QuditSpace

class qugradlab.hilbert_spaces.QuditSpace(basis: ndarray[int])

Bases: HilbertSpace, ABC

An abstract class defining the Hilbert space for a collection of qudits.

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

Methods

__init__	Initialises a new HilbertSpace.
basis_vector	Returns a column vector represnetation corresponding to the input basis state label.
computational_projector
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__(basis: ndarray[int])

Initialises a new HilbertSpace.

Parameters:

basis (NDArray[Shape[dim], int]) – The labels for the basis vectors.

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]

abstractmethod computational_projector() → ndarray[bool]

Important

This is an abstract method.

Generates a boolean filter for the computation basis states in basis.

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