qml.NumberOperator

class NumberOperator(wires)[source]

Bases: pennylane.operation.CVObservable

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

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
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

Wire values.

Returns

wire values

Return type

tuple[int]

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.

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