Figure 3. Comparison of pulse shapes for two adjacent reference points before and after several rounds of re-optimization. Point A corresponds to Cartan coordinates $(\frac 1 2, 0, 0)$ (the coordinates of $CNOT$ and $CZ$) and point B corresponds to coordinates $(\frac 1 2, \frac 1 4, \frac 1 4)$. Optimized controls for the two operations (from the same results as shown in Figure 4) are shown for the $\sigma_x \sigma_x$ control (top) and $\sigma_z^{(1)}$ control (bottom) of the Hamiltonian (6). Inset: locations of points A and B in the Weyl chamber. Left: the pulse shapes are initially significantly different between points A and B. Right: the pulses become far more similar after re-optimization, making interpolation easier, but still retain certain differences in their shapes that account for the differences in the resulting operations.