Digital Predistortion of Optical Fields for Fast and High-Fidelity Entangling Gates in Trapped-Ion Qubits

Abstract

High-fidelity quantum gates require precise classical control signals, yet the analog hardware delivering these signals introduces nonlinear distortions that degrade gate performance. We demonstrate digital predistortion of an acousto-optic modulator used to generate multi-tone entangling-gate waveforms in a trapped-ion processor based on $^{88}$Sr$^+$. By measuring and inverting the static nonlinear amplitude response of the modulator, we apply a feed-forward correction that extends its linear operating range and suppresses spurious intermodulation products. Spectral analysis of the gate beam shows 3--5 dB suppression of the dominant intermodulation tones, approximately doubling the usable diffraction efficiency at a $10^{-3}$ estimated gate-error threshold. Direct two-qubit Bell-state fidelity measurements confirm that predistortion consistently improves entangling-gate performance. The calibrate-and-invert methodology is device and platform agnostic, applicable to any nonlinear element in the classical control chain of a quantum processor.

Figures (3)

• Figure 1: AOM characterization and predistortion. (a) Amplitude transfer function: black crosses show photodiode-measured optical amplitude versus normalized RF input amplitude $A$; blue line is the polynomial fit (Eq. \ref{['eq:amplitude-poly']}); magenta line shows the effective AOM output when DPD is applied, demonstrating linearity up to $A_{\mathrm{corr}}$. Vertical dashed line: $A_{\mathrm{corr}}\approx0.566$. (b) Phase transfer function: black crosses show the phase delay $\phi(A)$ measured by heterodyne detection; purple line is the polynomial fit. The amplitude-dependent phase shift is not corrected by the amplitude-only DPD applied in this work. (c) Predistortion function: the orange curve gives the RF input amplitude required to produce a desired optical output amplitude, obtained by numerically inverting the polynomial fit in (a). Gray dotted diagonal: the $y=A$ line expected for a perfectly linear AOM, where no predistortion would be needed. Vertical dashed line: $A_{\mathrm{corr}}$, at which the predistortion reaches full drive ($A=1$); for higher target amplitudes the correction has no additional headroom and the drive is clamped.
• Figure 2: Spectral benchmarking of amplitude-only DPD for the Cardioid(1,2) waveform. Solid lines show heterodyne photodiode measurements; dashed lines show simulations incorporating the measured amplitude and phase transfer functions (Fig. \ref{['fig:aom_response']}). In both panels, the vertical dashed line marks $A_{\mathrm{corr}}$. (a) Gate-to-IM3 power ratio $R_{10}$. Higher values indicate weaker IM3 tone relative to the gate tone. Within $A\lesssim A_{\mathrm{corr}}$, DPD improves $R_{10}$ by $\sim$3--5 dB (blue) compared to uncorrected operation (red); for $A\gtrsim A_{\mathrm{corr}}$ the DPD advantage diminishes as expected. (b) Gate-tone power change due to DPD, $\Delta P_n = 10\log_{10}(P^{\mathrm{DPD}}_n/P^{\mathrm{NoDPD}}_n)$, versus $A$, for the two gate tones $n{=}1$ (at detuning $\xi_0$, green) and $n{=}2$ (at detuning $2\xi_0$, purple). The two tones track each other closely, as expected from their equal design amplitudes.
• Figure 3: Bell-state fidelity versus gate-rate parameter $\xi_{0}$. Solid lines: photodiode-derived fidelity estimates (aligned to gate data via two shared fit parameters; see text); shaded bands: gate-rate uncertainty from laser-power fluctuations. Blue filled squares with error bars: measured gate fidelities with DPD; red filled circles with error bars: without DPD. At a given gate rate, DPD consistently yields higher fidelity. The highlighted data points (thick black outlines) mark two gates at similar rates ($\xi_0 \approx 5.6$ kHz with DPD at $A=0.60$; $\xi_0 \approx 5.8$ kHz without DPD at $A=0.80$), whose fidelities differ by $\sim$5.5 percentage points. Inset: parity-fringe measurements for these two gates (blue open squares: DPD; red open circles: no DPD; solid lines: sinusoidal fits). Fitted contrasts: $C_{\mathrm{DPD}} = 0.958 \pm 0.003$, $C_{\mathrm{NoDPD}} = 0.890 \pm 0.004$; the higher contrast with DPD shows that the fidelity gain is driven by improved coherence of the entangling operation.