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arXiv:2608.26446

Detuning-robust Rydberg entangling gates from echoed pulses

Zhubing Jia, Yichao Yu, Xiye Hu, Lintao Li, Jacob Zheng, Christopher Monroe, Jacob P. Covey

quant-phphysics.atom-phSubmitted Aug 26, 2026• Announced Aug 28, 2026• 0 citations
v1 · Aug 26, 2026v2 · Sep 2, 2026
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Abstract

Rydberg-based two-qubit gate fidelities in neutral atom arrays are limited chiefly by laser intensity inhomogeneity and by detuning errors from frequency miscalibration, background-field drift, intermediate state light shift and Doppler shifts. Quantum optimal control can suppress the former, but no pulse can render a controlled-Z gate first-order insensitive to detuning. Here we show that this obstruction can be circumvented by designing Rydberg gate pulses with every leading-order detuning error relegated to single-qubit Z-rotations, which an echoed sequence removes. The resulting maximally-entangling ZZ gate has no leading-order response to arbitrary detunings on either atom, maintaining an infidelity below $10^{-3}$ much wider range of single-atom detunings than previous gate designs. We further show that a large fraction of residual error is dominated by population outside the computational subspace, which can be converted into heralded erasures. Our results significantly reduce the requirements on laser frequency stability and intensity homogeneity, field calibration and atomic temperature toward practical fault-tolerant quantum computing with neutral atoms.

Comments
11 pages, 9 figures

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Rydberg-based two-qubit gate fidelities in neutral atom arrays are limited chiefly by laser intensity inhomogeneity and by detuning errors from frequency miscalibration, background-field drift, intermediate state light shift and Doppler shifts. Quantum optimal control can suppress the former, but no pulse can render a controlled-Z gate first-order insensitive to detuning. Here we show that this obstruction can be circumvented by designing Rydberg gate pulses with every leading-order detuning error relegated to single-qubit Z-rotations, which an echoed sequence removes. The resulting maximally-entangling ZZ gate has no leading-order response to arbitrary detunings on either atom, maintaining an infidelity below 10−310^{-3}10−3 much wider range of single-atom detunings than previous gate designs. We further show that a large fraction of residual error is dominated by population outside the computational subspace, which can be converted into heralded erasures. Our results significantly reduce the requirements on laser frequency stability and intensity homogeneity, field calibration and atomic temperature toward practical fault-tolerant quantum computing with neutral atoms.
Error suppression to the experimental imperfections is a central challenge for useful quantum computing. Recent studies have shown the advantages of using single-modulated pulses based on optimal control, which can realize high-fidelity two-qubit gates in neutral-atom arrays. However, typical optimization minimizes only the ideal gate error in the absence of any decay, which allows the gate to be passively influenced by all error sources leading to an exponential increase of the insensitivity when error becomes larger. In the present work, we propose the realization of two-qubit CZ{C}_{Z}CZ​ gates with active robustness against two-photon detuning errors. Our method depends on a modified cost function in numerical optimization for shaping gate pulses, which minimizes, not only the ideal gate error but also the fluctuations of gate infidelity over a wide error range. We introduce a family of Rydberg blockade gates with active robustness towards the impacts of versatile noise sources such as Doppler dephasing and ac Stark shifts. The resulting gates with robust pulses can significantly increase the insensitivity to any type of errors acting on the two-photon detuning, benefiting from a relaxed requirement of colder atomic temperatures or more stable lasers for current experimental technology.
Error suppression to the experimental imperfections is a central challenge for useful quantum computing. Recent studies have shown the advantages of using single-modulated pulses based on optimal control which can realize high-fidelity two-qubit gates in neutral-atom arrays. However, typical optimization only minimizes the ideal gate error in the absence of any decay, which allows the gate to be passively influenced by all error sources leading to an exponential increase of sensitivity when the error becomes larger. In the present work, we propose the realization of two-qubit CZ gates with active robustness against two-photon detuning errors. Our method depends on a modified cost function in numerical optimization for shaping gate pulses, which can minimize, not only the ideal gate error but also the fluctuations of gate infidelity over a wide error range. We introduce a family of Rydberg blockade gates with active robustness towards the impacts of versatile noise sources such as Doppler dephasing and ac Stark shifts. The resulting gates with robust pulses can significantly increase the insensitivity to any type of errors acting on the two-photon detuning, benefiting from a relaxed requirement of colder atomic temperatures or more stable lasers for current experimental technology.
We investigate the robustness of two-qubit gates to deviations of experimental controls on a neutral atom platform utilizing Rydberg states. We construct robust controlled-Z gates---employing techniques from quantum optimal control---that retain high Bell-state fidelity F>0.999F>0.999F>0.999 in the presence of significant deviations of the coupling strength to the Rydberg state. Such deviations can arise from laser intensity noise and atomic motion in an inhomogeneous coupling field. We also discuss methods to mitigate errors due to deviations of the laser detuning. The designed pulses operate on timescales that are short compared to the fundamental decay timescale set by spontaneous emission and blackbody radiation. We account for the finite lifetime of the Rydberg state in both the optimization and fidelity calculations---this makes the gates conducive to noisy intermediate-scale quantum experiments, meaning that our protocols can reduce infidelity on near-term quantum computing devices. We calculate physical properties associated with infidelity for strontium-88 atoms---including lifetimes, polarizabilities, and blockade strengths---and use these calculations to identify optimal Rydberg states for our protocols, which allows for further minimization of infidelity.
Rydberg entangling gates driven by a two-photon transition in alkali atoms suffer from an adverse scaling of light-shift-induced errors. Robustness to such detuning errors is known to be impossible to achieve in the design of conventional Rydberg gate protocols, where only one of the qubit states is coupled to the Rydberg state. Here, we show that in a more general framework, in which both qubit states take part in the gate, full or partial robustness to these errors can be realized. We present two gate constructions, which either cancel the errors outright or convert them into single-qubit errors that can be corrected locally. We map the regimes -- in terms of light-shift strength, intensity inhomogeneity, and Rydberg decay rate -- in which these protocols outperform the widely used time-optimal Rydberg gate, and find that they already include the conditions of state-of-the-art experiments. Finally, we show the existence of a Rydberg `fly-by' entangling gate, an important primitive for an emerging class of neutral-atom quantum computing architectures.
We propose a controlled-Z gate scheme for Rydberg atoms based on level-crossing-free echoing rapid adiabatic population transfer. We design antisymmetric Rabi frequency pulses and symmetric detuning pulses, enabling the system to completely avoid level-crossing points throughout the evolution, and the dynamical phase is naturally eliminated by the time-reversal symmetry of the double-pulse sequence. We incorporate dissipative effects through the Lindblad master equation. The numerical simulation yields a two-qubit CZ gate fidelity of 0.9999. When the Rabi-frequency fluctuation is within ±2%\pm 2\%±2%, and the detuning offset is within ±1%\pm 1\%±1%, the fidelity can still remain above 0.999. Under the same dissipative model, the three-qubit CCZ gate achieves a fidelity of 0.999. When a single-parameter fluctuation does not exceed ±3%\pm 3\%±3%, the fidelity is always higher than 0.997. Our scheme requires no laser phase jumps or fast switching operations. The zero-area pulse structure suppresses first-order intensity noise, and the symmetric double-pulse sequence avoids spatially resolved laser switching, making it suitable for parallel gate operations in large-scale neutral-atom arrays.
Abstract The Doppler dephasing error due to residual thermal motion of atoms is a major cause of infidelity in neutral-atom quantum gates. Besides cooling and trapping advancements, few effective methods exist to mitigate this error. In the present work, we first propose an error-erasing strategy that utilizes a pair of off-resonant fields to continuously dress the protected Rydberg state with an auxiliary state, which can induce an opposite but enhanced sensitivity to the same source of Doppler dephasing error. Combining with the optimal control of laser pulses, we have realized a family of Rydberg two-qubit controlled-NOT gates in Rb and Cs atoms that are fully immune to the Doppler dephasing error. We numerically simulate this gate operation with fidelity F ≈ 0.9906 at any temperature for a lower-excited auxiliary state, and a higher fidelity of F ≈ 0.9960 can be attained for a ground auxiliary state even at a temperature of 500 µK. Finally, we predict a super-high fidelity of F > 0.9999 for 50 μ K is possible by using the robust pulses with a larger amplitude. Our results significantly reduce atomic temperature requirements for high-fidelity quantum gates, and may provide fundamental guidance to practical fault-tolerant quantum computing with neutral atoms.