qml.PolyXP¶

class PolyXP(q, wires, do_queue=True, id=None)[source]¶

Bases: pennylane.operation.CVObservable

An arbitrary second-order polynomial observable.

Represents an arbitrary observable \(P(\x,\p)\) that is a second order polynomial in the basis \(\mathbf{r} = (\I, \x_0, \p_0, \x_1, \p_1, \ldots)\).

For first-order observables the representation is a real vector \(\mathbf{d}\) such that \(P(\x,\p) = \mathbf{d}^T \mathbf{r}\).

For second-order observables the representation is a real symmetric matrix \(A\) such that \(P(\x,\p) = \mathbf{r}^T A \mathbf{r}\).

Used for evaluating arbitrary order-2 CV expectation values of CVParamShiftTape.

Details:

Number of wires: Any
Number of parameters: 1
Observable order: 2nd order in the quadrature operators
Heisenberg representation: \(A\)

Parameters

q (array[float]) – expansion coefficients
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

`eigvals`	Eigenvalues of an instantiated operator.
`ev_order`	Order in (x, p) that a CV observable is a polynomial of.
`grad_method`
`has_matrix`
`hash`	Integer hash that uniquely represents the operator.
`hyperparameters`	Dictionary of non-trainable variables that this operation depends on.
`id`	Custom string to label a specific operator instance.
`matrix`	Matrix representation of an instantiated operator in the computational basis.
`name`	String for the name of the operator.
`num_params`
`num_wires`
`parameters`	Trainable parameters that the operator depends on.
`return_type`	Measurement type that this observable is called with.
`supports_heisenberg`
`wires`	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 use qml.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 = 2¶

Order in (x, p) that a CV observable is a polynomial of.

Type: None, int

grad_method = 'F'¶

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 use qml.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¶

wires¶

Wires that the operator acts on.

Returns: wires
Return type: Wires

Methods

`compare`(other)	Compares with another `Hamiltonian`, `Tensor`, or `Observable`, 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).
`decomposition`()	Representation of the operator as a product of other operators.
`diagonalizing_gates`()	Sequence of gates that diagonalize the operator in the computational basis.
`expand`()	Returns a tape that has recorded the decomposition of the operator.
`generator`()	Generator of an operator that is in single-parameter-form.
`get_eigvals`()	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, or Observable, 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

decomposition().

Parameters

params (list) – trainable parameters of the operator, as stored in the parameters attribute
wires (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

diagonalizing_gates().

Parameters

params (list) – trainable parameters of the operator, as stored in the parameters attribute
wires (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

get_eigvals() and eigvals()

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

get_matrix() and matrix()

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, **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

sparse_matrix()

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

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

terms()

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

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

compute_decomposition().

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

compute_diagonalizing_gates().

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: QuantumTape

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 and SparseHamiltonian 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

compute_eigvals()

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

compute_matrix()

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)¶

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.RX(1.23456, wires=0)
>>> op.label()
"RX"
>>> op.label(decimals=2)
"RX\n(1.23)"
>>> op.label(base_label="my_label")
"my_label"
>>> op.label(decimals=2, base_label="my_label")
"my_label\n(1.23)"
>>> op.inv()
>>> op.label()
"RX⁻¹"

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)]

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

compute_sparse_matrix()

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

compute_terms()

Returns: list of coefficients \(c_i\) and list of operations \(O_i\)
Return type: tuple[list[tensor_like or float], list[Operation]]

qml.PolyXP¶

Attributes

Methods

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