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.
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