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
Get base name of the operator.
Eigenvalues of an instantiated operator.
Generator of the operation.
Boolean determining if the inverse of the operation was requested.
Matrix representation of an instantiated operator in the computational basis.
Get and set the name of the operator.
Current parameter values.
Wires of this operator.
-
a
= 1¶
-
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]
, wheregenerator
is an existing PennyLane operation class or \(2\times 2\) Hermitian array that acts as the generator of the current operationscaling_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, 1, 0.1], [-5.0, 1, -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
-
multiplier
= 5.0¶
-
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¶
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.
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, 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
-
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 the array
U
should be expanded to apply 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.
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