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 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 number 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).
creation_operator: Create a creation operator in the truncated Fock space.
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 = qctrl.functions.calculate_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 = qctrl.functions.calculate_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 = qctrl.functions.calculate_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 = qctrl.functions.calculate_graph(graph=graph, output_node_names=["state_offset"])
>>> result.output["state_offset"]["value"]
array([[0.+0.j],
       [0.+0.j],
       [3.+0.j]])