qml.PauliZ

class PauliZ(wires)[source]

Bases: pennylane.operation.Observable, pennylane.operation.DiagonalOperation

The Pauli Z operator

\[\begin{split}\sigma_z = \begin{bmatrix} 1 & 0 \\ 0 & -1\end{bmatrix}.\end{split}\]

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

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([[ 1, 0], [ 0, -1]])
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.

diagonalizing_gates()

Returns the list of operations such that they diagonalize the observable in the computational basis.

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

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([1], [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]

Returns the list of operations such that they diagonalize the observable in the computational basis.

Returns

A list of gates that diagonalize the observable in the computational basis.

Return type

list(qml.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.

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