# number_operator

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

Create a number 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 number 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.creation_operator : Create a creation operator in the truncated Fock space.

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

## Examples

Generate a number operator for a three-level system.

>>> graph.number_operator(3, name="n")
<Tensor: name="n", operation_name="number_operator", shape=(3, 3)>
>>> result = bo.execute_graph(graph=graph, output_node_names="n")
>>> result["output"]["n"]["value"]
array([[0.+0.j, 0.+0.j, 0.+0.j],
[0.+0.j, 1.+0.j, 0.+0.j],
[0.+0.j, 0.+0.j, 2.+0.j]])

Apply a number operator on the second excited state such that $N|2\rangle = 2|2\rangle$

>>> n = graph.number_operator(3)
>>> state = n @ graph.fock_state(3, 2)[:, None]
>>> state.name = "state"
>>> result = bo.execute_graph(graph=graph, output_node_names="state")
>>> result["output"]["state"]["value"]
array([[0.+0.j],
[0.+0.j],
[2.+0.j]])

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

>>> graph.number_operator(3, 1, name="n_offset")
<Tensor: name="n_offset", operation_name="number_operator", shape=(3, 3)>
>>> result = bo.execute_graph(graph=graph, output_node_names="n_offset")
>>> result["output"]["n_offset"]["value"]
array([[1.+0.j, 0.+0.j, 0.+0.j],
[0.+0.j, 2.+0.j, 0.+0.j],
[0.+0.j, 0.+0.j, 3.+0.j]])

Apply a number operator with an offset such that $N|3\rangle = 3|3\rangle$

>>> n_offset = graph.number_operator(3, 1)
>>> state_offset = n_offset @ graph.fock_state(3, 3, 1)[:, None]
>>> state_offset.name = "state_offset"
>>> result = bo.execute_graph(graph=graph, output_node_names="state_offset")
>>> result["output"]["state_offset"]["value"]
array([[0.+0.j],
[0.+0.j],
[3.+0.j]])