braket.pennylane_plugin.XY

class XY(phi, wires)

Bases: pennylane.operation.Operation

Parameterized ISWAP gate: https://arxiv.org/abs/1912.04424v1

\[\begin{split}\mathtt{XY}(\phi) = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & \cos(\phi / 2) & i \sin(\phi / 2) & 0 \\ 0 & i \sin(\phi / 2) & \cos(\phi / 2) & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}.\end{split}\]

Details:

• Number of wires: 2

• Number of parameters: 1

• Gradient recipe:

\[\frac{d}{d \phi} \mathtt{XY}(\phi) = \frac{1}{2} \left[ \mathtt{XY}(\phi + \pi / 2) + \mathtt{XY}(\phi - \pi / 2) \right]\]

Parameters

• phi (float) – the phase angle

• wires (int) – the subsystem the gate acts on

Attributes

base_name	Get base name of the operator.
do_check_domain	should we perform a domain check for the parameters?
eigvals	Eigenvalues of an instantiated operator.
generator	Generator of the operation.
grad_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.

do_check_domain = True

should we perform a domain check for the parameters?

Type

bool

Type

flag

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'

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 = 2

par_domain = 'R'

parameters

Current parameter values.

Fixed parameters are returned as is, free parameters represented by Variable instances are replaced by their current numerical value.

Returns

parameter values

Return type

list[Any]

string_for_inverse = '.inv'

wires

Wires of this operator.

Returns

wires

Return type

Wires

Methods

check_domain(p[, flattened])	Check the validity of a parameter.
decomposition(phi, wires)	Returns a template decomposing the operation into other quantum operations.
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.

check_domain(p, flattened=False)

Check the validity of a parameter.

Variable instances can represent any real scalars (but not arrays).

Parameters

• p (Number, array, Variable) – parameter to check

• flattened (bool) – True means p is an element of a flattened parameter sequence (affects the handling of ‘A’ parameters)

Raises

• TypeError – parameter is not an element of the expected domain

• ValueError – parameter is an element of an unknown domain

Returns

p

Return type

Number, array, Variable

static decomposition(phi, wires)

Returns a template decomposing the operation into other quantum operations.

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.