# pennylane_forest.CPHASE¶

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

Bases: pennylane.operation.Operation

CHPASE(phi, q, wires) Controlled-phase gate.

$\begin{split}CPHASE_{ij}(phi, q) = \begin{cases} 0, & i\neq j\\ 1, & i=j, i\neq q\\ e^{i\phi}, & i=j=q \end{cases}\in\mathbb{C}^{4\times 4}\end{split}$

Details:

• Number of wires: 2
• Number of parameters: 2
• Gradient recipe: $$\frac{d}{d\phi}CPHASE(\phi) = \frac{1}{2}\left[CPHASE(\phi+\pi/2)+CPHASE(\phi-\pi/2)\right]$$ Note that the gradient recipe only applies to parameter $$\phi$$. Parameter $$q\in\mathbb{N}_0$$ and thus CPHASE can not be differentiated with respect to $$q$$.
Parameters: phi (float) – the controlled phase angle q (int) – an integer between 0 and 3 that corresponds to a state $$\{00, 01, 10, 11\}$$ on which the conditional phase gets applied wires (int) – the subsystem the gate acts on
 base_name Get base name of the operator. basis control_wires For operations that are controlled, returns the set of control wires. eigvals Eigenvalues of an instantiated operator. generator Generator of the operation. grad_method grad_recipe id String for the ID of the operator. inverse Boolean determining if the inverse of the operation was requested. is_composable_rotation is_self_inverse is_symmetric_over_all_wires is_symmetric_over_control_wires 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. single_qubit_rot_angles The parameters required to implement a single-qubit gate as an equivalent Rot gate, up to a global phase. string_for_inverse wires Wires of this operator.
base_name

Get base name of the operator.

basis = None
control_wires

For operations that are controlled, returns the set of control wires.

Returns: The set of control wires of the operation. Wires
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 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 = None
id

String for the ID of the operator.

inverse

Boolean determining if the inverse of the operation was requested.

is_composable_rotation = None
is_self_inverse = None
is_symmetric_over_all_wires = None
is_symmetric_over_control_wires = None
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 array
name

Get and set the name of the operator.

num_params = 2
num_wires = 2
par_domain = 'R'
parameters

Current parameter values.

single_qubit_rot_angles

The parameters required to implement a single-qubit gate as an equivalent Rot gate, up to a global phase.

Returns: A list of values $$[\phi, \theta, \omega]$$ such that $$RZ(\omega) RY(\theta) RZ(\phi)$$ is equivalent to the original operation. tuple[float, float, float]
string_for_inverse = '.inv'
wires

Wires of this operator.

Returns: wires Wires
 adjoint([do_queue]) Create an operation that is the adjoint of this one. decomposition(q, wires) Returns a template decomposing the operation into other quantum operations. expand() 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. inv() Inverts the operation, such that the inverse will be used for the computations by the specific device. queue([context]) 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.

decomposition(q, wires)[source]

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. 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 list of multiplier, coefficient, shift for each term in the gradient recipe 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 Operator
queue(context=<class 'pennylane.queuing.QueuingContext'>)

Append the operator to the Operator queue.