Operators and States¶

Python operator and state primitives.

Generated operators use sparse storage internally where that preserves the structure of common open-system models. The public to_numpy and __array__ interfaces still expose dense arrays for convenient inspection and interoperability.

class openquantumsim.operators.Operator(data, space=None, label=None)[source]¶

Bases: object

Linear operator with an optional Hilbert-space descriptor.

Parameters:

data (Any)
space (HilbertSpace | None)
label (str | None)

data: Any¶

space: HilbertSpace | None = None¶

label: str | None = None¶

property shape: tuple[int, int]¶: Matrix shape.

property dim: int¶: Matrix dimension.

dag()[source]¶

Return the Hermitian adjoint.

Return type:: Operator

to_numpy()[source]¶

Return a dense NumPy array representation.

Return type:: ndarray[tuple[Any, …], dtype[complex128]]

openquantumsim.operators.eye(space_or_dim)[source]¶

Identity operator.

Parameters:: space_or_dim (HilbertSpace | int)
Return type:: Operator

openquantumsim.operators.destroy(space_or_dim)[source]¶

Bosonic annihilation operator for a finite-dimensional truncation.

Parameters:: space_or_dim (HilbertSpace | int)
Return type:: Operator

openquantumsim.operators.create(space_or_dim)[source]¶

Bosonic creation operator.

Parameters:: space_or_dim (HilbertSpace | int)
Return type:: Operator

openquantumsim.operators.identity(space_or_dim)[source]¶

Identity operator (alias of eye()).

Parameters:: space_or_dim (HilbertSpace | int)
Return type:: Operator

openquantumsim.operators.position(space_or_dim)[source]¶

Dimensionless position quadrature (a + a^dagger) / sqrt(2).

Parameters:: space_or_dim (HilbertSpace | int)
Return type:: Operator

openquantumsim.operators.momentum(space_or_dim)[source]¶

Dimensionless momentum quadrature -i (a - a^dagger) / sqrt(2).

Parameters:: space_or_dim (HilbertSpace | int)
Return type:: Operator

openquantumsim.operators.num(space_or_dim)[source]¶

Bosonic number operator.

Parameters:: space_or_dim (HilbertSpace | int)
Return type:: Operator

openquantumsim.operators.sigmax(space_or_dim=None)[source]¶

Pauli sigma-x operator.

Parameters:: space_or_dim (HilbertSpace | int | None)
Return type:: Operator

openquantumsim.operators.sigmay(space_or_dim=None)[source]¶

Pauli sigma-y operator.

Parameters:: space_or_dim (HilbertSpace | int | None)
Return type:: Operator

openquantumsim.operators.sigmaz(space_or_dim=None)[source]¶

Pauli sigma-z operator.

Parameters:: space_or_dim (HilbertSpace | int | None)
Return type:: Operator

openquantumsim.operators.sigmam(space_or_dim=None)[source]¶

Two-level lowering operator |down><up|.

Parameters:: space_or_dim (HilbertSpace | int | None)
Return type:: Operator

openquantumsim.operators.sigmap(space_or_dim=None)[source]¶

Two-level raising operator |up><down|.

Parameters:: space_or_dim (HilbertSpace | int | None)
Return type:: Operator

openquantumsim.operators.spin_jm(space_or_dim)[source]¶

Spin-S lowering operator in the Dicke basis ordered by descending m.

Parameters:: space_or_dim (SpinSpace | DickeSpace | int)
Return type:: Operator

openquantumsim.operators.spin_jp(space_or_dim)[source]¶

Spin-S raising operator.

Parameters:: space_or_dim (SpinSpace | DickeSpace | int)
Return type:: Operator

openquantumsim.operators.spin_jx(space_or_dim)[source]¶

Spin-S x operator.

Parameters:: space_or_dim (SpinSpace | DickeSpace | int)
Return type:: Operator

openquantumsim.operators.spin_jz(space_or_dim)[source]¶

Spin-S z operator in the Dicke basis ordered by descending m.

Parameters:: space_or_dim (SpinSpace | DickeSpace | int)
Return type:: Operator

openquantumsim.operators.dicke_jm(space_or_dim)[source]¶

Collective Dicke lowering operator J_-.

Parameters:: space_or_dim (DickeSpace | int)
Return type:: Operator

openquantumsim.operators.dicke_jp(space_or_dim)[source]¶

Collective Dicke raising operator J_+.

Parameters:: space_or_dim (DickeSpace | int)
Return type:: Operator

openquantumsim.operators.dicke_jx(space_or_dim)[source]¶

Collective Dicke drive operator J_x.

Parameters:: space_or_dim (DickeSpace | int)
Return type:: Operator

openquantumsim.operators.dicke_jz(space_or_dim)[source]¶

Collective Dicke inversion operator J_z.

Parameters:: space_or_dim (DickeSpace | int)
Return type:: Operator

openquantumsim.operators.dicke_excitation(space_or_dim)[source]¶

Collective excitation-number operator in the symmetric Dicke manifold.

Parameters:: space_or_dim (DickeSpace | int)
Return type:: Operator

openquantumsim.operators.collective_lowering(space_or_dim)[source]¶

Alias for the Dicke collective lowering operator J_-.

Parameters:: space_or_dim (DickeSpace | int)
Return type:: Operator

openquantumsim.operators.collective_raising(space_or_dim)[source]¶

Alias for the Dicke collective raising operator J_+.

Parameters:: space_or_dim (DickeSpace | int)
Return type:: Operator

openquantumsim.operators.collective_x(space_or_dim)[source]¶

Alias for the Dicke collective drive operator J_x.

Parameters:: space_or_dim (DickeSpace | int)
Return type:: Operator

openquantumsim.operators.collective_z(space_or_dim)[source]¶

Alias for the Dicke collective inversion operator J_z.

Parameters:: space_or_dim (DickeSpace | int)
Return type:: Operator

openquantumsim.operators.collective_excitation(space_or_dim)[source]¶

Alias for the Dicke collective excitation-number operator.

Parameters:: space_or_dim (DickeSpace | int)
Return type:: Operator

openquantumsim.operators.tensor(*items)[source]¶

Kronecker product of operators.

Parameters:: items (Operator)
Return type:: Operator

openquantumsim.operators.basis(space_or_dim, index)[source]¶

Basis ket as a column vector.

Parameters:

space_or_dim (HilbertSpace | int)
index (int | str)

Return type:

ndarray[tuple[Any, …], dtype[complex128]]

openquantumsim.operators.fock(space_or_dim, n)[source]¶

Fock basis state |n>.

Parameters:

space_or_dim (HilbertSpace | int)
n (int)

Return type:

ndarray[tuple[Any, …], dtype[complex128]]

openquantumsim.operators.dicke_state(space, excitations)[source]¶

Symmetric Dicke state with a fixed number of excited spins.

Parameters:

space (DickeSpace)
excitations (int)

Return type:

ndarray[tuple[Any, …], dtype[complex128]]

openquantumsim.operators.ket2dm(ket)[source]¶

Convert a ket to a density matrix.

Parameters:: ket (ndarray[tuple[Any, ...], dtype[complex128]])
Return type:: ndarray[tuple[Any, …], dtype[complex128]]

openquantumsim.operators.coherent(space_or_dim, alpha)[source]¶

Truncated coherent state.

Parameters:

space_or_dim (FockSpace | int)
alpha (complex)

Return type:

ndarray[tuple[Any, …], dtype[complex128]]

openquantumsim.operators.coherent_dm(space_or_dim, alpha)[source]¶

Density matrix of a truncated coherent state.

Parameters:

space_or_dim (FockSpace | int)
alpha (complex)

Return type:

ndarray[tuple[Any, …], dtype[complex128]]

openquantumsim.operators.thermal_dm(space_or_dim, nbar)[source]¶

Truncated thermal density matrix for a bosonic mode.

Parameters:

space_or_dim (FockSpace | int)
nbar (float)

Return type:

ndarray[tuple[Any, …], dtype[complex128]]