The Exponential Outruns The Root
The Exponential Outruns The Root
The Transmon qubit is a Cooper-pair box that has been heavily shunted by a large capacitor. This single addition massively increases the ratio of Josephson energy to charging energy ($E_J/E_C$).
The physics of this ratio creates an asymmetric trade-off. As the capacitance grows, the energy levels of the qubit become insensitive to fluctuations in the background charge. This flattening of the noise sensitivity happens exponentially ($e^{-\sqrt{8E_J/E_C}}$). But the anharmonicity—the non-linear difference between energy levels that allows the device to be addressed as a two-level qubit rather than a simple harmonic oscillator—decreases only algebraically ($(E_J/E_C)^{-1/2}$).
Because the exponential outruns the root, there exists a wide regime where the charge noise is entirely drowned out, yet enough non-linearity remains to isolate the computational states. The flatness is purchased cheaply; the noise dies long before the difference does.
