The off-resonant two-photon driving produced parasitic ac-Stark shifts of the energy levels, which we compensated for by using dynamically adjusted phases. Following (15), the ac-Stark shifts can be calculated from the second-order perturbation theory as Embedded Image, where V(t) consists of the off-diagonal elements of the two-photon drive Hamiltonian Embedded Image in the frame rotating with the drive. The energies En are the detunings of the drive from the 0–1 and 1–2 transitions, E0 = 0, E1 = ℏΔ, and E2 = 0. The resulting ac-Stark shifts εn,k = Embedded ImagekEmbedded Imagen − (EkEn) are ε01(t) = ℏ|Ω2ph|2/Δ, ε12 = − 5ℏ|Ω2ph|2/(4Δ), and ε0,2 = − ℏ|Ω2ph|2/(4Δ). To compensate for the shifts in the energy levels, we dynamically modified the phases of all the three drives as Embedded Image. As a result, the frequencies of the drives matched the ac-Stark shifted qutrit transition frequencies at all instants of time.

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