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, \(|\psi\rangle\), with shape (..., 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, \(|\phi\rangle\), with shape (..., 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

inner_product

Inner product of two vectors.

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 = qctrl.functions.calculate_graph(
...     graph=graph, output_node_names=["infidelity"]
... )
>>> result.output["infidelity"]["value"]
array([1., 0.])