Figure 6. Infidelities at 2197 test points within the parameter space of single-qubit rotations (see Equation (9)). Average and worst-case infidelities are shown in Table I. We observe a region of extremely poor interpolation quality (yellow), indicating that the pulses on either side of this area have very different shapes and actions. Intuitively, the pulses on the two different sides of this boundary take different routes around the Bloch sphere to reach the target unitary. Subsequent rounds of neighbor-average re-optimization reduce the size of this poor interpolation region and eventually eliminate it, resulting in an average interpolation infidelity (across all test points) of $3.5 \pm 6.6 \times 10^{-6}$ after three rounds of re-optimization.