# 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 at [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

Graph.annihilation_operator : Create an annihilation operator in the truncated Fock space.

Graph.coherent_state : Create a coherent state (or a batch of them).

Graph.fock_state : Create a Fock state (or a batch of them).

Graph.number_operator : Create a number operator in the truncated Fock space.

## Examples

Generate a creation operator for a two-level system.

array([[0.+0.j, 0.+0.j],
[1.+0.j, 0.+0.j]])

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

>>> state = adagger @ graph.fock_state(2, 0)[:, None]
>>> state.name = "state"
>>> result = bo.execute_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.

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 $a^\dagger|1\rangle = \sqrt{2}|2\rangle$