qml.PolyXP

class PolyXP(q, wires)

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 by QNode._pd_analytic() for evaluating arbitrary order-2 CV expectation values.

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

Attributes

do_check_domain
eigvals	Eigenvalues of an instantiated observable.
ev_order
grad_method
matrix	Matrix representation of an instantiated operator in the computational basis.
name	String for the name of the operator.
num_params
num_wires
par_domain
parameters	Current parameter values.
return_type
supports_heisenberg
wires	Wire values.

do_check_domain = True

eigvals

Eigenvalues of an instantiated observable.

The order of the eigenvalues needs to match the order of the computational basis vectors when the observable is diagonalized using diagonalizing_gates. This is a requirement for using qubit observables in quantum functions.

Example:

>>> U = qml.PauliZ(wires=1)
>>> U.eigvals
>>> array([1, -1])

Returns

eigvals representation

Return type

array

ev_order = 2

grad_method = 'F'

matrix

Matrix representation of an instantiated operator in the computational basis.

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

par_domain = 'A'

parameters

Current parameter values.

Fixed parameters are returned as is, free parameters represented by Variable instances are replaced by their current numerical value.

Returns

parameter values

Return type

list[Any]

return_type = None

supports_heisenberg = True

wires

Wire values.

Returns

wire values

Return type

tuple[int]

Methods

check_domain(p[, flattened])	Check the validity of a parameter.
diagonalizing_gates()	Returns the list of operations such that they diagonalize the observable in the computational basis.
heisenberg_expand(U, num_wires)	Expand the given local Heisenberg-picture array into a full-system one.
heisenberg_obs(num_wires)	Representation of the observable in the position/momentum operator basis.
queue()	Append the operator to the Operator queue.

check_domain(p, flattened=False)

Check the validity of a parameter.

Variable instances can represent any real scalars (but not arrays).

Parameters

• p (Number, array, Variable) – parameter to check

• flattened (bool) – True means p is an element of a flattened parameter sequence (affects the handling of ‘A’ parameters)

Raises

• TypeError – parameter is not an element of the expected domain

• ValueError – parameter is an element of an unknown domain

Returns

p

Return type

Number, array, Variable

diagonalizing_gates()

Returns the list of operations such that they diagonalize the observable in the computational basis.

Returns

A list of gates that diagonalize the observable in the computational basis.

Return type

list(qml.Operation)

heisenberg_expand(U, num_wires)

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)

• num_wires (int) – total number of wires in the quantum circuit. If zero, return U as is.

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(num_wires)

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

num_wires (int) – total number of wires in the quantum circuit

Returns

\(q\)

Return type

array[float]

queue()

Append the operator to the Operator queue.