# qml.templates.layers.BasicEntanglerLayers¶

class BasicEntanglerLayers(weights, wires=None, rotation=None, do_queue=True)[source]

Layers consisting of one-parameter single-qubit rotations on each qubit, followed by a closed chain or ring of CNOT gates.

The ring of CNOT gates connects every qubit with its neighbour, with the last qubit being considered as a neighbour to the first qubit.

The number of layers $$L$$ is determined by the first dimension of the argument weights. When using a single wire, the template only applies the single qubit gates in each layer.

Note

This template follows the convention of dropping the entanglement between the last and the first qubit when using only two wires, so the entangler is not repeated on the same wires. In this case, only one CNOT gate is applied in each layer:

Parameters
• weights (tensor_like) – Weight tensor of shape (L, len(wires)). Each weight is used as a parameter for the rotation.

• wires (Iterable) – wires that the template acts on

• rotation (pennylane.ops.Operation) – one-parameter single-qubit gate to use, if None, RX is used as default

Raises

ValueError – if inputs do not have the correct format

The template is used inside a qnode:

import pennylane as qml
from pennylane.templates import BasicEntanglerLayers
from math import pi

n_wires = 3
dev = qml.device('default.qubit', wires=n_wires)

@qml.qnode(dev)
def circuit(weights):
BasicEntanglerLayers(weights=weights, wires=range(n_wires))
return [qml.expval(qml.PauliZ(wires=i)) for i in range(n_wires)]

>>> circuit([[pi, pi, pi]])
[1., 1., -1.]


Parameter shape

The shape of the weights argument can be computed by the static method shape() and used when creating randomly initialised weight tensors:

shape = BasicEntanglerLayers.shape(n_layers=2, n_wires=2)
weights = np.random.random(size=shape)


No periodic boundary for two wires

When using two wires, the convention is to drop the periodic boundary condition. This means that the connection from the second to the first wire is omitted.

n_wires = 2
dev = qml.device('default.qubit', wires=n_wires)

@qml.qnode(dev)
def circuit(weights):
BasicEntanglerLayers(weights=weights, wires=range(n_wires))
return [qml.expval(qml.PauliZ(wires=i)) for i in range(n_wires)]

>>> circuit([[pi, pi]])
[-1, 1]


Changing the rotation gate

Any single-qubit gate can be used as a rotation gate, as long as it only takes a single parameter. The default is the RX gate.

@qml.qnode(dev)
def circuit(weights):
BasicEntanglerLayers(weights=weights, wires=range(n_wires), rotation=qml.RZ)
return [qml.expval(qml.PauliZ(wires=i)) for i in range(n_wires)]


Accidentally using a gate that expects more parameters throws a ValueError: Wrong number of parameters.

 base_name Get base name of the operator. eigvals Eigenvalues of an instantiated operator. generator Generator of the operation. grad_method Gradient computation method. grad_recipe Gradient recipe for the parameter-shift method. inverse Boolean determining if the inverse of the operation was requested. matrix Matrix representation of an instantiated operator in the computational basis. name Get and set the name of the operator. num_params num_wires par_domain parameters Current parameter values. string_for_inverse wires Wires of this operator.
base_name

Get base name of the operator.

eigvals
generator

Generator of the operation.

A length-2 list [generator, scaling_factor], where

• generator is an existing PennyLane operation class or $$2\times 2$$ Hermitian array that acts as the generator of the current operation

• scaling_factor represents a scaling factor applied to the generator operation

For example, if $$U(\theta)=e^{i0.7\theta \sigma_x}$$, then $$\sigma_x$$, with scaling factor $$s$$, is the generator of operator $$U(\theta)$$:

generator = [PauliX, 0.7]


Default is [None, 1], indicating the operation has no generator.

grad_method

• 'A': analytic differentiation using the parameter-shift method.

• 'F': finite difference numerical differentiation.

• None: the operation may not be differentiated.

Default is 'F', or None if the Operation has zero parameters.

grad_recipe = None

Gradient recipe for the parameter-shift method.

This is a tuple with one nested list per operation parameter. For parameter $$\phi_k$$, the nested list contains elements of the form $$[c_i, a_i, s_i]$$ where $$i$$ is the index of the term, resulting in a gradient recipe of

$\frac{\partial}{\partial\phi_k}f = \sum_{i} c_i f(a_i \phi_k + s_i).$

If None, the default gradient recipe containing the two terms $$[c_0, a_0, s_0]=[1/2, 1, \pi/2]$$ and $$[c_1, a_1, s_1]=[-1/2, 1, -\pi/2]$$ is assumed for every parameter.

Type

tuple(Union(list[list[float]], None)) or None

inverse

Boolean determining if the inverse of the operation was requested.

matrix
name

Get and set the name of the operator.

num_params = 1
num_wires = -1
par_domain = 'A'
parameters

Current parameter values.

string_for_inverse = '.inv'
wires

Wires of this operator.

Returns

wires

Return type

Wires

 adjoint([do_queue]) Create an operation that is the adjoint of this one. decomposition(*params, wires) Returns a template decomposing the operation into other quantum operations. Returns a tape containing the decomposed operations, rather than a list. get_parameter_shift(idx[, shift]) Multiplier and shift for the given parameter, based on its gradient recipe. Inverts the operation, such that the inverse will be used for the computations by the specific device. Append the operator to the Operator queue. shape(n_layers, n_wires) Returns the shape of the weight tensor required for this template.
adjoint(do_queue=False)

Create an operation that is the adjoint of this one.

Adjointed operations are the conjugated and transposed version of the original operation. Adjointed ops are equivalent to the inverted operation for unitary gates.

Parameters

do_queue – Whether to add the adjointed gate to the context queue.

Returns

static decomposition(*params, wires)

Returns a template decomposing the operation into other quantum operations.

expand()[source]

Returns a tape containing the decomposed operations, rather than a list.

Returns

Returns a quantum tape that contains the operations decomposition, or if not implemented, simply the operation itself.

Return type

JacobianTape

get_parameter_shift(idx, shift=1.5707963267948966)

Multiplier and shift for the given parameter, based on its gradient recipe.

Parameters

idx (int) – parameter index

Returns

multiplier, shift

Return type

float, float

inv()

Inverts the operation, such that the inverse will be used for the computations by the specific device.

This method concatenates a string to the name of the operation, to indicate that the inverse will be used for computations.

Any subsequent call of this method will toggle between the original operation and the inverse of the operation.

Returns

operation to be inverted

Return type

Operator

queue()

Append the operator to the Operator queue.

static shape(n_layers, n_wires)[source]

Returns the shape of the weight tensor required for this template.

Parameters
• n_layers (int) – number of layers

• n_wires (int) – number of qubits

Returns

shape

Return type

tuple[int]