qml.PCPhase¶

class
PCPhase
(phi, dim, wires)[source]¶ Bases:
pennylane.operation.Operation
A projectorcontrolled phase gate.
This gate applies a complex phase \(e^{i\phi}\) to the first \(dim\) basis vectors of the input state while applying a complex phase \(e^{i \phi}\) to the remaining basis vectors. For example, consider the 2qubit case where \(dim = 3\):
\[\begin{split}\Pi(\phi) = \begin{bmatrix} e^{i\phi} & 0 & 0 & 0 \\ 0 & e^{i\phi} & 0 & 0 \\ 0 & 0 & e^{i\phi} & 0 \\ 0 & 0 & 0 & e^{i\phi} \end{bmatrix}.\end{split}\]Details:
Number of wires: Any (the operation can act on any number of wires)
Number of parameters: 1
Number of dimensions per parameter: (0,)
 Parameters
phi (float) – rotation angle \(\phi\)
dim (int) – the dimension of the subspace
wires (Iterable[int, str], Wires) – the wires the operation acts on
do_queue (bool) – Indicates whether the operator should be immediately pushed into the Operator queue (optional)
id (str or None) – String representing the operation (optional)
Example:
We can define a circuit using
PCPhase
as follows:>>> dev = qml.device('default.qubit', wires=2) >>> @qml.qnode(dev) >>> def example_circuit(): ... qml.PCPhase(0.27, dim = 2, wires=range(2)) ... return qml.state()
The resulting operation applies a complex phase \(e^{0.27i}\) to the first \(dim = 2\) basis vectors and \(e^{0.27i}\) to the remaining basis vectors.
>>> print(np.round(qml.matrix(example_circuit)(),2)) [[0.96+0.27j 0. +0.j 0. +0.j 0. +0.j ] [0. +0.j 0.96+0.27j 0. +0.j 0. +0.j ] [0. +0.j 0. +0.j 0.960.27j 0. +0.j ] [0. +0.j 0. +0.j 0. +0.j 0.960.27j]]
We can also choose a different \(dim\) value to apply the phase shift to a different set of basis vectors as follows:
>>> pc_op = qml.PCPhase(1.23, dim=3, wires=[1, 2]) >>> print(np.round(qml.matrix(pc_op),2)) [[0.33+0.94j 0. +0.j 0. +0.j 0. +0.j ] [0. +0.j 0.33+0.94j 0. +0.j 0. +0.j ] [0. +0.j 0. +0.j 0.33+0.94j 0. +0.j ] [0. +0.j 0. +0.j 0. +0.j 0.330.94j]]
Attributes
Arithmetic depth of the operator.
Holdover from when inplace inversion changed then name.
The basis of an operation, or for controlled gates, of the target operation.
Batch size of the operator if it is used with broadcasted parameters.
Control wires of the operator.
Gradient recipe for the parametershift method.
Integer hash that uniquely represents the operator.
Dictionary of nontrainable variables that this operation depends on.
Custom string to label a specific operator instance.
This property determines if an operator is hermitian.
String for the name of the operator.
Number of dimensions per trainable parameter that the operator depends on.
Number of trainable parameters that the operator depends on.
Number of wires the operator acts on.
Trainable parameters that the operator depends on.
Wires that the operator acts on.

arithmetic_depth
¶ Arithmetic depth of the operator.

base_name
¶ Holdover from when inplace inversion changed then name. To be removed.

basis
= 'Z'¶ The basis of an operation, or for controlled gates, of the target operation. If not
None
, should take a value of"X"
,"Y"
, or"Z"
.For example,
X
andCNOT
havebasis = "X"
, whereasControlledPhaseShift
andRZ
havebasis = "Z"
. Type
str or None

batch_size
¶ Batch size of the operator if it is used with broadcasted parameters.
The
batch_size
is determined based onndim_params
and the provided parameters for the operator. If (some of) the latter have an additional dimension, and this dimension has the same size for all parameters, its size is the batch size of the operator. If no parameter has an additional dimension, the batch size isNone
. Returns
Size of the parameter broadcasting dimension if present, else
None
. Return type
int or None

control_wires
¶ Control wires of the operator.
For operations that are not controlled, this is an empty
Wires
object of length0
. Returns
The control wires of the operation.
 Return type

grad_method
= 'A'¶

grad_recipe
= None¶ Gradient recipe for the parametershift 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

has_adjoint
= True¶

has_decomposition
= True¶

has_diagonalizing_gates
= False¶

has_generator
= True¶

has_matrix
= True¶

hash
¶ Integer hash that uniquely represents the operator.
 Type
int

hyperparameters
¶ Dictionary of nontrainable variables that this operation depends on.
 Type
dict

id
¶ Custom string to label a specific operator instance.

is_hermitian
¶ This property determines if an operator is hermitian.

name
¶ String for the name of the operator.

ndim_params
= (0,)¶ Number of dimensions per trainable parameter that the operator depends on.
 Type
tuple[int]

num_params
= 1¶ Number of trainable parameters that the operator depends on.
 Type
int

num_wires
= 1¶ Number of wires the operator acts on.

parameter_frequencies
= [(2,)]¶

parameters
¶ Trainable parameters that the operator depends on.
Methods
adjoint
()Computes the adjoint of the operator.
compute_decomposition
(*params[, wires])Representation of the operator as a product of other operators (static method).
compute_diagonalizing_gates
(*params, wires, …)Sequence of gates that diagonalize the operator in the computational basis (static method).
compute_eigvals
(*params, **hyperparams)Get the eigvals for the Picontrolled phase unitary.
compute_matrix
(*params, **hyperparams)Get the matrix representation of Picontrolled phase unitary.
compute_sparse_matrix
(*params, **hyperparams)Representation of the operator as a sparse matrix in the computational basis (static method).
Representation of the operator as a product of other operators.
Sequence of gates that diagonalize the operator in the computational basis.
eigvals
()Eigenvalues of the operator in the computational basis.
expand
()Returns a tape that contains the decomposition of the operator.
Generator of an operator that is in singleparameterform.
label
([decimals, base_label, cache])The label of the operator when displayed in a circuit.
map_wires
(wire_map)Returns a copy of the current operator with its wires changed according to the given wire map.
matrix
([wire_order])Representation of the operator as a matrix in the computational basis.
pow
(z)Computes the operator raised to z.
queue
([context])Append the operator to the Operator queue.
simplify
()Simplifies the operator if possible.
The parameters required to implement a singlequbit gate as an equivalent
Rot
gate, up to a global phase.sparse_matrix
([wire_order])Representation of the operator as a sparse matrix in the computational basis.
terms
()Representation of the operator as a linear combination of other operators.
validate_subspace
(subspace)Validate the subspace for qutrit operations.

static
compute_decomposition
(*params, wires=None, **hyperparams)[source]¶ Representation of the operator as a product of other operators (static method).
\[O = O_1 O_2 \dots O_n.\]Note
Operations making up the decomposition should be queued within the
compute_decomposition
method.See also
 Parameters
params (list) – trainable parameters of the operator, as stored in the
parameters
attributewires (Iterable[Any], Wires) – wires that the operator acts on
hyperparams (dict) – nontrainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
 Returns
decomposition of the operator
 Return type
list[Operator]

static
compute_diagonalizing_gates
(*params, wires, **hyperparams)¶ Sequence of gates that diagonalize the operator in the computational basis (static method).
Given the eigendecomposition \(O = U \Sigma U^{\dagger}\) where \(\Sigma\) is a diagonal matrix containing the eigenvalues, the sequence of diagonalizing gates implements the unitary \(U^{\dagger}\).
The diagonalizing gates rotate the state into the eigenbasis of the operator.
See also
 Parameters
params (list) – trainable parameters of the operator, as stored in the
parameters
attributewires (Iterable[Any], Wires) – wires that the operator acts on
hyperparams (dict) – nontrainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
 Returns
list of diagonalizing gates
 Return type
list[Operator]

static
compute_eigvals
(*params, **hyperparams)[source]¶ Get the eigvals for the Picontrolled phase unitary.

static
compute_matrix
(*params, **hyperparams)[source]¶ Get the matrix representation of Picontrolled phase unitary.

static
compute_sparse_matrix
(*params, **hyperparams)¶ Representation of the operator as a sparse matrix in the computational basis (static method).
The canonical matrix is the textbook matrix representation that does not consider wires. Implicitly, this assumes that the wires of the operator correspond to the global wire order.
See also
 Parameters
params (list) – trainable parameters of the operator, as stored in the
parameters
attributehyperparams (dict) – nontrainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
 Returns
sparse matrix representation
 Return type
scipy.sparse._csr.csr_matrix

decomposition
()¶ Representation of the operator as a product of other operators.
\[O = O_1 O_2 \dots O_n\]A
DecompositionUndefinedError
is raised if no representation by decomposition is defined.See also
 Returns
decomposition of the operator
 Return type
list[Operator]

diagonalizing_gates
()¶ Sequence of gates that diagonalize the operator in the computational basis.
Given the eigendecomposition \(O = U \Sigma U^{\dagger}\) where \(\Sigma\) is a diagonal matrix containing the eigenvalues, the sequence of diagonalizing gates implements the unitary \(U^{\dagger}\).
The diagonalizing gates rotate the state into the eigenbasis of the operator.
A
DiagGatesUndefinedError
is raised if no representation by decomposition is defined.See also
 Returns
a list of operators
 Return type
list[Operator] or None

eigvals
()¶ Eigenvalues of the operator in the computational basis.
If
diagonalizing_gates
are specified and implement a unitary \(U^{\dagger}\), the operator can be reconstructed as\[O = U \Sigma U^{\dagger},\]where \(\Sigma\) is the diagonal matrix containing the eigenvalues.
Otherwise, no particular order for the eigenvalues is guaranteed.
Note
When eigenvalues are not explicitly defined, they are computed automatically from the matrix representation. Currently, this computation is not differentiable.
A
EigvalsUndefinedError
is raised if the eigenvalues have not been defined and cannot be inferred from the matrix representation.See also
 Returns
eigenvalues
 Return type
tensor_like

expand
()¶ Returns a tape that contains the decomposition of the operator.
 Returns
quantum tape
 Return type

generator
()[source]¶ Generator of an operator that is in singleparameterform.
For example, for operator
\[U(\phi) = e^{i\phi (0.5 Y + Z\otimes X)}\]we get the generator
>>> U.generator() (0.5) [Y0] + (1.0) [Z0 X1]
The generator may also be provided in the form of a dense or sparse Hamiltonian (using
Hermitian
andSparseHamiltonian
respectively).The default value to return is
None
, indicating that the operation has no defined generator.

label
(decimals=None, base_label=None, cache=None)[source]¶ The label of the operator when displayed in a circuit.

map_wires
(wire_map)¶ Returns a copy of the current operator with its wires changed according to the given wire map.
 Parameters
wire_map (dict) – dictionary containing the old wires as keys and the new wires as values
 Returns
new operator
 Return type

matrix
(wire_order=None)¶ Representation of the operator as a matrix in the computational basis.
If
wire_order
is provided, the numerical representation considers the position of the operator’s wires in the global wire order. Otherwise, the wire order defaults to the operator’s wires.If the matrix depends on trainable parameters, the result will be cast in the same autodifferentiation framework as the parameters.
A
MatrixUndefinedError
is raised if the matrix representation has not been defined.See also
 Parameters
wire_order (Iterable) – global wire order, must contain all wire labels from the operator’s wires
 Returns
matrix representation
 Return type
tensor_like

queue
(context=<class 'pennylane.queuing.QueuingManager'>)¶ Append the operator to the Operator queue.

single_qubit_rot_angles
()¶ The parameters required to implement a singlequbit 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.
 Return type
tuple[float, float, float]

sparse_matrix
(wire_order=None)¶ Representation of the operator as a sparse matrix in the computational basis.
If
wire_order
is provided, the numerical representation considers the position of the operator’s wires in the global wire order. Otherwise, the wire order defaults to the operator’s wires.A
SparseMatrixUndefinedError
is raised if the sparse matrix representation has not been defined.See also
 Parameters
wire_order (Iterable) – global wire order, must contain all wire labels from the operator’s wires
 Returns
sparse matrix representation
 Return type
scipy.sparse._csr.csr_matrix

terms
()¶ Representation of the operator as a linear combination of other operators.
\[O = \sum_i c_i O_i\]A
TermsUndefinedError
is raised if no representation by terms is defined. Returns
list of coefficients \(c_i\) and list of operations \(O_i\)
 Return type
tuple[list[tensor_like or float], list[Operation]]

static
validate_subspace
(subspace)¶ Validate the subspace for qutrit operations.
This method determines whether a given subspace for qutrit operations is defined correctly or not. If not, a ValueError is thrown.
 Parameters
subspace (tuple[int]) – Subspace to check for correctness