# qml.templates.layers.StronglyEntanglingLayers¶

class StronglyEntanglingLayers(weights, wires, ranges=None, imprimitive=None, do_queue=True)[source]

Layers consisting of single qubit rotations and entanglers, inspired by the circuit-centric classifier design arXiv:1804.00633.

The argument weights contains the weights for each layer. The number of layers $$L$$ is therefore derived from the first dimension of weights.

The 2-qubit gates, whose type is specified by the imprimitive argument, act chronologically on the $$M$$ wires, $$i = 1,...,M$$. The second qubit of each gate is given by $$(i+r)\mod M$$, where $$r$$ is a hyperparameter called the range, and $$0 < r < M$$. If applied to one qubit only, this template will use no imprimitive gates.

This is an example of two 4-qubit strongly entangling layers (ranges $$r=1$$ and $$r=2$$, respectively) with rotations $$R$$ and CNOTs as imprimitives:

Note

The two-qubit gate used as the imprimitive or entangler must not depend on parameters.

Parameters
• weights (tensor_like) – weight tensor of shape (L, M, 3)

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

• ranges (Sequence[int]) – sequence determining the range hyperparameter for each subsequent layer; if None using $$r=l \mod M$$ for the $$l$$ th layer and $$M$$ wires.

• imprimitive (pennylane.ops.Operation) – two-qubit gate to use, defaults to CNOT

Parameter shape

The expected shape for the weight tensor can be computed with the static method shape() and used when creating randomly initialised weight tensors:

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

 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. id String for the ID of the operator. 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

id

String for the ID of the operator.

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 expected shape of the weights tensor.
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

list of multiplier, coefficient, shift for each term in the gradient recipe

Return type

list[[float, 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 expected shape of the weights tensor.

Parameters
• n_layers (int) – number of layers

• n_wires (int) – number of wires

Returns

shape

Return type

tuple[int]