An asymmetric and fast Rydberg gate protocol for long range entanglement

TL;DR

The paper presents an asymmetric, detuned $π-2π-π$ Rydberg gate that achieves high fidelity without requiring very strong blockade, enabling long-range entanglement. By detuning the $2π$ pulse and allowing unequal Rabi frequencies, the protocol eliminates rotation error in the ideal limit and can reach within a factor of $2.39$ (or $1.68$ for large asymmetry) of the lifetime-limited fidelity, while generalizing to arbitrary controlled phases. It combines time-optimal pulse designs via GRAPE and robust-control strategies to mitigate $Ω$ and $V$ variations, achieving faster operation with tunable robustness at the cost of longer pulses. The approach demonstrates potential for scalable, long-range quantum gates and non-local codes, with experimental progress showing high-fidelity operations in Cs at micron-scale spacings under realistic conditions.

Abstract

We analyze a new Rydberg gate design based on the original $π-2π-π$ protocol [Jaksch, et. al. Phys. Rev. Lett. {\bf 85}, 2208 (2000)] that is modified to enable high fidelity operation without requiring a strong Rydberg interaction. The gate retains the $π-2π-π$ structure with an additional detuning added to the $2π$ pulse on the target qubit. The protocol reaches within a factor of 2.39 (1.68) of the fundamental fidelity limit set by Rydberg lifetime for equal (asymmetric) Rabi frequencies on the control and target qubits. We generalize the gate protocol to arbitrary controlled phases. We design optimal target-qubit phase waveforms to generalize the gate across a range of interaction strengths and we find that, within this family of gates, the constant-phase protocol is time-optimal for a fixed laser Rabi frequency and tunable interaction strength. Robust control methods are used to design gates that are robust against variations in Rydberg Rabi frequency or interaction strength.

Figures (6)

• Figure 1: Protocol for a Rydberg $\sf CZ$ gate. a) Atomic levels with qubits encoded in $\ket{0}, \ket{1}$ that are separated by $\omega_q$. State $\ket{0}$ is coupled to $\ket{r}$ with Rabi frequency $\Omega$. The Rydberg levels decay at rate $1/\tau$ and the two-atom interaction strength is $V$. b) A three pulse gate protocol is: 1) $\pi$ pulse on control qubit, 2) $2\pi$ pulse on target, 3) $\pi$ pulse on control. c) A modified gate protocol is the same as in a) and b) except that the $2\pi$ pulse on the target is detuned by $\Delta$.
• Figure 2: Rydberg-scattering-limited gate error for the asymmetric protocol with $\Omega_c=p\Omega.$ The dashed line labeled DDP shows the bound of $\epsilon_{\rm DDP} V\tau=2.57$ from Doultsinos2025b and the line labeled mTO is the modified time optimal gate of Ref. Poole2025a, Table II, gate 11. The inset shows the gate duration for the asymmetric and the modified time-optimal gates.
• Figure 3: General phase gate dependence on Rabi rate $\Omega$ from solutions of Eq. (\ref{['eq.Deltapm']}) for $n_1=2, n_2=1.$ The inset shows the corresponding gate phase.
• Figure 4: Time-optimal solutions for the target pulse as the ratio $\Omega/V$ is varied. (a) GRAPE-optimized target pulse duration as a function of Rabi frequency $\Omega/V$ for a fixed interaction strength $V$. The limiting durations $\tau=2\pi/\Omega$ and $\tau=\pi/V$ discussed in the main text are shown by solid green and dashed grey lines, respectively. The duration of the analytic gate is shown by the orange triangle. Inset: Gate duration for fixed $\Omega$ as $V$ is varied. In this case the analytic gate is the global minimum. (b) Optimized gate waveform for $\Omega/V=5$, for which dynamics approximate the limit $\Omega\rightarrow\infty$. This waveform approximates the interaction gate and achieves effective free evolution with large detunings; here $|\Delta|_{\rm max}\approx 2.5\Omega$.
• Figure 5: Properties of target atom phase waveforms for a CZ gate designed to be robust against Rabi frequency fluctuations. a) The phase waveform for the analytic (orange, flat), and robust (blue) pulses. The robust pulse is twice as long as the analytic pulse and exhibits significant phase modulation. The maximal detuning corresponds to $|\Delta|_{\rm max}\approx2\Omega_0$. b) Gate fidelity without Rydberg decay as a function of fractional Rabi frequency error ($\delta\Omega/\Omega_0$) for both pulses. The robust pulse maintains high fidelity across the full $\pm5\%$ range, with roughly sevenfold reduction in gate error at the extremes. c) Average gate error as a function of gate duration for Rabi-frequency-robust control, for normally distributed Rabi errors as described in the main text with $\sigma=2 \,\%$. As the gate duration increases, robust control achieves lower average gate error (Eq. \ref{['eqn.averageinfidelity']}) in the absence of decay (blue circles). The improvement is reduced when Rydberg decay is included (pink squares). At $t/t_{\mathrm{optimal}}=2$ (shown in green circles), the gain from robustness is balanced by error from decay, resulting in a plateau followed by an eventual rise in gate error.