Trapped-ion two-qubit gates with >99.99% fidelity without ground-state cooling

TL;DR

The study tackles the bottleneck of high-fidelity two-qubit gates in trapped-ion systems that traditionally require ground-state cooling. It introduces the smooth gate, an adiabatic-elimination strategy that ramps the gate detuning $\delta(t)$ while keeping the drive strength $\Omega_g$ fixed to suppress residual spin-motion entanglement and maintain gate speed. Experimentally, the authors achieve a two-qubit error as low as $8.4\times10^{-5}$ without ground-state cooling, with fidelity staying below $5\times10^{-4}$ up to $\bar{n}=9.4$ on the gate mode, demonstrating robust performance above the Doppler limit. The results have broad implications for scalable, electronic (laser-free) trapped-ion quantum computing, including simplified architectures, reduced cooling and transport overhead, and potential large-scale speedups for quantum circuits. Overall, the smooth gate offers a practical path to high-fidelity, temperature-insensitive quantum logic suitable for large QCCD implementations.

Abstract

We introduce the 'smooth gate', an entangling method for trapped-ion qubits where residual spin-motion entanglement errors are adiabatically eliminated by ramping the gate detuning. We demonstrate electronically controlled two-qubit gates with an estimated error of $8.4(7)\times10^{-5}$ without ground-state cooling. We further show that the error remains $\lesssim 5\times10^{-4}$ for ions with average phonon occupation up to $\bar{n}=9.4(3)$ on the gate mode. These results indicate that trapped-ion quantum computation can achieve high fidelity at temperatures above the Doppler limit, which enables faster and simpler device operation.

Figures (7)

• Figure 1: A) Illustration of the dynamics for 'diabatic' and 'adiabatic' geometric phase gates. The pink (rightward) curves represent the well positions of the 'forced' eigenstates and the grey curves represent the 'null' eigenstates in the frame of Eq. (\ref{['eq:geo_general_lab']}). Diabatic gates (top) rapidly turn on a spin-dependent force, causing the forced states to oscillate about new equilibrium positions. We 'catch' the displaced motion at $t_{g}$ by rapidly turning off the spin-dependent force precisely when the motion returns to its initial state. For adiabatic gates (bottom), we slowly adjust the wells such that the displaced motion closely follows its instantaneous equilibrium position throughout the operation. B) Phase-space trajectory of an adiabatic gate in the frame of Eq. (\ref{['eq:geo_general_lab']}) (green oval), and after transforming into the rotating frame with respect to the ions' bare harmonic motion (blue spiral) as described in Appendix \ref{['app:rotating_frame']}. C) Frequency dynamics during a smooth gate. The dashed purple line is the gate mode frequency $\omega_{m}$ and the solid green line shows the frequency of the spin-dependent force.
• Figure 2: Filter function comparison for smooth gate (pink bottom left), Walsh-3 gate (blue middle left), and Walsh-1 gate (purple top left). Each gate assumes a gradient Rabi frequency of $\Omega_{g}=2\pi\times 5~$kHz. The parameters are chosen such that the smooth and Walsh-3 gates have the same $t_{g}$. Results are for average phonon numbers $\bar{n}=0$ (solid) and $\bar{n}=10$ (dashed) in the gate mode.
• Figure 3: Measured populations of $\ket{\uparrow\uparrow}$, $\ket{\downarrow\downarrow}$, and $\ket{\uparrow\downarrow}$ and $\ket{\downarrow\uparrow}$, versus minimum gate detuning $\delta_\text{min}$, for the $t_{g}\simeq 226~\mu$s pulse sequence described in the text. The dashed vertical line shows the value of $\delta_\text{min}$ where $P_{\uparrow\uparrow} \approx P_{\downarrow\downarrow} \approx 0.5$, corresponding to $\theta_g \approx \pi/2$.
• Figure 4: SLERB of smooth gates with Doppler-cooled ions. (Left) Populations $P_{\text{survival}}$, $P_{\text{flip}}$, and $P_{\mathrm{leak}}$ after $N=2-500$ Cliffords. Each data point consists of 100 shots each of 50 random sequences of lengths {2, 5, 10, 20, 50, 150, 300, 400, 500}, and of 100 random sequences of lengths {1, 100, 200}. (Right) The leakage rate, SU(2) error rate, and inferred two-qubit gate error, extracted by fitting decay curves to the populations in the left plot. Truncating the data at different maximum sequence lengths allows characterization of non-Markovianity at the $\approx 3 \times 10^{-5}$ level. In all analyses, we assumed state-preparation and measurement (SPAM) errors to be negligible, i.e., no y-offset for the fit. Note that an extra rotation is compiled into the inverting Clifford to randomize the expected final state between $\ket{\downarrow\downarrow}$ and $\ket{\uparrow\uparrow}$, providing first-order insensitivity to any asymmetry in SPAM errors between the two states (Pauli randomization). The error bars are the $68\%$ confidence intervals extracted using non-parametric bootstrapping with 10,000 resamples.
• Figure 5: Average survival and leakage probability after 50 randomizations of SLERB sequences of length $N=100$, at the Doppler temperature. The results for smooth gates are shown as diamonds, and compared to Walsh-1 MS gates (dots). A static error of the gate mode frequency was simulated by adding an offset to $\delta_g$ in the case of the MS gate, or to $\delta(t)$ for the smooth gate.