qml.U3¶
-
class
U3
(theta, phi, lambda, wires)[source]¶ Bases:
pennylane.operation.Operation
Arbitrary single qubit unitary.
\[\begin{split}U_3(\theta, \phi, \lambda) = \begin{bmatrix} \cos(\theta/2) & -\exp(i \lambda)\sin(\theta/2) \\ \exp(i \phi)\sin(\theta/2) & \exp(i (\phi + \lambda))\cos(\theta/2) \end{bmatrix}\end{split}\]The \(U_3\) gate is related to the single-qubit rotation \(R\) (
Rot
) and the \(R_\phi\) (PhaseShift
) gates via the following relation:\[U_3(\theta, \phi, \lambda) = R_\phi(\phi+\lambda) R(\lambda,\theta,-\lambda)\]Note
If the
U3
gate is not supported on the targeted device, PennyLane will attempt to decompose the gate intoPhaseShift
andRot
gates.Details:
Number of wires: 1
Number of parameters: 3
Gradient recipe: \(\frac{d}{d\phi}f(U_3(\theta, \phi, \lambda)) = \frac{1}{2}\left[f(U_3(\theta+\pi/2, \phi, \lambda)) - f(U_3(\theta-\pi/2, \phi, \lambda))\right]\) where \(f\) is an expectation value depending on \(U_3(\theta, \phi, \lambda)\). This gradient recipe applies for each angle argument \(\{\theta, \phi, \lambda\}\).
- Parameters
theta (float) – polar angle \(\theta\)
phi (float) – azimuthal angle \(\phi\)
lambda (float) – quantum phase \(\lambda\)
wires (Sequence[int] or int) – the subsystem the gate 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.
-
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
= 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
= 3¶
-
num_wires
= 1¶
-
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]
-
string_for_inverse
= '.inv'¶
Methods
check_domain
(p[, flattened])Check the validity of a parameter.
decomposition
(theta, phi, lam, 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
(theta, phi, lam, wires)[source]¶ 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.
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