qml.templates.layers.SimplifiedTwoDesign¶

class
SimplifiedTwoDesign
(initial_layer_weights, weights, wires, do_queue=True)[source]¶ Bases:
pennylane.operation.Operation
Layers consisting of a simplified 2design architecture of PauliY rotations and controlledZ entanglers proposed in Cerezo et al. (2020).
A 2design is an ensemble of unitaries whose statistical properties are the same as sampling random unitaries with respect to the Haar measure up to the first 2 moments.
The template is not a strict 2design, since it does not consist of universal 2qubit gates as building blocks, but has been shown in Cerezo et al. (2020) to exhibit important properties to study “barren plateaus” in quantum optimization landscapes.
The template starts with an initial layer of single qubit PauliY rotations, before the main \(L\) layers are applied. The basic building block of the main layers are controlledZ entanglers followed by a pair of PauliY rotation gates (one for each wire). Each layer consists of an “even” part whose entanglers start with the first qubit, and an “odd” part that starts with the second qubit.
This is an example of two layers, including the initial layer:
The argument
initial_layer_weights
contains the rotation angles of the initial layer of PauliY rotations, whileweights
contains the pairs of PauliY rotation angles of the respective layers. Each layer takes \(\lfloor M/2 \rfloor + \lfloor (M1)/2 \rfloor = M1\) pairs of angles, where \(M\) is the number of wires. The number of layers \(L\) is derived from the first dimension ofweights
. Parameters
initial_layer_weights (tensor_like) – weight tensor for the initial rotation block, shape
(M,)
weights (tensor_like) – tensor of rotation angles for the layers, shape
(L, M1, 2)
wires (Iterable) – wires that the template acts on
Usage Details
template  here shown for two layers  is used inside a
QNode
:import pennylane as qml from pennylane.templates import SimplifiedTwoDesign from math import pi n_wires = 3 dev = qml.device('default.qubit', wires=n_wires) @qml.qnode(dev) def circuit(init_weights, weights): SimplifiedTwoDesign(initial_layer_weights=init_weights, weights=weights, wires=range(n_wires)) return [qml.expval(qml.PauliZ(wires=i)) for i in range(n_wires)] init_weights = [pi, pi, pi] weights_layer1 = [[0., pi], [0., pi]] weights_layer2 = [[pi, 0.], [pi, 0.]] weights = [weights_layer1, weights_layer2] >>> circuit(init_weights, weights) [1., 1., 1.]
Parameter shapes
A list of shapes for the two weights arguments can be computed with the static method
shape()
and used when creating randomly initialised weight tensors:shapes = SimplifiedTwoDesign.shape(n_layers=2, n_wires=2) weights = [np.random.random(size=shape) for shape in shapes]
Attributes
Get base name of the operator.
Eigenvalues of an instantiated operator.
Generator of the operation.
Gradient computation method.
Gradient recipe for the parametershift method.
Boolean determining if the inverse of the operation was requested.
Matrix representation of an instantiated operator in the computational basis.
Get and set the name of the operator.
Current parameter values.
Wires of this operator.

base_name
¶ Get base name of the operator.

eigvals
¶

generator
¶ Generator of the operation.
A length2 list
[generator, scaling_factor]
, wheregenerator
is an existing PennyLane operation class or \(2\times 2\) Hermitian array that acts as the generator of the current operationscaling_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
¶ Gradient computation method.
'A'
: analytic differentiation using the parametershift method.'F'
: finite difference numerical differentiation.None
: the operation may not be differentiated.
Default is
'F'
, orNone
if the Operation has zero parameters.

grad_recipe
= None¶ Gradient recipe for the parametershift 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
= 2¶

num_wires
= 1¶

par_domain
= 'A'¶

parameters
¶ Current parameter values.

string_for_inverse
= '.inv'¶
Methods
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.
expand
()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.
inv
()Inverts the operation, such that the inverse will be used for the computations by the specific device.
queue
()Append the operator to the Operator queue.
shape
(n_layers, n_wires)Returns a list of shapes for the 2 parameter tensors.

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
The adjointed operation.

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

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.
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