Fluxonium Qubit¶

The Hamiltonian of the fluxonium qubit [Manucharyan2009] in phase basis representation is given by

\[H=-4E_\text{C}\partial_\phi^2-E_\text{J}\cos(\phi-\varphi_\text{ext}) +\frac{1}{2}E_L\phi^2.\]

Here, \(E_C\) is the charging energy, \(E_J\) the Josephson energy, \(E_L\) the inductive energy, and \(\varphi_\text{ext}=2\pi \Phi_\text{ext}/\Phi_0\) the external flux in dimensionless form. The Fluxonium class internally uses the \(E_C\)-\(E_L\) harmonic-oscillator basis [Zhu2013] with truncation level specified by cutoff.

An instance of the fluxonium qubit is created as follows:

fluxonium = scqubits.Fluxonium(EJ = 8.9,
                               EC = 2.5,
                               EL = 0.5,
                               flux = 0.33,
                               cutoff = 110)

Here, the flux threading the circuit loop is specified by flux which records the flux in units of the magnetic flux quantum, \(\Phi_\text{ext}/\Phi_0\).

From within a Jupyter notebook, a fluxonium instance can alternatively be created with:

fluxonium = scqubits.Fluxonium.create()

This functionality is enabled if the ipywidgets package is installed, and displays GUI forms prompting for the entry of the required parameters.

Wavefunctions and visualization of eigenstates¶

Implemented operators¶

The following operators are implemented for use in matrix element calculations.

Fluxonium Qubit¶

Wavefunctions and visualization of eigenstates¶

Implemented operators¶

Computation and visualization of matrix elements¶

Estimation of coherence times¶

Fluxonium Qubit¶

Calculational methods related to Hamiltonian and energy spectra¶

Wavefunctions and visualization of eigenstates¶

Implemented operators¶

Computation and visualization of matrix elements¶

Estimation of coherence times¶