Tunable Transmon Qubit¶

The flux-tunable transmon qubit [Koch2007] is a simple modification of the fixed-frequency transmon obtained. It is obtained by replacing the Josephson junction by a SQUID loop of two Josephson junctions. A flux threaded through this loop can then be used to change the effective Josephson energy of the circuit and thus make the transmon tunable.

\[H = 4E_\text{C}(\hat{n}-n_g)^2+\frac{1}{2}E_\text{J,eff}(\Phi_\text{ext})\sum_n(|n\rangle\langle n+1|+\text{h.c.}),\]

expressed in the charge basis. Here, the parameters are those of the fixed-frequency transmon except for the effective Josephson energy \(E_\text{J,eff}(\Phi_\text{ext}) = E_{\text{J,max}} \sqrt{\cos^2(\pi\Phi_\text{ext}/\Phi_0)+ d^2 \sin^2 (\pi\Phi_\text{ext}/\Phi_0)}\), where \(E_\text{J,max} = E_\text{J1} + E_\text{J2}\) is the maximum Josephson energy, and \(d=(E_\text{J1}-E_\text{J2})/(E_\text{J1}+E_\text{J2})\) is the relative junction asymmetry.

An instance of a tunable transmon qubit is created like this:

tune_tmon = scqubits.TunableTransmon(
   EJmax=50.0,
   EC=0.5,
   d=0.01,
   flux=0.0,
   ng=0.0,
   ncut=30
)

From within Jupyter notebook, a GUI-based creation is supported via:

tune_tmon = scqubits.TunableTransmon.create()

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

Tunable Transmon Qubit¶

Wavefunctions and visualization of eigenstates¶

Implemented operators¶

Computation and visualization of matrix elements¶

Estimation of coherence times¶

Tunable Transmon 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¶