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arXiv:2604.12279

Numerically optimized amplitude-robust controlled-Z gate for ultracold neutral atoms with individual addressing capability

K. V. Kozenko, V. V. Gromyko, I. I. Beterov, I. I. Ryabtsev

quant-phSubmitted Apr 14, 2026• Announced Apr 15, 2026• 0 citations• Revised Oct 1, 2026 (v2)
v1 · Apr 14, 2026v2 · Oct 1, 2026
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Abstract

We numerically optimized a scheme for a symmetric controlled-Z (CZ) gate based on the Rydberg blockade in neutral atoms, with the aim of increasing its robustness to variations in the Rabi frequency. The scheme exploits analytically defined phase profiles of the laser pulse and proves almost an order of magnitude more robust to Rabi-frequency variations than previously proposed protocols. We designed this amplitude-robust protocol with a smooth pulse shape and optimized it for a finite Rydberg blockade strength, which makes it suitable for experimental implementation in both single-photon and two-photon configurations. We further show that the protocol can be applied to individually addressed Rydberg excitation, accounting for the asymmetry of the Rabi frequencies of two atoms excited by tightly focused laser beams. This allows the effects of residual thermal motion of the trapped atoms to be reduced. Finally, we examined the performance of the protocol for single-photon and two-photon Rydberg excitation schemes at finite blockade strength, and demonstrated its advantages for individual addressing at finite temperatures of the trapped atoms.

Comments
15 pages, 10 figures

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We numerically optimized a scheme for a symmetric controlled-Z (CZ) gate based on the Rydberg blockade in neutral atoms, with the aim of increasing its robustness to variations in the Rabi frequency. The scheme exploits analytically defined phase profiles of the laser pulse and proves almost an order of magnitude more robust to Rabi-frequency variations than previously proposed protocols. We designed this amplitude-robust protocol with a smooth pulse shape and optimized it for a finite Rydberg blockade strength, which makes it suitable for experimental implementation in both single-photon and two-photon configurations.
We further show that the protocol can be applied to individually addressed Rydberg excitation, accounting for the asymmetry of the Rabi frequencies of two atoms excited by tightly focused laser beams. This allows the effects of residual thermal motion of the trapped atoms to be reduced. Finally, we examined the performance of the protocol for single-photon and two-photon Rydberg excitation schemes at finite blockade strength, and demonstrated its advantages for individual addressing at finite temperatures of the trapped atoms.
We designed a scheme for a neutral atom Rydberg blockade CZC_ZCZ​ gate based on the double sequence of adiabatic pulses applied symmetrically to both atoms and using counterdiabatic driving for Rydberg excitation. This provides a substantial reduction in the quantum gate operation time compared to previously proposed double adiabatic schemes, and makes our scheme competitive with modern time-optimal protocols for high-fidelity entangling gates with neutral atoms. Our approach creates a bridge between fully adiabatic and time-optimal gate schemes. The use of adiabatic passage reduces the sensitivity of gate fidelity to variations in laser intensity, while counterdiabatic driving provides short gate times. The intensity and phase profiles of the laser pulse acting on the atoms are described analytically depending only on the gate duration. We demonstrated the applicability of this scheme for single-photon and two-photon schemes of Rydberg excitation in rubidium and cesium atoms, and, for the first time, discussed the implementation of a CZC_ZCZ​ gate using three-photon excitation of rubidium atoms. In contrast to many modern CZC_ZCZ​ gate protocols, our scheme does not generate intrinsic single-qubit phase shifts, although they still appear in two-photon configuration. We also designed a numerically optimized amplitude-robust gate with an analytically defined phase profile of the laser pulse and compared its performance with the counteradiabatic gate scheme.
We have numerically simulated a two-qubit CZ gate for ultracold neutral atoms based on Rydberg blockade, utilizing three-photon excitation to Rydberg states. The three-photon laser excitation overcomes lack of individual addressability for entangling gates in atomic arrays, which is a key limitation of conventional schemes of quantum information processing with neutral atoms. This is achieved by mitigating sensitivity to laser intensity fluctuations caused by spatial motion of atoms in optical tweezers. Our goal is to investigate the gate performance when three-photon laser excitation is used. We considered Levine-Pichler gate which applies an abrupt phase jump at the center of the control laser pulse. Our simulation accounts for the influence of spontaneous decay of intermediate and Rydberg states and finite Rydberg excitation energies. We obtained the maximum fidelity of the CZ gate around 99.7% for the model based on probability amplitudes and 99.72% for the model based on density matrices. This value exceeds the threshold required for the application of quantum error correction protocols, demonstrating the promise of this gate for experimental realization. This work was supported by BASIS foundation Grant No. № 25-1-1-57-5
We propose an adiabatic protocol for implementing a controlled-phase gate ${\mathrm{CZ}}_{\ensuremath{\theta}}$ with continuous $\ensuremath{\theta}$ of neutral atoms through a symmetrical two-photon excitation process via the second resonance line, 6P6P6P in 87Rb{}^{87}\mathrm{Rb}87Rb, with a single-temporal-modulation-coupling of the ground state and intermediate state. Relying on different adiabatic paths, the phase factor $\ensuremath{\theta}$ of the ${\mathrm{CZ}}_{\ensuremath{\theta}}$ gate can be accumulated on the logic qubit state ∣11⟩|11⟩∣11⟩ alone by calibrating the shape of the temporal pulse where strict zero amplitudes at the start and end of the pulse are not needed. For a wide range of $\ensuremath{\theta}$, we can obtain the fidelity of the ${\mathrm{CZ}}_{\ensuremath{\theta}}$ gate over 99.7% in less than $1\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{s}$, in the presence of spontaneous emission from intermediate and Rydberg states. And in particular for $\ensuremath{\theta}=\ensuremath{\pi}$, we benchmark the performance of the CZ gate by taking into account various experimental imperfections, such as Doppler shifts, fluctuation of Rydberg-Rydberg interaction strength, inhomogeneous Rabi frequency, and noise of driving fields, etc., and show that the predicted fidelity is able to maintain at about 98.4% after correcting the measurement error. This gate protocol provides a robustness against the fluctuation of pulse amplitude and a flexible way for adjusting the entangling phase, which may contribute to the experimental implementation of near-term noisy intermediate-scale quantum computation and algorithm with neutral-atom systems.
Abstract High-fidelity controlled-Z (CZ ) gates are essential and mandatory to build a large-scale quantum computer. In neutral atoms, the strong dipole–dipole interactions between their Rydberg states make them one of the pioneering platforms to implement CZ gates. Here we numerically investigate the optimized pulses to generate a high-fidelity Rydberg C Z gate in a three-level ladder-type atomic system. By tuning the temporal shapes of Gaussian or segmented pulses, the populations on the intermediate excited states are shown to be suppressed within the symmetric gate operation protocol, which leads to a C Z gate with a high Bell fidelity up to 99.92 % . These optimized pulses are robust to thermal fluctuations and the excitation field variations. Our results promise a high-fidelity and fast gate operation under amenable and controllable experimental parameters, which goes beyond the adiabatic operation regime under a finite blockade strength.
We analyze neutral atom Rydberg CZ{C}_{Z}CZ​ gates based on adiabatic pulses applied symmetrically to both atoms. Analysis with smooth pulse shapes and Cs atom parameters predicts the gates can create Bell states with fidelity F>0.999\mathcal{F}>0.999F>0.999 by using adiabatic rapid passage pulses. With globally optimized adiabatic pulse shapes, in a two-photon excitation process, we generate Bell states with fidelity F=0.997\mathcal{F}=0.997F=0.997. The analysis fully accounts for spontaneous emission from intermediate and Rydberg states, including the Rydberg lifetime in a room-temperature environment, but does not include errors arising from laser noise. The gate protocols do not require individual addressing and are shown to be robust against Doppler shifts due to atomic motion.
We identify time-optimal laser pulses to implement the controlled-Z gate and its three qubit generalization, the C 2 Z gate, for Rydberg atoms in the blockade regime. Pulses are optimized using a combination of numerical and semi-analytical quantum optimal control techniques that result in smooth Ansätze with just a few variational parameters. For the CZ gate, the time-optimal implementation corresponds to a global laser pulse that does not require single site addressability of the atoms, simplifying experimental implementation of the gate. We employ quantum optimal control techniques to mitigate errors arising due to the finite lifetime of Rydberg states and finite blockade strengths, while several other types of errors affecting the gates are directly mitigated by the short gate duration. For the considered error sources, we achieve theoretical gate fidelities compatible with error correction using reasonable experimental parameters for CZ and C 2 Z gates.