Fig. 2: Evolution from the fluxonium to the inductively shunted transmon spectrum.

a Circuit (inset) and spectrum of a typical fluxonium device with EJ/h = 3 GHz, EL/h = 0.5 GHz and EC/h = 0.45 GHz47 as a function of external flux. The red and blue colors indicate the fluxon and plasmon transition of the ground to the first excited state, respectively. b and c show the potential for plasmon and fluxon transitions at zero and half flux, respectively. d First column shows the transformation of the fluxonium to the IST qubit spectrum by increasing the EJ/EC ratio (EC/h = 150 MHz and EL/h = 500 MHz), where the color scale indicates the calculated matrix elements. The second column shows the full spectrum of the IST qubit, including the diamond-shaped flux levels with ultra-small matrix elements. The low dispersion plasmon levels are in agreement with the transmon spectrum shown in panel (e) for the same EJ and EC.