qml.PauliY

class PauliY(wires)

Bases: pennylane.operation.Observable, pennylane.operation.Operation

The Pauli Y operator

\[\begin{split}\sigma_y = \begin{bmatrix} 0 & -i \\ i & 0\end{bmatrix}.\end{split}\]

Details:

• Number of wires: 1

• Number of parameters: 0

Parameters

wires (Sequence[int] or int) – the wire the operation acts on

Attributes

base_name	Get base name of the operator.
do_check_domain
eigvals
generator	Generator of the operation.
grad_method	Gradient computation method.
grad_recipe
inverse	Boolean determining if the inverse of the operation was requested.
matrix
name	Get and set the name of the operator.
num_params
num_wires
par_domain
parameters	Current parameter values.
return_type
string_for_inverse
wires	Wire values.

base_name

Get base name of the operator.

do_check_domain = True

eigvals = array([ 1, -1])

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

Gradient computation 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

inverse

Boolean determining if the inverse of the operation was requested.

matrix = array([[ 0.+0.j, -0.-1.j], [ 0.+1.j, 0.+0.j]])

name

Get and set the name of the operator.

num_params = 0

num_wires = 1

par_domain = None

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]

return_type = None

string_for_inverse = '.inv'

wires

Wire values.

Returns

wire values

Return type

tuple[int]

Methods

check_domain(p[, flattened])	Check the validity of a parameter.
decomposition(*params, wires)	Returns a template decomposing the operation into other quantum operations.
diagonalizing_gates()	Rotates the specified wires such that they are in the eigenbasis of PauliY.
get_parameter_shift(idx)	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(*params, wires)

Returns a template decomposing the operation into other quantum operations.

diagonalizing_gates()

Rotates the specified wires such that they are in the eigenbasis of PauliY.

For the Pauli-Y observable,

\[Y = U^\dagger Z U\]

where \(U=HSZ\).

Returns

A list of gates that diagonalize PauliY in the

computational basis.

Return type

list(Operation)

get_parameter_shift(idx)

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.