# qml.templates.embeddings.IQPEmbedding¶

class IQPEmbedding(features, wires, n_repeats=1, pattern=None, do_queue=True, id=None)[source]

Encodes $$n$$ features into $$n$$ qubits using diagonal gates of an IQP circuit.

The embedding has been proposed by Havlicek et al. (2018).

The basic IQP circuit can be repeated by specifying n_repeats. Repetitions can make the embedding “richer” through interference.

Warning

IQPEmbedding calls a circuit that involves non-trivial classical processing of the features. The features argument is therefore not differentiable when using the template, and gradients with respect to the features cannot be computed by PennyLane.

An IQP circuit is a quantum circuit of a block of Hadamards, followed by a block of gates that are diagonal in the computational basis. Here, the diagonal gates are single-qubit RZ rotations, applied to each qubit and encoding the $$n$$ features, followed by two-qubit ZZ entanglers, $$e^{-i x_i x_j \sigma_z \otimes \sigma_z}$$. The entangler applied to wires (wires[i], wires[j]) encodes the product of features features[i]*features[j]. The pattern in which the entanglers are applied is either the default, or a custom pattern:

• If pattern is not specified, the default pattern will be used, in which the entangling gates connect all pairs of neighbours:

• Else, pattern is a list of wire pairs [[a, b], [c, d],...], applying the entangler on wires [a, b], [c, d], etc. For example, pattern = [[0, 1], [1, 2]] produces the following entangler pattern:

Since diagonal gates commute, the order of the entanglers does not change the result.

Parameters
• features (tensor_like) – tensor of features to encode

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

• n_repeats (int) – number of times the basic embedding is repeated

• pattern (list[int]) – specifies the wires and features of the entanglers

Raises

ValueError – if inputs do not have the correct format

A typical usage example of the template is the following:

import pennylane as qml
from pennylane.templates import IQPEmbedding

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

@qml.qnode(dev)
def circuit(features):
IQPEmbedding(features, wires=range(3))
return [qml.expval(qml.PauliZ(w)) for w in range(3)]

circuit([1., 2., 3.])


Repeating the embedding

The embedding can be repeated by specifying the n_repeats argument:

@qml.qnode(dev)
def circuit(features):
IQPEmbedding(features, wires=range(3), n_repeats=4)
return [qml.expval(qml.PauliZ(w)) for w in range(3)]

circuit([1., 2., 3.])


Every repetition uses exactly the same quantum circuit.

Using a custom entangler pattern

A custom entangler pattern can be used by specifying the pattern argument. A pattern has to be a nested list of dimension (K, 2), where K is the number of entanglers to apply.

pattern = [[1, 2], [0, 2], [1, 0]]

@qml.qnode(dev)
def circuit(features):
IQPEmbedding(features, wires=range(3), pattern=pattern)
return [qml.expval(qml.PauliZ(w)) for w in range(3)]

circuit([1., 2., 3.])


Since diagonal gates commute, the order of the wire pairs has no effect on the result.

from pennylane import numpy as np

pattern1 = [[1, 2], [0, 2], [1, 0]]
pattern2 = [[1, 0], [0, 2], [1, 2]]  # a reshuffling of pattern1

@qml.qnode(dev)
def circuit(features, pattern):
IQPEmbedding(features, wires=range(3), pattern=pattern, n_repeats=3)
return [qml.expval(qml.PauliZ(w)) for w in range(3)]

res1 = circuit([1., 2., 3.], pattern=pattern1)
res2 = circuit([1., 2., 3.], pattern=pattern2)

assert np.allclose(res1, res2)


Non-consecutive wires

In principle, the user can also pass a non-consecutive wire list to the template. For single qubit gates, the i’th feature is applied to the i’th wire index (which may not be the i’th wire). For the entanglers, the product of i’th and j’th features is applied to the wire indices at the i’th and j’th position in wires.

For example, for wires=[2, 0, 1] the RZ block applies the first feature to wire 2, the second feature to wire 0, and the third feature to wire 1.

Likewise, using the default pattern, the entangler block applies the product of the first and second feature to the wire pair [2, 0], the product of the second and third feature to [2, 1], and so forth.

 base_name Get base name of the operator. basis The basis of an operation, or for controlled gates, of the target operation. control_wires For operations that are controlled, returns the set of control wires. 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. hash returns an integer hash uniquely representing the operator id String for the ID of the operator. inverse Boolean determining if the inverse of the operation was requested. is_composable_rotation True if composing multiple copies of the operation results in an addition (or alternative accumulation) of parameters. is_self_inverse True if the operation is its own inverse. is_symmetric_over_all_wires True if the operation is the same if you exchange the order of wires. is_symmetric_over_control_wires True if the operation is the same if you exchange the order of all but the last wire. 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. single_qubit_rot_angles The parameters required to implement a single-qubit gate as an equivalent Rot gate, up to a global phase. string_for_inverse wires Wires of this operator.
base_name

Get base name of the operator.

basis = None

The basis of an operation, or for controlled gates, of the target operation. If not None, should take a value of "X", "Y", or "Z".

For example, X and CNOT have basis = "X", whereas ControlledPhaseShift and RZ have basis = "Z".

Type

str or None

control_wires

For operations that are controlled, returns the set of control wires.

Returns

The set of control wires of the operation.

Return type

Wires

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

hash

returns an integer hash uniquely representing the operator

Type

int

id

String for the ID of the operator.

inverse

Boolean determining if the inverse of the operation was requested.

is_composable_rotation = None

True if composing multiple copies of the operation results in an addition (or alternative accumulation) of parameters.

For example, qml.RZ is a composable rotation. Applying qml.RZ(0.1, wires=0) followed by qml.RZ(0.2, wires=0) is equivalent to performing a single rotation qml.RZ(0.3, wires=0).

If set to None, the operation will be ignored during compilation transforms that merge adjacent rotations.

Type

bool or None

is_self_inverse = None

True if the operation is its own inverse.

If None, all instances of the given operation will be ignored during compilation transforms involving inverse cancellation.

Type

bool or None

is_symmetric_over_all_wires = None

True if the operation is the same if you exchange the order of wires.

For example, qml.CZ(wires=[0, 1]) has the same effect as qml.CZ(wires=[1, 0]) due to symmetry of the operation.

If None, all instances of the operation will be ignored during compilation transforms that check for wire symmetry.

Type

bool or None

is_symmetric_over_control_wires = None

True if the operation is the same if you exchange the order of all but the last wire.

For example, qml.Toffoli(wires=[0, 1, 2]) has the same effect as qml.Toffoli(wires=[1, 0, 2]), but neither are the same as qml.Toffoli(wires=[0, 2, 1]).

If None, all instances of the operation will be ignored during compilation transforms that check for control-wire symmetry.

Type

bool or None

matrix
name

Get and set the name of the operator.

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

Current parameter values.

single_qubit_rot_angles

The parameters required to implement a single-qubit gate as an equivalent Rot gate, up to a global phase.

Returns

A list of values $$[\phi, \theta, \omega]$$ such that $$RZ(\omega) RY(\theta) RZ(\phi)$$ is equivalent to the original operation.

Return type

tuple[float, float, float]

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. queue([context]) Append the operator to the Operator queue.
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(context=<class 'pennylane.queuing.QueuingContext'>)

Append the operator to the Operator queue.