creation_operator

Graph.creation_operator(dimension, offset=0, *, name=None)

Create a creation operator in the truncated Fock space.

Parameters:

dimension (int) – The size of the state representation in the truncated Fock space. By default, the Fock space is truncated as [0, dimension). If non-zero offset is passed, the space is then truncated at [offset, dimension + offset).
offset (int, optional) – The lowest level of Fock state in the representation. Defaults to 0.
name (str or None, optional) – The name of the node.

Returns:

A 2D tensor representing the creation operator.

Return type:

Tensor

See also

annihilation_operator: Create an annihilation operator in the truncated Fock space.
coherent_state: Create a coherent state (or a batch of them).
fock_state: Create a Fock state (or a batch of them).
number_operator: Create a number operator in the truncated Fock space.

Examples

Generate a creation operator for a two-level system.

>>> graph.creation_operator(2, name="adagger")
<Tensor: name="adagger", operation_name="creation_operator", shape=(2, 2)>
>>> result = qctrl.functions.calculate_graph(graph=graph, output_node_names=["adagger"])
>>> result.output["adagger"]["value"]
array([[0.+0.j, 0.+0.j],
       [1.+0.j, 0.+0.j]])

Apply a creation operator on the ground state such that \(a^\dagger|0\rangle = |1\rangle\).

>>> adagger = graph.creation_operator(2)
>>> state = adagger @ graph.fock_state(2, 0)[:, None]
>>> state.name = "state"
>>> result = qctrl.functions.calculate_graph(graph=graph, output_node_names=["state"])
>>> result.output["state"]["value"]
array([[0.+0.j],
       [1.+0.j]])

Generate a creation operator for a three-level system with an offset.

>>> graph.creation_operator(3, 1, name="adagger_offset")
<Tensor: name="adagger_offset", operation_name="creation_operator", shape=(3, 3)>
>>> result = qctrl.functions.calculate_graph(graph=graph, output_node_names=["adagger_offset"])
>>> result.output["adagger_offset"]["value"]
array([[0.+0.j, 0.+0.j, 0.+0.j],
       [1.41421356+0.j, 0.+0.j, 0.+0.j],
       [0.+0.j, 1.73205081+0.j, 0.+0.j]])

Apply a creation operator with an offset such that \(a^\dagger|1\rangle = \sqrt{2}|2\rangle\).

>>> adagger_offset = graph.creation_operator(3, 1)
>>> state_offset = adagger_offset @ graph.fock_state(3, 1, 1)[:, None]
>>> state.name = "offset"
>>> result = qctrl.functions.calculate_graph(graph=graph, output_node_names=["offset"])
>>> result.output["offset"]["value"]
array([[0.        +0.j],
       [1.41421356+0.j],
       [0.        +0.j]])