# qml.operation.Channel¶

class Channel(*params, wires=None, do_queue=True, id=None)[source]

Bases: pennylane.operation.Operation, abc.ABC

Base class for quantum channels.

As with Operation, the following class attributes must be defined for all channels:

To define a noisy channel, the following attribute of Channel can be used to list the corresponding Kraus matrices.

• _kraus_matrices

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

Parameters

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

Keyword Arguments
• wires (Sequence[int]) – Subsystems the channel 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.

 base_name Get base name of the operator. 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. id String for the ID of the operator. inverse Boolean determining if the inverse of the operation was requested. kraus_matrices Kraus matrices of an instantiated channel in the computational basis. 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.

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': 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

id

String for the ID of the operator.

inverse

Boolean determining if the inverse of the operation was requested.

kraus_matrices

Kraus matrices of an instantiated channel in the computational basis.

** Example**

>>> U = qml.AmplitudeDamping(0.1, wires=1)
>>> U.kraus_matrices
>>> [array([[1.       , 0.       ],
[0.       , 0.9486833]]), array([[0.        , 0.31622777],
[0.        , 0.        ]])]

Returns

list of Kraus matrices

Return type

list(array)

matrix
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.

string_for_inverse = '.inv'
wires

Wires of this operator.

Returns

wires

Return type

Wires

 adjoint([do_queue]) Create an operation that is the adjoint of this one. decomposition(*params, wires) Returns a template decomposing the operation into other quantum operations. Returns a tape containing the decomposed operations, rather than a list. 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.
adjoint(do_queue=False)

Create an operation that is the adjoint of this one.

Adjointed operations are the conjugated and transposed version of the original operation. Adjointed ops are equivalent to the inverted operation for unitary gates.

Parameters

do_queue – Whether to add the adjointed gate to the context queue.

Returns

static decomposition(*params, wires)

Returns a template decomposing the operation into other quantum operations.

expand()

Returns a tape containing the decomposed operations, rather than a list.

Returns

Returns a quantum tape that contains the operations decomposition, or if not implemented, simply the operation itself.

Return type

JacobianTape

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

list of multiplier, coefficient, shift for each term in the gradient recipe

Return type

list[[float, 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.