draw(circuit, expansion_strategy="device")(weights, seed=12))
0: ─╭X──RZ(0.10)──╭●─╭X───────────┤ <Z>
1: ─╰●──RX(-2.10)─╰X─╰●──RZ(1.40)─┤
**Automatic creation of random circuits**
To automate the process of creating different circuits with ``RandomLayers``,
you can set ``seed=None`` to avoid specifying a seed. However, in this case care needs
to be taken. In the default setting, a quantum node is **mutable**, which means that the quantum function is
re-evaluated every time it is called. This means that the circuit is re-constructed from scratch
each time you call the qnode:
.. code-block:: python
@qml.qnode(dev)
def circuit_rnd(weights):
qml.RandomLayers(weights=weights, wires=range(2), seed=None)
return qml.expval(qml.PauliZ(0))
first_call = circuit_rnd(weights)
second_call = circuit_rnd(weights)
>>> np.allclose(first_call, second_call)
False
This can be rectified by making the quantum node **immutable**.
.. code-block:: python
@qml.qnode(dev, mutable=False)
def circuit_rnd(weights):
qml.RandomLayers(weights=weights, wires=range(2), seed=None)
return qml.expval(qml.PauliZ(0))
first_call = circuit_rnd(weights)
second_call = circuit_rnd(weights)
>>> np.allclose(first_call, second_call)
True
**Parameter shape**
The expected shape for the weight tensor can be computed with the static method
:meth:`~.RandomLayers.shape` and used when creating randomly
initialised weight tensors:
.. code-block:: python
shape = qml.RandomLayers.shape(n_layers=2, n_rotations=3)
weights = np.random.random(size=shape)
"""
num_wires = AnyWires
grad_method = None
def __init__(
self,
weights,
wires,
ratio_imprim=0.3,
imprimitive=None,
rotations=None,
seed=42,
id=None,
):
shape = qml.math.shape(weights)
if len(shape) != 2:
raise ValueError(f"Weights tensor must be 2-dimensional; got shape {shape}")
self._hyperparameters = {
"ratio_imprim": ratio_imprim,
"imprimitive": imprimitive or qml.CNOT,
"rotations": tuple(rotations) if rotations else (qml.RX, qml.RY, qml.RZ),
"seed": seed,
}
super().__init__(weights, wires=wires, id=id)
@property
def num_params(self):
return 1
[docs] @staticmethod
def compute_decomposition(
weights, wires, ratio_imprim, imprimitive, rotations, seed
): # 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:`~.RandomLayers.decomposition`.
Args:
weights (tensor_like): weight tensor
wires (Any or Iterable[Any]): wires that the operator acts on
ratio_imprim (float): value between 0 and 1 that determines the ratio of imprimitive to rotation gates
imprimitive (pennylane.ops.Operation): two-qubit gate to use
rotations (list[pennylane.ops.Operation]): List of Pauli-X, Pauli-Y and/or Pauli-Z gates.
seed (int): seed to generate random architecture
Returns:
list[.Operator]: decomposition of the operator
**Example**
>>> weights = torch.tensor([[0.1, -2.1, 1.4]])
>>> rotations=[qml.RY, qml.RX]
>>> qml.RandomLayers.compute_decomposition(weights, wires=["a", "b"], ratio_imprim=0.3,
... imprimitive=qml.CNOT, rotations=rotations, seed=42)
[RY(tensor(0.1000), wires=['b']),
RY(tensor(-2.1000), wires=['b']),
CNOT(wires=['b', 'a']),
CNOT(wires=['b', 'a']),
RX(tensor(1.4000), wires=['a'])]
"""
wires = qml.wires.Wires(wires)
rng = np.random.default_rng(seed)
shape = qml.math.shape(weights)
n_layers = qml.math.shape(weights)[0]
op_list = []
for l in range(n_layers):
i = 0
while i < shape[1]:
if rng.random() > ratio_imprim:
# apply a random rotation gate to a random wire
gate = rng.choice(rotations)
rnd_wire = wires.select_random(1, seed=rng)
op_list.append(gate(weights[l][i], wires=rnd_wire))
i += 1
else:
# apply the entangler to two random wires
if len(wires) > 1:
rnd_wires = wires.select_random(2, seed=rng)
op_list.append(imprimitive(wires=rnd_wires))
return op_list
[docs] @staticmethod
def shape(n_layers, n_rotations):
r"""Returns the expected shape of the weights tensor.
Args:
n_layers (int): number of layers
n_rotations (int): number of rotations
Returns:
tuple[int]: shape
"""
return n_layers, n_rotations
```

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