qml.ControlledAddition¶

class ControlledAddition(s, wires)[source]¶

Bases: pennylane.operation.CVOperation

Controlled addition operation.

\[\text{CX}(s) = \int dx \ket{x}\bra{x} \otimes D\left({\frac{1}{\sqrt{2\hbar}}}s x\right) = e^{-i s \: \hat{x} \otimes \hat{p}/\hbar}.\]

Details:

Number of wires: 2
Number of parameters: 1
Gradient recipe: \(\frac{d}{ds}f(\text{CX}(s)) = \frac{1}{2 a} \left[f(\text{CX}(s+a)) - f(\text{CX}(s-a))\right]\), where \(a\) is an arbitrary real number (\(0.1\) by default) and \(f\) is an expectation value depending on \(\text{CX}(s)\).
Heisenberg representation:

\[\begin{split}M = \begin{bmatrix} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & -s \\ 0 & s & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 & 1 \end{bmatrix}\end{split}\]

Parameters

s (float) – addition multiplier
wires (Sequence[int] or int) – the wire the operation acts on

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`
`grad_recipe`
`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`
`num_wires`
`par_domain`
`parameters`	Current parameter values.
`shift`
`string_for_inverse`
`supports_heisenberg`
`supports_parameter_shift`
`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 = 'A'¶

grad_recipe = [(5.0, 0.1)]¶

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 = 1¶

num_wires = 2¶

par_domain = 'R'¶

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]

shift = 0.1¶

string_for_inverse = '.inv'¶

supports_heisenberg = True¶

supports_parameter_shift = True¶

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)	Multiplier and shift for the given parameter, based on its gradient recipe.
`heisenberg_expand`(U, wires)	Expand the given local Heisenberg-picture array into a full-system one.
`heisenberg_pd`(idx)	Partial derivative of the Heisenberg picture transform matrix.
`heisenberg_tr`(wires[, inverse])	Heisenberg picture representation of the linear transformation carried out by the gate at current parameter values.
`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)¶

Multiplier and shift for the given parameter, based on its gradient recipe.

Parameters: idx (int) – parameter index
Returns: multiplier, shift
Return type: float, float

heisenberg_expand(U, wires)¶

Expand the given local Heisenberg-picture array into a full-system one.

Parameters

U (array[float]) – array to expand (expected to be of the dimension 1+2*self.num_wires)
wires (Wires) – wires on the device that the observable gets applied to

Raises

ValueError – if the size of the input matrix is invalid or num_wires is incorrect

Returns

expanded array, dimension 1+2*num_wires

Return type

array[float]

heisenberg_pd(idx)¶

Partial derivative of the Heisenberg picture transform matrix.

Computed using grad_recipe.

Parameters: idx (int) – index of the parameter with respect to which the partial derivative is computed.
Returns: partial derivative
Return type: array[float]

heisenberg_tr(wires, inverse=False)¶

Heisenberg picture representation of the linear transformation carried out by the gate at current parameter values.

Given a unitary quantum gate \(U\), we may consider its linear transformation in the Heisenberg picture, \(U^\dagger(\cdot) U\).

If the gate is Gaussian, this linear transformation preserves the polynomial order of any observables that are polynomials in \(\mathbf{r} = (\I, \x_0, \p_0, \x_1, \p_1, \ldots)\). This also means it maps \(\text{span}(\mathbf{r})\) into itself:

\[U^\dagger \mathbf{r}_i U = \sum_j \tilde{U}_{ij} \mathbf{r}_j\]

For Gaussian CV gates, this method returns the transformation matrix for the current parameter values of the Operation. The method is not defined for non-Gaussian (and non-CV) gates.

Parameters

wires (Wires) – wires on the device that the observable gets applied to
inverse (bool) – if True, return the inverse transformation instead

Raises

RuntimeError – if the specified operation is not Gaussian or is missing the _heisenberg_rep method

Returns

\(\tilde{U}\), the Heisenberg picture representation of the linear transformation

Return type

array[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.

qml.ControlledAddition¶

Attributes

Methods

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