# qml.P¶

class P(wires)[source]

The momentum quadrature observable $$\hat{p}$$.

When used with the expval() function, the momentum expectation value $$\braket{\hat{p}}$$ is returned. This corresponds to the mean displacement in the phase space along the $$p$$ axis.

Details:

• Number of wires: 1

• Number of parameters: 0

• Observable order: 1st order in the quadrature operators

• Heisenberg representation:

$d = [0, 0, 1]$
Parameters

wires (Sequence[int] or int) – the wire the operation acts on

 do_check_domain eigvals Eigenvalues of an instantiated observable. ev_order 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 Wires of this operator.
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 = 1
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 = 0
num_wires = 1
par_domain = None
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

Wires of this operator.

Returns

wires

Return type

Wires

 check_domain(p[, flattened]) Check the validity of a parameter. compare(other) Compares with another Hamiltonian, Tensor, or Observable, to determine if they are equivalent. Returns the list of operations such that they diagonalize the observable in the computational basis. heisenberg_expand(U, wires) Expand the given local Heisenberg-picture array into a full-system one. heisenberg_obs(wires) Representation of the observable in the position/momentum operator basis. 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

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

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, 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)

• wires (Wires) – wires on the device the array U should be expanded to apply to

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(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

wires (Wires) – wires on the device that the observable gets applied to

Returns

$$q$$

Return type

array[float]

queue()

Append the operator to the Operator queue.