Robust Two-Qubit Geometric Phase Gates using Amplitude and Frequency Ramping

Abstract

We demonstrate a method for generating entanglement between trapped atomic ions based on adiabatically ramped state-dependent forces. By ramping both the amplitude of the state-dependent force and the motional mode frequencies, we realize an entangling operation that is robust to motional mode occupation and drifts in the mode frequencies. We measure Bell state fidelities above 0.99 across a broad range of ramp parameters and with motional occupations up to 10 phonons. This technique enables high-fidelity entangling operations without ground-state cooling, has a reduced calibration overhead, and is well suited for both quantum logic spectroscopy applications and scalable quantum computing architectures.

Figures (4)

• Figure 1: Gate pulse sequence and motional trajectories. Panel (a) shows the time-dependent amplitude envelopes $\Omega_g(t)$ of the magnetic gradient drive at $\omega_{g}$ (top) and $\Omega_\mu(t)$ of the bichromatic magnetic fields at $\omega_{0} \pm \delta$ (middle), as well as the frequency of the motional mode $\omega_m(t)$ (bottom). We plot the detuning $\Delta$ between the state-dependent force (thick arrow) and the motional mode (dotted arrow) in (b), and a cartoon of the motional phase space trajectory in (c), for the three highlighted regions in (a). We first ramp on $\Omega_g(t)$ in a time $\tau_g$. Next, in the orange region (i), $\Omega_\mu$ (and thus the SDF) is ramped on over $\tau_\mu$ at far-detuned $\Delta_0$. In the blue region (ii), the motional frequency is ramped from $\Delta_0$ to $\Delta_1$ over duration $\tau_m$. In the purple region (iii), the motional frequency is held constant at $\Delta_1$, followed by time-reversed versions of all ramps to complete the sequence.
• Figure 2: Bell state infidelity as a function of motional ramp duration and adiabaticity. Points for each ramp duration correspond to initial motional states with mean phonon occupations of $\bar{n} \approx 0, 2, 5,$ and $10$, distinguished by progressively lighter shading to indicate increasing $\bar{n}$. The inset compares the unramped gate (red) with a $50~\mu\mathrm{s}$ ramp (green), illustrating the suppressed dependence of the ramped gate fidelity on the initial phonon occupation.
• Figure 3: Bell state infidelity as a function of SDF detuning offset $\varepsilon$ for ramped and non-ramped conditions. Experimental data (blue) correspond to a ramped gate with parameters otherwise matching Fig. \ref{['fig:rampdependence']} data with ramp duration $\tau_{m}=50~\mu\mathrm{s}$ on a ground-state-cooled ion, with a quadratic fit (dotted blue line). We also plot numerical simulations of an unramped gate (green) and gates with 50 $\mu$s (purple) and 300 $\mu$s (brown) motional ramp durations. All numerical simulations were performed in the ion frame and account for all four radial modes. Experimental fidelities are limited by qubit and motional dephasing, which are not included in simulations.
• Figure 4: Spectrum of state-dependent forces in the bichromatic interaction picture. Panel (a) shows the frequencies and relative strengths of the different SDFs at the operating point (pink and black lines), along with the frequencies of the four radial modes at the near-detuned point (dotted lines). Panel (b) shows the range of frequencies spanned by each mode during the ramp, with the solid (dotted) lines indicating the far-detuned (near-detuned) limits of the ramp.