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, optional) – The name of the node.
- Returns
A 2D tensor representing the number operator.
- Return type
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]])