qml.QuadOperator¶
-
class
QuadOperator
(phi, wires, do_queue=True, id=None)[source]¶ Bases:
pennylane.operation.CVObservable
The generalized quadrature observable \(\x_\phi = \x cos\phi+\p\sin\phi\).
When used with the
expval()
function, the expectation value \(\braket{\hat{\x_\phi}}\) is returned. This corresponds to the mean displacement in the phase space along axis at angle \(\phi\).Details:
Number of wires: 1
Number of parameters: 1
Observable order: 1st order in the quadrature operators
Heisenberg representation:
\[d = [0, \cos\phi, \sin\phi]\]
- Parameters
phi (float) – axis in the phase space at which to calculate the generalized quadrature observable
wires (Sequence[Any] or Any) – the wire 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)
Attributes
Eigenvalues of an instantiated operator.
Order in (x, p) that a CV observable is a polynomial of.
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.
Matrix representation of an instantiated operator in the computational basis.
String for the name of the operator.
Trainable parameters that the operator depends on.
Measurement type that this observable is called with.
Wires that the operator acts on.
-
eigvals
¶ Eigenvalues of an instantiated operator. Note that the eigenvalues are not guaranteed to be in any particular order.
Warning
The
eigvals
property is deprecated and will be removed in an upcoming release. Please useqml.eigvals
instead.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
-
ev_order
= 1¶ Order in (x, p) that a CV observable is a polynomial of.
- Type
None, int
-
grad_method
= 'A'¶
-
has_matrix
= False¶
-
hash
¶ Integer hash that uniquely represents the operator.
- Type
int
-
hyperparameters
¶ Dictionary of non-trainable variables that this operation depends on.
- Type
dict
-
id
¶ Custom string to label a specific operator instance.
-
matrix
¶ Matrix representation of an instantiated operator in the computational basis.
Warning
The
matrix
property is deprecated and will be removed in an upcoming release. Please useqml.matrix
instead.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
¶ String for the name of the operator.
-
num_params
= 1¶
-
num_wires
= 1¶
-
parameters
¶ Trainable parameters that the operator depends on.
-
return_type
= None¶ Measurement type that this observable is called with.
- Type
None or ObservableReturnTypes
-
supports_heisenberg
= True¶
Methods
compare
(other)Compares with another
Hamiltonian
,Tensor
, orObservable
, to determine if they are equivalent.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).
compute_terms
(*params, **hyperparams)Representation of the operator as a linear combination of other operators (static method).
Representation of the operator as a product of other operators.
Sequence of gates that diagonalize the operator in the computational basis.
expand
()Returns a tape that has recorded the decomposition of the operator.
Generator of an operator that is in single-parameter-form.
Eigenvalues of the operator in the computational basis (static method).
get_matrix
([wire_order])Representation of the operator as a matrix in the computational basis.
heisenberg_expand
(U, wire_order)Expand the given local Heisenberg-picture array into a full-system one.
heisenberg_obs
(wire_order)Representation of the observable in the position/momentum operator basis.
label
([decimals, base_label, cache])A customizable string representation of the operator.
queue
([context])Append the operator to the Operator queue.
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.
-
compare
(other)¶ Compares with another
Hamiltonian
,Tensor
, orObservable
, to determine if they are equivalent.Observables/Hamiltonians are equivalent if they represent the same operator (their matrix representations are equal), and they are defined on the same wires.
Warning
The compare method does not check if the matrix representation of a
Hermitian
observable is equal to an equivalent observable expressed in terms of Pauli matrices. To do so would require the matrix form of Hamiltonians and Tensors be calculated, which would drastically increase runtime.- Returns
True if equivalent.
- Return type
(bool)
Examples
>>> ob1 = qml.PauliX(0) @ qml.Identity(1) >>> ob2 = qml.Hamiltonian([1], [qml.PauliX(0)]) >>> ob1.compare(ob2) True >>> ob1 = qml.PauliX(0) >>> ob2 = qml.Hermitian(np.array([[0, 1], [1, 0]]), 0) >>> ob1.compare(ob2) False
-
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 \(U\).
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 \(U\), 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
attributehyperparams (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
get_matrix()
andmatrix()
- Parameters
params (list) – trainable parameters of the operator, as stored in the
parameters
attributehyperparams (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, **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) – non-trainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
- Returns
matrix representation
- Return type
scipy.sparse.coo.coo_matrix
-
static
compute_terms
(*params, **hyperparams)¶ Representation of the operator as a linear combination of other operators (static method).
\[O = \sum_i c_i O_i\]See also
- Parameters
params (list) – trainable parameters of the operator, as stored in the
parameters
attributehyperparams (dict) – non-trainable hyperparameters of the operator, as stored in the
hyperparameters
attribute
- Returns
list of coefficients and list of operations
- Return type
tuple[list[tensor_like or float], list[Operation]]
-
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 \(U\).
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
-
expand
()¶ Returns a tape that has recorded the decomposition of the operator.
- Returns
quantum tape
- Return type
-
generator
()¶ Generator of an operator that is in single-parameter-form.
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.
-
get_eigvals
()¶ Eigenvalues of the operator in the computational basis (static method).
If
diagonalizing_gates
are specified and implement a unitary \(U\), 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
-
get_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
-
heisenberg_expand
(U, wire_order)¶ Expand the given local Heisenberg-picture array into a full-system one.
- Parameters
U (array[float]) – array to expand (expected to be of the dimension
1+2*self.num_wires
)wire_order (Wires) – global wire order defining which subspace the operator acts on
- Raises
ValueError – if the size of the input matrix is invalid or num_wires is incorrect
- Returns
expanded array, dimension
1+2*num_wires
- Return type
array[float]
-
heisenberg_obs
(wire_order)¶ Representation of the observable in the position/momentum operator basis.
Returns the expansion \(q\) of the observable, \(Q\), in the basis \(\mathbf{r} = (\I, \x_0, \p_0, \x_1, \p_1, \ldots)\).
For first-order observables returns a real vector such that \(Q = \sum_i q_i \mathbf{r}_i\).
For second-order observables returns a real symmetric matrix such that \(Q = \sum_{ij} q_{ij} \mathbf{r}_i \mathbf{r}_j\).
- Parameters
wire_order (Wires) – global wire order defining which subspace the operator acts on
- Returns
\(q\)
- Return type
array[float]
-
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 caries information between label calls in the same drawing
- Returns
label to use in drawings
- Return type
str
Example:
>>> op = qml.QuadOperator(1.234, wires=0) >>> op.label() 'cos(φ)x\n+sin(φ)p' >>> op.label(decimals=2) 'cos(1.23)x\n+sin(1.23)p' >>> op.label(base_label="Quad", decimals=2) 'Quad\n(1.23)'
-
queue
(context=<class 'pennylane.queuing.QueuingContext'>)¶ Append the operator to the Operator queue.
-
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.Note
The wire_order argument is currently not implemented, and using it will raise an error.
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
matrix representation
- Return type
scipy.sparse.coo.coo_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.See also
- Returns
list of coefficients \(c_i\) and list of operations \(O_i\)
- Return type
tuple[list[tensor_like or float], list[Operation]]
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