qml.templates.embeddings.IQPEmbedding¶

class
IQPEmbedding
(features, wires, n_repeats=1, pattern=None, do_queue=True)[source]¶ Bases:
pennylane.operation.Operation
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 nontrivial classical processing of the features. Thefeatures
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 singlequbit
RZ
rotations, applied to each qubit and encoding the \(n\) features, followed by twoqubit 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 featuresfeatures[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
Usage Details
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)
, whereK
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)
Nonconsecutive wires
In principle, the user can also pass a nonconsecutive 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]
theRZ
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.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
= 1¶

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.

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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