Comparison of Two Optimization Methods for a Rydberg Quantum Gate

TL;DR

This work compares an effective shortcut-to-adiabaticity (eCD) strategy with a brute-force Boulder Opal optimization (BOO) for implementing a high-fidelity CZ gate on Rydberg atoms. The analysis shows that BOO generally achieves higher fidelities across protocol times and amplitude constraints, while eCD offers analytic guidance and can perform well in restricted regimes, particularly under specific constraint regimes. The study highlights the critical role of experimental pulse constraints, spectral filtering, and Rydberg blockade strength $V$ in determining which optimization method is advantageous. The results suggest that combining optimization with compensation mechanisms and extending to multi-qubit gates could further enhance gate performance on state-of-the-art quantum platforms.

Abstract

A shortcut-to-adiabaticity is compared with a numerically optimized protocol for implementing a high-fidelity quantum gate on Rydberg atoms. The counterdiabatic method offers an analytical framework for accelerating high-fidelity gates by mimicking the time evolution of a counterdiabatic Hamiltonian using fast-oscillating fields. This approach is contrasted with a numerically optimized gate designed using the Boulder Opal platform. The numerically optimized gate achieves higher fidelities while demonstrating robustness against errors similar to that of the effective counterdiabatic gate. The study serves as an example of the performance of analytic shortcut-to-adiabatic-inspired protocols compared to brute-force numerical optimization techniques for state-of-the-art quantum computing platforms. It stresses the important role played by constraints on the optimized pulses in time and in amplitude that are crucial in determining the quality of the optimization method.

Figures (2)

• Figure 1: Color-coded infidelities as a function of protocol time $T$ for the eCD gate $H_\text{eCD}(t) + V\ket{r}\bra{r}$ (a) and the BOO gate (b) with two cuts along constant pulse scaling $s$ shown in (c). The covered protocol times are $0.027\;\mu$s $\leq T \leq 0.54\;\mu$s, where $0.54\;\mu$s is the time used by Saffman et al. in Saffman2020. The maximum Rabi pulse and the detuning are $\Omega_\text{max}/(2\pi)=s\cdot 17$ MHz, $\Delta_\text{max}/(2\pi) = s\cdot 23$ MHz, where $s$ is scaling the pulse amplitude in comparison to the ones used in Saffman2020. The pulse heights in the eCD field are adjusted by the eCD frequency $\omega$, in the BOO by a cutoff in frequency space. The horizontal lines in (a) and (b) show cuts at $s=1$ (dotted line) and $s=4.8$ (solid line) plotted in (c). The eCD result is shown in red and the BOO in blue color. The Rydberg blockade is fixed to $V/(2\pi)=500$ MHz in all cases.
• Figure 2: Stability comparison between the original gate (dotted black line), the BOO gate (dashed blue line), and the eCD gate (solid red line). The detuning scan (without amplitude errors) is shown on the left and the amplitude scan (without detuning error) on the right. The amplitudes are $\Delta_\text{max}/(2\pi) = 23$ MHz and $\Omega_\text{max}/(2\pi)=17$ MHz and the same time $T = 0.54\;\mu$s for all protocols. The eCD frequencies $\omega$ are adjusted such that the eCD maximal pulse amplitudes are equal to those of the two protocols. The BOO gate was not explicitly optimized for better stability regarding pulse errors.