# 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, optional) – The name of the node.

Returns

A 2D tensor representing the creation operator.

Return type

Tensor

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")
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")
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]])