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.