# qml.NumberOperator¶

class NumberOperator(wires)[source]

The photon number observable $$\langle \hat{n}\rangle$$.

The number operator is defined as $$\hat{n} = \a^\dagger \a = \frac{1}{2\hbar}(\x^2 +\p^2) -\I/2$$.

When used with the expval() function, the mean photon number $$\braket{\hat{n}}$$ is returned.

Details:

• Number of wires: 1

• Number of parameters: 0

• Observable order: 2nd order in the quadrature operators

• Heisenberg representation:

$\begin{split}M = \frac{1}{2\hbar}\begin{bmatrix} -\hbar & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1 \end{bmatrix}\end{split}$
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 = 2
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. 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

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 that the observable gets applied 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.