qml.ops.op_math.SProd¶

class
SProd
(scalar, base, id=None)[source]¶ Bases:
pennylane.ops.op_math.symbolicop.ScalarSymbolicOp
Arithmetic operator representing the scalar product of an operator with the given scalar.
 Parameters
scalar (float or complex) – the scale factor being multiplied to the operator.
base (Operator) – the operator which will get scaled.
 Keyword Arguments
id (str or None) – id for the scalar product operator. Default is None.
Note
Currently this operator can not be queued in a circuit as an operation, only measured terminally.
See also
s_prod()
Example
>>> sprod_op = SProd(1.23, qml.PauliX(0)) >>> sprod_op 1.23*(PauliX(wires=[0])) >>> qml.matrix(sprod_op) array([[0. , 1.23], [1.23, 0. ]]) >>> sprod_op.terms() ([1.23], [PauliX(wires=[0]])
Usage Details
The SProd operation can also be measured inside a qnode as an observable. If the circuit is parameterized, then we can also differentiate through the observable.
dev = qml.device("default.qubit", wires=1) @qml.qnode(dev, diff_method="best") def circuit(scalar, theta): qml.RX(theta, wires=0) return qml.expval(qml.s_prod(scalar, qml.Hadamard(wires=0)))
>>> scalar, theta = (1.2, 3.4) >>> qml.grad(circuit, argnum=[0,1])(scalar, theta) (array(0.68362956), array(0.21683382))
Attributes
Arithmetic depth of the operator.
The base operator.
Batch size of the operator if it is used with broadcasted parameters.
The trainable parameters
Whether the Operator returns defined diagonalizing gates.
Whether or not the Operator returns a defined matrix.
Integer hash that uniquely represents the operator.
Dictionary of nontrainable variables that this operation depends on.
Custom string to label a specific operator instance.
If the base operator is hermitian and the scalar is real, then the scalar product 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.
Wires that the operator acts on.

arithmetic_depth
¶

base
¶ The base operator.

batch_size
¶

data
¶

has_adjoint
= True¶

has_decomposition
= False¶

has_diagonalizing_gates
¶ Whether the Operator returns defined diagonalizing gates.
 Type
Bool

has_generator
= False¶

has_matrix
¶ Whether or not the Operator returns a defined matrix.
 Type
Bool

hash
¶

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

id
¶ Custom string to label a specific operator instance.

is_hermitian
¶ If the base operator is hermitian and the scalar is real, then the scalar product operator is hermitian.

name
¶ String for the name of the operator.

ndim_params
¶ Number of dimensions per trainable parameter of the operator.
By default, this property returns the numbers of dimensions of the parameters used for the operator creation. If the parameter sizes for an operator subclass are fixed, this property can be overwritten to return the fixed value.
 Returns
Number of dimensions for each trainable parameter.
 Return type
tuple

num_params
¶ Number of trainable parameters that the operator depends on. Usually 1 + the number of trainable parameters for the base op.
 Returns
number of trainable parameters
 Return type
int

num_wires
¶ Number of wires the operator acts on.

parameters
¶ Trainable parameters that the operator depends on.

wires
¶
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, **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
()Return the eigenvalues of the specified operator.
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 produced for the SProd op.
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)Returns the operator raised to a 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])Computes, by default, a scipy.sparse.csr_matrix representation of this Tensor.
terms
()Representation of the operator as a linear combination of other operators.
validate_subspace
(subspace)Validate the subspace for qutrit operations.

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.
 Returns
The adjointed operation.

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) – 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)¶ 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) – nontrainable 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) – nontrainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
 Returns
matrix representation
 Return type
tensor_like

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
attribute**hyperparams (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
()[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 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]¶ Return the eigenvalues of the specified operator.
This method uses prestored eigenvalues for standard observables where possible and stores the corresponding eigenvectors from the eigendecomposition.
 Returns
array containing the eigenvalues of the operator.
 Return type
array

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

generator
()¶ 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.

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

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)[source]¶ Computes, by default, a scipy.sparse.csr_matrix representation of this Tensor.
This is useful for larger qubit numbers, where the dense matrix becomes very large, while consisting mostly of zero entries.
 Parameters
wire_order (Iterable) – Wire labels that indicate the order of wires according to which the matrix is constructed. If not provided,
self.wires
is used. Returns
sparse matrix representation
 Return type
scipy.sparse._csr.csr_matrix

terms
()[source]¶ 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