BosonQuditSpace

class qugradlab.hilbert_spaces.bosonic.BosonQuditSpace(n_single_particle_states: int, truncation_level: int)

Bases: BosonSpace, QuditSpace

A BosonSpace with a computational structure. The computational subspace consists of the states which have unoccupied and singly occupied single particle states.

Attributes

basis	An array of positive integers labeling the Hilbert space basis
dim	The Hilbert space dimension
inverse	An array satisfying the property self.inverse[self.basis[i]]=i
n_single_particle_states	The number of single particle states
truncation_level	The maximum number of bosons per single particle state

Methods

__init__	Initialises a BosonSpace
basis_vector	Returns a column vector represnetation corresponding to the input basis state label.
computational_projector	Generates a boolean filter for the computation basis states in basis.
computational_subspace	Initialises a qugrad.HilbertSpace corresponding the computation subspace.
dialate_operator	Dialates an operator \(\hat O\) that acts on the computational subspace to an operator \(\hat O\oplus 0\) that acts on the whole Hilbert space.
get_subspace	Generates a new subspace by filtering the basis state labels.
labels	Generates a string (list of strings) that represent the state(s).
project_operator	Projects an operator that acts on the Hilbert space to an operator that acts only on the computational subspace.

__init__(n_single_particle_states: int, truncation_level: int)

Initialises a BosonSpace

Parameters:

• n_single_particle_states (int) – The number of single particle states

• truncation_level (int) – The maximum number of bosons per single particle state

basis_vector(basis_state_label: int) → ndarray[complex128]

Returns a column vector represnetation corresponding to the input basis state label.

Parameters:

basis_state_label (int) – A positive integer denoting the label of the basis state to generate the basis vector for.

Returns:

The basis vector corresponding to the input basis state label.

Return type:

NDArray[Shape[dim], np.complex128]

computational_projector() → ndarray[bool]

Generates a boolean filter for the computation basis states in basis. The computational subspace consists of the states which have unoccupied and singly occupied single particle states.

Returns:

A boolean filter for the computation basis states in basis.

Return type:

NDArray[Shape[dim], bool]

computational_subspace() → HilbertSpace

Initialises a qugrad.HilbertSpace corresponding the computation subspace.

Returns:

The computational subspace

Return type:

qugrad.HilbertSpace

dialate_operator(operator: ndarray) → ndarray

Dialates an operator \(\hat O\) that acts on the computational subspace to an operator \(\hat O\oplus 0\) that acts on the whole Hilbert space.

Parameters:

operator (NDArray[Shape[computational_subspace().dim, computational_subspace().dim] complex]) – The operator that acts on the computational subspace

Returns:

The dialated operator that acts on the whole Hilbert space

Return type:

NDArray[Shape[dim, dim] complex]

get_subspace(filter: ndarray[bool]) → HilbertSpace

Generates a new subspace by filtering the basis state labels.

Parameters:

filter (NDArray[Shape[dim], bool]) – True entries are retained in the new subspace.

Returns:

The filtered subspace.

Return type:

HilbertSpace

labels(states: int | list[int] | None = None) → str | list[str]

Generates a string (list of strings) that represent the state(s).

Parameters:

states (int | list[int], optional) – The state(s) to label. If None then the labels for all states in basis are returned. By default None.

Returns:

The label(s) for the specified states.

Return type:

str | list[str]

project_operator(operator: ndarray) → ndarray

Projects an operator that acts on the Hilbert space to an operator that acts only on the computational subspace.

Parameters:

operator (NDArray[Shape[dim, dim] complex]) – The operator that acts on the whole Hilbert space

Returns:

The projected operator that acts on the computational subspace.

Return type:

NDArray[Shape[computational_subspace().dim, computational_subspace().dim] complex]

property basis: ndarray[int]

An array of positive integers labeling the Hilbert space basis

property dim

The Hilbert space dimension

property inverse: ndarray[int]

An array satisfying the property self.inverse[self.basis[i]]=i

property n_single_particle_states: int

The number of single particle states

property truncation_level: int

The maximum number of bosons per single particle state