Figure 7. Dependence of single-qudit gate durations from qudit dimension $$d$$ for four generalized single-qudit gates. Each data point shows the minimum duration of applying Incremental Pulse Re-seeding (IPR) from ten different starting times. The unexpected discrepancy between $$d=6$$ and $$d=7$$ for the generalized $$T_d$$ gate suggests a highly complicated optimization space and shows that shorter pulses for some $$d$$ values may be possible. For each gate the scaling of duration with dimension $$d$$ is analyzed with quadratic and linear regressions, where the latter is less accurate but captures the essential behavior in this low-dimensional regime.