Bad Qubits — Learn Quantum by Doing

Multiple choice

The Landau-Zener formula gives the diabatic transition probability near an avoided crossing as

P_\text{diabatic} = \exp(-\pi \Delta_\text{min}^2 / (2 \hbar \alpha))

. How do the minimum gap

\Delta_\text{min}

and the sweep rate

\alpha

affect the chance of an error (jumping out of the ground state)?

Neither the gap nor the sweep rate matters; the transition probability is always exactly 1/2
Both a larger gap and a faster sweep suppress the transition equally
A larger gap exponentially enhances the transition, while a faster sweep suppresses it
A larger gap $\Delta_\text{min}$ exponentially suppresses the transition (wider gaps are safe), while a faster sweep (larger $\alpha$ ) exponentially enhances it (speed kills)