AC Stark shift (or light shift) is the frequency shift of a qubit when driven by an off-resonant microwave pulse. The shift depends on detuning $\delta = \omega_{\text{drive}} - \omega_{\text{qubit}}$ and drive strength $\Omega$ (Rabi frequency).

For weak driving:

$$\Delta \omega_{\text{Stark}} \approx \frac{\Omega^2}{4\delta}$$

The shift is proportional to drive power and inversely proportional to detuning.

Leakage errors: off-resonant drives shift the qubit frequency, potentially bringing higher levels into resonance. This can cause unwanted transitions to $|2\rangle$.

Two-qubit gates: in some gate schemes (e.g., echoed cross-resonance), AC Stark shifts reduce gate fidelity if not properly compensated.

Drive calibration: AC Stark shift causes nonlinearity in Rabi frequency vs. drive power. Accounting for this is important for precise gate tuning.

scqubits can estimate AC Stark shifts via perturbation theory or numerically by solving the time-dependent Schrödinger equation with a driving term.