Figure 5. Evolution of state populations when applying the \(H_4\) pulse of shortest duration (\(76\,\mathrm{ns}\)) to a qudit with \(d=4\). Every computational basis state is transformed into superposition of all four basis states with nearly equal population, deviations only arising from the remaining \(0.1\%\) infidelity. At all times the populations of the guard states \(\ket{4}\) and \(\ket{5}\) are below \(2 \times 10^{-3}\) and \(10^{-6}\), respectively.