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
See also
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") <Tensor: name="adagger", operation_name="creation_operator", shape=(2, 2)> >>> result = qctrl.functions.calculate_graph(graph=graph, output_node_names=["adagger"]) >>> result.output["adagger"]["value"] 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") <Tensor: name="adagger_offset", operation_name="creation_operator", shape=(3, 3)> >>> result = qctrl.functions.calculate_graph(graph=graph, output_node_names=["adagger_offset"]) >>> result.output["adagger_offset"]["value"] 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]])