qml.ops.op_math.Pow¶
- class Pow(base=None, z=1, id=None)[source]¶
Bases:
pennylane.ops.op_math.symbolicop.ScalarSymbolicOp
Symbolic operator denoting an operator raised to a power.
- Parameters
base (Operator) – the operator to be raised to a power
z=1 (float) – the exponent
Example
>>> sqrt_x = Pow(qml.X(0), 0.5) >>> sqrt_x.decomposition() [SX(wires=[0])] >>> qml.matrix(sqrt_x) array([[0.5+0.5j, 0.5-0.5j], [0.5-0.5j, 0.5+0.5j]]) >>> qml.matrix(qml.SX(0)) array([[0.5+0.5j, 0.5-0.5j], [0.5-0.5j, 0.5+0.5j]]) >>> qml.matrix(Pow(qml.T(0), 1.234)) array([[1. +0.j , 0. +0.j ], [0. +0.j , 0.56597465+0.82442265j]])
Attributes
Arithmetic depth of the operator.
The base operator.
Batch size of the operator if it is used with broadcasted parameters.
The trainable parameters
bool(x) -> bool
bool(x) -> bool
bool(x) -> bool
bool(x) -> bool
bool(x) -> bool
bool(x) -> bool
Integer hash that uniquely represents the operator.
Dictionary of non-trainable 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 of the operator.
Number of trainable parameters that the operator depends on.
Number of wires the operator acts on.
Trainable parameters that the operator depends on.
A
PauliSentence
representation of the Operator, orNone
if it doesn't have one.Wires that the operator acts on.
The exponent.
- arithmetic_depth¶
- base¶
The base operator.
- basis¶
- batch_size¶
- data¶
The trainable parameters
- has_adjoint¶
- has_decomposition¶
- has_diagonalizing_gates¶
- has_generator¶
- has_matrix¶
- has_sparse_matrix¶
- hash¶
- hyperparameters¶
Dictionary of non-trainable variables that this operation depends on.
- Type
dict
- id¶
Custom string to label a specific operator instance.
- is_hermitian¶
- name¶
String for the name of the operator.
- ndim_params¶
- num_params¶
- num_wires¶
Number of wires the operator acts on.
- parameters¶
Trainable parameters that the operator depends on.
- pauli_rep¶
A
PauliSentence
representation of the Operator, orNone
if it doesn’t have one.
- wires¶
- z¶
The exponent.
Methods
adjoint
()Create an operation that is the adjoint of this one.
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)Eigenvalues of the operator in the computational basis (static method).
compute_matrix
(*params, **hyperparams)Representation of the operator as a canonical matrix in the computational basis (static method).
compute_sparse_matrix
(*params[, base, z])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.
Generator of an operator that is in single-parameter-form.
label
([decimals, base_label, cache])A customizable string representation of the operator.
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)A list of new operators equal to this one raised to the given power.
queue
([context])Append the operator to the Operator queue.
simplify
()Reduce the depth of nested operators to the minimum.
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.
- adjoint()[source]¶
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.
Warning
The adjoint of a fractional power of an operator is not well-defined due to branch cuts in the power function. Therefore, an
AdjointUndefinedError
is raised when the powerz
is not an integer.The integer power check is a type check, so that floats like
2.0
are not considered to be integers.- Returns
The adjointed operation.
- Raises
AdjointUndefinedError – If the exponent
z
is not of typeint
.
- static compute_decomposition(*params, wires=None, **hyperparameters)¶
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) – non-trainable 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) – non-trainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
- Returns
list of diagonalizing gates
- Return type
list[Operator]
- static compute_eigvals(*params, **hyperparams)¶
Eigenvalues of the operator in the computational basis (static method).
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.
See also
- Parameters
*params (list) – trainable parameters of the operator, as stored in the
parameters
attribute**hyperparams (dict) – non-trainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
- Returns
eigenvalues
- Return type
tensor_like
- static compute_matrix(*params, **hyperparams)¶
Representation of the operator as a canonical 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
attribute**hyperparams (dict) – non-trainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
- Returns
matrix representation
- Return type
tensor_like
- static compute_sparse_matrix(*params, base=None, z=0)[source]¶
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
attribute**hyperparams (dict) – non-trainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
- Returns
sparse matrix representation
- Return type
scipy.sparse._csr.csr_matrix
- decomposition()[source]¶
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()[source]¶
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 of an operator to a power is the same as the diagonalizing gates as the original operator. As we can see,
\[O^2 = U \Sigma U^{\dagger} U \Sigma U^{\dagger} = U \Sigma^2 U^{\dagger}\]This formula can be extended to inversion and any rational number.
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()[source]¶
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
- generator()[source]¶
Generator of an operator that is in single-parameter-form.
The generator of a power operator is
z
times the generator of the base matrix.\[U(\phi)^z = e^{i\phi (z G)}\]See also
generator()
- label(decimals=None, base_label=None, cache=None)[source]¶
A customizable string representation of the operator.
- Parameters
decimals=None (int) – If
None
, no parameters are included. Else, specifies how to round the parameters.base_label=None (str) – overwrite the non-parameter component of the label
cache=None (dict) – dictionary that carries information between label calls in the same drawing
- Returns
label to use in drawings
- Return type
str
Example:
>>> op = qml.RX(1.23456, wires=0) >>> op.label() "RX" >>> op.label(base_label="my_label") "my_label" >>> op = qml.RX(1.23456, wires=0, id="test_data") >>> op.label() "RX("test_data")" >>> op.label(decimals=2) "RX\n(1.23,"test_data")" >>> op.label(base_label="my_label") "my_label("test_data")" >>> op.label(decimals=2, base_label="my_label") "my_label\n(1.23,"test_data")"
If the operation has a matrix-valued parameter and a cache dictionary is provided, unique matrices will be cached in the
'matrices'
key list. The label will contain the index of the matrix in the'matrices'
list.>>> op2 = qml.QubitUnitary(np.eye(2), wires=0) >>> cache = {'matrices': []} >>> op2.label(cache=cache) 'U(M0)' >>> cache['matrices'] [tensor([[1., 0.], [0., 1.]], requires_grad=True)] >>> op3 = qml.QubitUnitary(np.eye(4), wires=(0,1)) >>> op3.label(cache=cache) 'U(M1)' >>> cache['matrices'] [tensor([[1., 0.], [0., 1.]], requires_grad=True), tensor([[1., 0., 0., 0.], [0., 1., 0., 0.], [0., 0., 1., 0.], [0., 0., 0., 1.]], requires_grad=True)]
- 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 base matrix representation has not been defined.See also
- Parameters
wire_order (Iterable) – global wire order, must contain all wire labels from the
wires (operator's) –
- Returns
matrix representation
- Return type
tensor_like
- pow(z)[source]¶
A list of new operators equal to this one raised to the given power.
- Parameters
z (float) – exponent for the operator
- Returns
list[
Operator
]
- queue(context=<class 'pennylane.queuing.QueuingManager'>)¶
Append the operator to the Operator queue.
- simplify()[source]¶
Reduce the depth of nested operators to the minimum.
- Returns
simplified operator
- Return type
- 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]]