Fluxonium

Fluxonium qubit: an LC circuit shunted by a Josephson junction with a large inductance.

class HybridSuperQubits.fluxonium.Fluxonium(Ec, El, Ej, phase, dimension, flux_grouping='EL')[source]

Bases: QubitBase

Parameters:: flux_grouping (Literal['EL', 'EJ'])

PARAM_LABELS: dict[str, str] = {'Ec': '$E_C$', 'Ej': '$E_J$', 'El': '$E_L$', 'phase': '$\\Phi_{\\mathrm{ext}} / \\Phi_0$'}

OPERATOR_LABELS: dict[str, str] = {'d_hamiltonian_d_EL': '\\partial \\hat{H} / \\partial E_L', 'd_hamiltonian_d_ng': '\\partial \\hat{H} / \\partial n_g', 'd_hamiltonian_d_phase': '\\partial \\hat{H} / \\partial \\phi_{{ext}}', 'n_operator': '\\hat{n}', 'phase_operator': '\\hat{\\phi}'}

__init__(Ec, El, Ej, phase, dimension, flux_grouping='EL')[source]

Initializes the Ferbo class with the given parameters.

Parameters:

Ec (float) – Charging energy.
El (float) – Inductive energy.
Ej (float) – Josephson energy.
phase (float) – External magnetic phase.
dimension (int) – Dimension of the Hilbert space.
flux_grouping (Literal["EL", "EJ"], optional) – Flux grouping (‘EL’ or ‘EJ’) (default is ‘EL’).

property phase_zpf: float

Returns the zero-point fluctuation of the phase.

Returns:: Zero-point fluctuation of the phase.
Return type:: float

property n_zpf: float

Returns the zero-point fluctuation of the charge number.

Returns:: Zero-point fluctuation of the charge number.
Return type:: float

phi_osc()[source]

Returns the oscillator length for the LC oscillator composed of the inductance and capacitance.

Returns:: Oscillator length.
Return type:: float

n_operator()[source]

Returns the charge number operator.

Returns:: The charge number operator.
Return type:: np.ndarray

phase_operator()[source]

Returns the total phase operator.

Returns:: The total phase operator.
Return type:: np.ndarray

hamiltonian()[source]

Returns the Hamiltonian of the system.

Returns:: The Hamiltonian of the system.
Return type:: np.ndarray

d_hamiltonian_d_EL()[source]

Return type:: ndarray

d_hamiltonian_d_ng()[source]

Returns the derivative of the Hamiltonian with respect to the number of charge offset.

Returns:: The derivative of the Hamiltonian with respect to the number of charge offset.
Return type:: np.ndarray

d2_hamiltonian_d_ng2()[source]

Returns the second derivative of the Hamiltonian with respect to the number of charge offset.

Returns:: The second derivative of the Hamiltonian with respect to the number of charge offset.
Return type:: np.ndarray

d_hamiltonian_d_phase()[source]

Returns the derivative of the Hamiltonian with respect to the external magnetic phase.

Returns:: The derivative of the Hamiltonian with respect to the external magnetic phase.
Return type:: np.ndarray

d2_hamiltonian_d_phase2()[source]

Returns the second derivative of the Hamiltonian with respect to the external magnetic phase.

Returns:: The second derivative of the Hamiltonian with respect to the external magnetic phase.
Return type:: np.ndarray

d_hamiltonian_d_EJ()[source]

Returns the derivative of the Hamiltonian with respect to the Josephson energy Ej.

Returns:: The derivative of the Hamiltonian with respect to Ej.
Return type:: np.ndarray

wavefunction(which=0, phi_grid=None, esys=None, basis='phase')[source]

Returns a wave function in the phi basis.

Parameters:

which (int, optional) – Index of desired wave function (default is 0).
phi_grid (np.ndarray, optional) – Custom grid for phi; if None, a default grid is used.
basis (Literal["phase", "charge"], optional) – Basis in which to return the wavefunction (‘phase’ or ‘charge’) (default is ‘phase’).
rotate (bool, optional) – Whether to rotate the basis (default is False).
esys (tuple[ndarray, ndarray])

Returns:

Wave function data containing basis labels, amplitudes, and energy.

Return type:

Dict[str, Any]

potential(phi)[source]

Calculates the potential energy for given values of phi.

Parameters:: phi (Union[float, np.ndarray]) – The phase values at which to calculate the potential.
Returns:: The potential energy values.
Return type:: np.ndarray

tphi_1_over_f_flux(A_noise=1e-06, esys=None, get_rate=False, **kwargs)[source]

Parameters:

A_noise (float)
esys (tuple[ndarray, ndarray])
get_rate (bool)

Return type:

float

plot_wavefunction(which=0, phi_grid=None, esys=None, scaling=1, plot_potential=False, basis='phase', mode='abs', **kwargs)[source]

Plot the wave function in the phi basis.

Parameters:

which (Union[int, Iterable[int]], optional) – Index or indices of desired wave function(s) (default is 0).
phi_grid (np.ndarray, optional) – Custom grid for phi; if None, a default grid is used.
esys (Tuple[np.ndarray, np.ndarray], optional) – Precomputed eigenvalues and eigenvectors.
scaling (float, optional) – Scaling factor for the wavefunction (default is 1).
plot_potential (bool, optional) – Whether to plot the potential (default is False).
basis (Literal["phase", "charge"], optional) – Basis in which to return the wavefunction (‘phase’ or ‘charge’) (default is ‘phase’).
mode (Literal["abs", "real", "imag"], optional) – Mode of the wavefunction (‘abs’, ‘real’, or ‘imag’) (default is ‘abs’).
**kwargs –
Additional arguments for plotting. Can include: - fig_ax: Tuple[plt.Figure, plt.Axes], optional

Figure and axes to use for plotting. If not provided, a new figure and axes are created.

Returns:

The figure and axes of the plot.

Return type:

Tuple[plt.Figure, plt.Axes]