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.