Transmon Qubit¶
The transmon qubit [Koch2007] is described by the Hamiltonian
\[H=4E_\text{C}(\hat{n}-n_g)^2-\frac{1}{2}E_\text{J}\sum_n(|n\rangle\langle n+1|+\text{h.c.}),\]
expressed in discrete charge basis. Here, \(E_C\) is the charging energy,
\(E_J\) the Josephson energy, and
\(n_g\) the offset charge. Within the Transmon class,
charge-basis representation is employed with a
charge-number cutoff specified by ncut. This cutoff must be chosen sufficiently large for convergence.
An instance of the transmon qubit is initialized as follows:
transmon = scqubits.Transmon(EJ=30.02,
EC=1.2,
ng=0.3,
ncut=31)
From within Jupyter notebook, a transmon instance can alternatively be created with:
transmon = scqubits.Transmon.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.