qml.operation.Operation

class Operation(*params, wires=None, do_queue=True)

Bases: pennylane.operation.Operator

Base class for quantum operations supported by a device.

As with Operator, the following class attributes must be defined for all operations:

• num_params

• num_wires

• par_domain

The following two class attributes are optional, but in most cases should be clearly defined to avoid unexpected behavior during differentiation.

• grad_method

• grad_recipe

Finally, there are some additional optional class attributes that may be set, and used by certain quantum optimizers:

• generator

Parameters

params (tuple[float, int, array, Variable]) – operation parameters

Keyword Arguments

• wires (Sequence[int]) – Subsystems it acts on. If not given, args[-1] is interpreted as wires.

• do_queue (bool) – Indicates whether the operation should be immediately pushed into a BaseQNode circuit queue. This flag is useful if there is some reason to run an Operation outside of a BaseQNode context.

Attributes

base_name	Get base name of the operator.
do_check_domain
eigvals	Eigenvalues of an instantiated operator.
generator	Generator of the operation.
grad_method	Gradient computation 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	Number of parameters the operator takes.
num_wires	Number of wires the operator acts on.
par_domain	Domain of the gate parameters.
parameters	Current parameter values.
string_for_inverse
wires	Wires of this operator.

base_name

Get base name of the operator.

do_check_domain = True

eigvals

Eigenvalues of an instantiated operator.

Note that the eigenvalues are not guaranteed to be in any particular order.

Example:

>>> U = qml.RZ(0.5, wires=1)
>>> U.eigvals
>>> array([0.96891242-0.24740396j, 0.96891242+0.24740396j])

Returns

eigvals representation

Return type

array

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

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

Matrix representation of an instantiated operator in the computational basis.

Example:

>>> U = qml.RY(0.5, wires=1)
>>> U.matrix
>>> array([[ 0.96891242+0.j, -0.24740396+0.j],
           [ 0.24740396+0.j,  0.96891242+0.j]])

Returns

matrix representation

Return type

array

name

Get and set the name of the operator.

num_params

Number of parameters the operator takes.

num_wires

Number of wires the operator acts on.

par_domain

Domain of the gate parameters.

• 'N': natural numbers (including zero).

• 'R': floats.

• 'A': arrays of real or complex values.

• 'L': list of arrays of real or complex values.

• None: if there are no parameters.

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(*params, 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(*params, 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.