state_infidelity

Graph.state_infidelity(x, y, *, name=None)

Calculate the infidelity of two pure states.

Parameters

• x (np.ndarray or Tensor) – A pure state, $|\psi\rangle$(..., D). Note that the last dimension must be the same as y, and the batch dimension, if any, must be broadcastable with y.
• y (np.ndarray or Tensor) – A pure state, $|\phi\rangle$(..., D). Note that the last dimension must be the same as x, and the batch dimension, if any, must be broadcastable with x.
• name (str or None , optional) – The name of the node.

Returns

The infidelity of two pure states, with shape (...).

Return type

Tensor

SEE ALSO

Graph.density_matrix_infidelity : Infidelity between two density matrices.

Graph.inner_product : Inner product of two vectors.

Graph.unitary_infidelity : Infidelity between a unitary and target operators.

Notes

The infidelity of two pure states $|\psi\rangle$ and $|\phi\rangle$ is defined as $1 - | \langle \psi | \phi \rangle |^2$

For more information about the state fidelity, see fidelity of quantum states on Wikipedia.

Examples

>>> graph.state_infidelity(
...     np.array([0, 1]), np.array([[1, 0], [0, 1]]), name="infidelity"
... )
<Tensor: name="infidelity", operation_name="state_infidelity", shape=(2,)>
>>> result = bo.execute_graph(graph=graph, output_node_names="infidelity")
>>> result["output"]["infidelity"]["value"]
array([1., 0.])