qml.Identity

class Identity(wires)[source]

Bases: pennylane.operation.CVObservable

The identity observable \(\I\).

The expectation of this observable

\[E[\I] = \text{Tr}(\I \rho)\]

corresponds to the trace of the quantum state, which in exact simulators should always be equal to 1.

do_check_domain

eigvals

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

Wires of this operator.

do_check_domain = True
eigvals = array([1, 1])
ev_order = 1
grad_method = None
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.

diagonalizing_gates()

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.

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()[source]

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.

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