# qml.PauliY¶

class PauliY(wires)[source]

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

 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 Wires of this operator.
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

• '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

Wires of this operator.

Returns

wires

Return type

Wires

 check_domain(p[, flattened]) Check the validity of a parameter. compare(other) Compares with another Hamiltonian, Tensor, or Observable, to determine if they are equivalent. decomposition(wires) Returns a template decomposing the operation into other quantum operations. Rotates the specified wires such that they are in the eigenbasis of PauliY. 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. 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

compare(other)

Compares with another Hamiltonian, Tensor, or Observable, to determine if they are equivalent.

Observables/Hamiltonians are equivalent if they represent the same operator (their matrix representations are equal), and they are defined on the same wires.

Warning

The compare method does not check if the matrix representation of a Hermitian observable is equal to an equivalent observable expressed in terms of Pauli matrices. To do so would require the matrix form of Hamiltonians and Tensors be calculated, which would drastically increase runtime.

Returns

True if equivalent.

Return type

(bool)

Examples

>>> ob1 = qml.PauliX(0) @ qml.Identity(1)
>>> ob2 = qml.Hamiltonian(, [qml.PauliX(0)])
>>> ob1.compare(ob2)
True
>>> ob1 = qml.PauliX(0)
>>> ob2 = qml.Hermitian(np.array([[0, 1], [1, 0]]), 0)
>>> ob1.compare(ob2)
False

static decomposition(wires)[source]

Returns a template decomposing the operation into other quantum operations.

diagonalizing_gates()[source]

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, 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.