Drastically suppressing the error of ballistic readout of qubits

The thermal jitter of transmission of magnetic flux quanta in long Josephson junctions is studied. While for large-to-critical damping and small values of bias current the physically obvious dependence of the jitter versus length $\sigma\sim\sqrt{L}$ is confirmed, for small damping starting from the experimentally relevant $\alpha=0.03$ and below strong deviation from $\sigma\sim\sqrt{L}$ is observed, up to nearly complete independence of the jitter versus length, which is exciting from fundamental point of view, but also intriguing from the point of view of possible applications.