Transmon Qubit Calculator
With this calculator you can convert between charging energy (Ec) and total capacitance (CΣ), between Josephson energy (EJ), Josephson inductance (LJ), junction critical current (Ic) or room temperature junction resistance (R), and from charging and Josephson energies calculate relevant qubit transition frequencies. Other calculations are added below including Qubit’s Purcell decay, chi-shift, conversion between spectral linewidth and coherence times, etc.
All frequencies are in natural units.
|EJ||Junction/SQUID Josephson energy|
|LJ||Junction/SQUID Josephson inductance|
|Ic||Junction/SQUID critical current|
|R||Junction/SQUID room temperature resistance for 30/40 nm thin Al films|
|fge||Maximal qubit ground (g) to first excited state (e) transition frequency|
|fef||Maximal qubit first (e) to second excited state (f) transition frequency|
|fgf||Maximal qubit ground (g) to second excited state (f) transition frequency|
|α||Qubit anharmonicity ≈ Ec|
|fres||Readout resonator frequency|
|Qres||Readout resonator Q-factor|
|κres||Readout resonator: spectral linewidth|
|g||Resonator-qubit coupling constant|
|Δ||Qubit-resonator transition frequency difference|
|TPurcell||Qubit’s Purcell decay time|
|κPurcell||Qubit’s Purcell spectral linewidth|
|χ-shift||Half of the fres difference between qubit being in the g or e state.|
|T1||Energy relaxation time|
|dffwhm||Full width at half maximum – spectral linewidth|
|ncrit||Critical photon number|
Thank you for providing this page!
I just understood, that I use it quite frequently, because it is convinient for simple transmons calculations.
I started using it when I joined my PhD. I still do.