Figure 6. Distribution of naive random-guess optimizations of the \(X_8\) gate for invididual durations between \(180\,\mathrm{ns}\) and \(230\,\mathrm{ns}\). Each boxplot consists of \(20\) fidelities from \(20\) individual Juqbox optimizations, with the blue line indicating the median value, the box indicating the middle \(50\%\) of fidelities, and the whiskers indicating the full range of values. (a) The full data, showing a general increase in fidelity as duration increases. (b) Focusing on the area of interest (fidelities close to \(99.9\%\)). The IPR scheme outperforms random guessing, finding a minimum duration of \(T_\mathrm{best}=195\,\mathrm{ns}\) at \(99.9\%\) fidelity, whereas none of the 20 random guesses at that duration reached the same fidelity.