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arXiv:2608.27426

Detuning- and Stark-robust Rydberg gates

Elie Bataille, Gyohei Nomura, Manuel Endres

quant-phcond-mat.quant-gasphysics.atom-phSubmitted Aug 27, 2026• Announced Aug 28, 2026• 0 citations
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Abstract

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.

Comments
E.B. and G.N contributed equally to this work

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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.
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 within a much wider range of single-atom detunings than the time-optimal gates. 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.
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.
Generating entanglement between two Rydberg atoms is at the core of neutral-atom quantum computers. Current two-qubit gates operate in the Rydberg-blockade regime, in which the full strength of the van der Waals interaction between the two Rydberg atoms is not directly exploited, to avoid sensitivity to the position noise of the tweezer-trapped atoms, at the cost of a longer time spent in the Rydberg state. Here, we propose a set of techniques based on coherent control of the atomic motion obtained by combining optical tweezers and a two-dimensional optical lattice, and a sequence of multiple on/off pulses. The protocols keep the two-qubit gate error contribution from position noise below 10−410^{-4}10−4, heat the atom by less than~Δn=0.01Δn = 0.01Δn=0.01, while being robust to alignment errors of the potential up to 505050~nm and thermal excitation up to nˉ=3\bar{n} = 3nˉ=3. This toolbox opens the path for new two-qubit Rydberg gates directly, or partially, driven by the interaction, in which the atoms spend only ∼10\sim 10∼10~ns in the Rydberg state, minimizing the increasingly dominant error source originating from its finite lifetime.
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.
Neutral atoms in optical tweezer arrays have emerged as a leading platform for quantum information processing. The fidelity of entangling gates mediated by Rydberg interactions has improved rapidly and is increasingly constrained by blackbody-radiation-induced transitions, which shorten Rydberg lifetimes and create contaminant states that can cause correlated errors. Cryogenic environments can suppress these transition rates by more than an order of magnitude. However, realizing a universal gate set in such an environment has remained an outstanding challenge. Here, we demonstrate a universal quantum gate set in a cryogenic 133^{133}133Cs atom array, with a single-qubit gate fidelity of 99.970(2)% and a raw two-qubit entangling-gate fidelity of 99.76(8)%, within the range of leading room-temperature implementations. The entangling gate uses direct single-photon coupling between the electronic ground state and a Rydberg PPP state, avoiding scattering and light shifts associated with two-photon coupling. The gate operates at a modest Rabi frequency of 2π×4.32π\times4.32π×4.3 MHz. The measured fidelity agrees with our error model dominated by atomic motion, indicating a straightforward route to higher fidelity through improved cooling, while the fundamental error contribution from Rydberg decay is below 3×10−43\times10^{-4}3×10−4. These results establish a path to entangling-gate fidelities substantially beyond the current state of the art through cryogenic suppression of Rydberg decay, reducing the overhead for fault-tolerant computation.