Symmetric C Z gate for ultracold neutral atoms based on counterdiabatic driving at Rydberg excitation

arXiv:2510.04766 · quant-ph, physics.atom-ph · Submitted 2025-10-06 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Symmetric C Z gate for ultracold neutral atoms based on counterdiabatic driving at Rydberg excitation".

Mira: This scientific paper presents a novel scheme for implementing a symmetric Controlled-Z (CZ) gate in ultracold neutral atoms using counterdiabatic driving during Rydberg excitation,

Kai: First, who's behind it and why it matters.

Paper summary: Kai: So, to recap where we are, this paper by Beterov Rzhanov et al. is presenting a scheme for a symmetric CZ gate in ultracold neutral atoms using counterdiabatic driving during Rydberg excitation. The central thesis is that they've devised a double sequence of adiabatic pulses combined with counterdiabatic driving that substantially cuts down the gate operation time compared to prior double adiabatic methods, making it competitive with modern time-optimal protocols.

Mira: They are claiming this method acts as a bridge between fully adiabatic and time-optimal protocols, which is important because it aims to deliver high-fidelity entangling gates while maintaining robustness against variations in laser intensity and Rabi frequency. The paper focuses on how this specific combination of techniques manages these competing demands for speed and accuracy.

Lev: It seems the fundamental contribution here is not just a new pulse shape, but a framework that links the adiabatic evolution with the counterdiabatic driving term mathematically, specifically defining H CD(t) in relation to zero(t) and delta(t). I need to make sure I understand how this mathematical bridge actually translates into a practical experimental sequence we can follow on our trap.

Kai: Right, Lev, the paper details this by showing that the counterdiabatic pulse is defined analytically depending only on the gate duration time. This analytical definition is what makes it much more tractable than some of the purely numerical optimization approaches used before.

Mira: The key claim from their analysis is that this combination of adiabatic passage reduces sensitivity to laser intensity variations, while the counterdiabatic driving term itself provides the mechanism necessary to speed up the gate operation significantly.

Lev: So, if we look at Section IV where they discuss adiabatic rapid passage for two-photon schemes, what's the main takeaway there regarding fidelity versus time? Is there a specific point where they show that increasing speed hurts accuracy more than expected?

Kai: They demonstrate that the overall performance of their gate is comparable to modern time-optimal protocols, which is a key comparison point. They are showing that you don't have to sacrifice too much fidelity just to gain speed.

Mira: That comparison against time-optimal protocols suggests that their scheme isn't just theoretically interesting; it has a measurable performance level we can compare against existing high-speed benchmarks in the field of neutral atom quantum computing.

Lev: That gives me some confidence for Lev; if the performance metrics are comparable to what we see in literature, then it makes a strong case for moving this onto a testbed where we can actually measure those fidelities.

Kai: And they've shown feasibility across different excitation schemes, covering both single-photon and two-photon excitation in rubidium and cesium, which shows the versatility of this approach.

Mira: The scope is broad because they discuss three-photon laser excitation as well, showing that this method isn't limited to simpler configurations; it can be applied to more complex entanglement tasks.

Lev: That complexity means we need to check how these specific frequency dependencies behave in a real system where those multiple frequencies are interacting simultaneously.

Conclusion: Kai: So, wrapping up this discussion on the paper "Symmetric C Z gate for ultracold neutral atoms based on counterdiabatic driving at Rydberg excitation," the authors are proposing a method that uses counterdiabatic driving to achieve a faster CZ gate by blending adiabatic and time-optimal concepts. They are essentially showing how you can build a robust entangling operation without needing massive blockade strengths.

Mira: What I see is that the main implication lies in providing a practical pathway for implementing fast gates in neutral atom systems where you need to manage the trade-off between gate speed and noise resilience through the use of adiabatic passage. The high fidelity limit they found, F = zero point nine nine nine nine at room temperature for single-photon excitation, suggests this is a solid benchmark we can aim for in building future quantum hardware.

Lev: From an error correction perspective, if this scheme allows us to operate faster with that fidelity, it means the gate overhead in running error correction cycles is lower. It implies that the complexity of implementing high-speed gates doesn't necessarily mean we are losing too much accuracy overall, which is a positive indicator for scaling up systems.

Kai: I think the real impact here is showing that this approach offers a way to achieve near-optimal gate speeds while keeping fidelity high enough to be useful for error correction applications. It gives us a concrete path forward on how to design these gates experimentally.

Mira: The paper's description of the pulse profiles being described analytically without relying on extensive numerical optimization is also significant because it simplifies the experimental design phase considerably, moving it away from a purely iterative process toward something more straightforward to realize in the lab.

Lev: That simplification in the experimental design process is critical for anyone trying to move from theory to a working quantum device; if you can map out the required laser pulses cleanly, you reduce the risk of introducing experimental errors during implementation.

Kai: It really boils down to providing a well-defined, high-performance protocol that sits nicely between slow adiabatic methods and purely fast ones. This paper provides the blueprint for how to design these gates experimentally in ultracold neutral atom platforms.

Rzhanov Institute of Semiconductor Physics SB RAS · Novosibirsk State University · Novosibirsk State Technical University · Institute of Laser Physics SB RAS

quant-ph, physics.atom-ph

Submitted: 2025-10-06

Updated: 2026-04-21

Comments: 13 pages, 9 figures

Journal ref: Phys. Rev. A 113, 042614 (2026)

DOI: 10.1103/g6sw-w48t

Code: https://github.com/beterov/Counterdiabatic-Rydberg-CZ-gate

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 83/100

The gist: This scientific paper presents a novel scheme for implementing a symmetric Controlled-Z (CZ) gate in ultracold neutral atoms using counterdiabatic driving during Rydberg excitation, offering a

Key concepts

Counterdiabatic Driving (CD)
This is a specific mathematical term used in quantum control that introduces a driving term into the system's Hamiltonian. Its primary purpose here is to 'speed up the gate' operation, allowing for shorter gate times without sacrificing high fidelity, which is crucial when compared to purely adiabatic methods.
Adiabatic Passage
This technique involves slowly changing laser pulses over time. When applied correctly, it ensures the system remains in its desired quantum state throughout the evolution. In this context, it helps reduce how much the gate's accuracy changes if there are small fluctuations in the laser intensity.
Controlled-Z (CZ) Gate
A CZ gate is a fundamental operation in quantum computing that entangles two qubits. It performs a specific conditional phase shift on the system based on whether both atoms are excited to a Rydberg state simultaneously, which is essential for creating complex quantum circuits.

Terminology

Summary

This scientific paper presents a novel scheme for implementing a symmetric Controlled-Z (CZ) gate in ultracold neutral atoms using counterdiabatic driving during Rydberg excitation, offering a significant reduction in gate operation time compared to prior double adiabatic methods. The central finding is that this approach bridges the gap between fully adiabatic and time-optimal protocols, providing high-fidelity entangling gates while maintaining robustness against variations in laser intensity and Rabi frequency.

The Core Mechanism

The scheme utilizes a double sequence of adiabatic pulses applied symmetrically to both atoms and using counterdiabatic driving for Rydberg excitation. This method is designed to achieve a substantial reduction in quantum gate operation time compared to previously proposed double adiabatic schemes, making it competitive with modern time-optimal protocols. The 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.

Gate Implementation Details

The scheme is demonstrated for single-photon and two-photon schemes of Rydberg excitation in rubidium and cesium atoms, with a discussion on implementing a CZ gate using three-photon excitation of rubidium atoms for the first time. Key aspects include:

  1. The adiabatic sequence results in accumulation of π phase shift after excitation and de-excitation of two-atom system prepared initially in each of the states 01i, 10i, 11i.

  2. The counterdiabatic pulse represents a term necessary to speedup the gate, and it is defined analytically depending only on the gate duration.

  3. The scheme does not generate intrinsic single-qubit phase shifts for single-photon excitation, although they still appear in two-photon configuration.

Theoretical Framework and Hamiltonian

The theoretical framework involves analyzing a two-level system interacting with a chirped laser pulse, described by the Hamiltonian:

((

H 0 (t) = 2 / omega0 (t) δ (t)) (1)

where the adiabatic evolution is characterized by a mixing angle θ(t).

((

The counterdiabatic driving term is added as H CD with: H CD (t) = 2 / (-iomegaCD (t)) iomegaCD (t) 0 (3)

with the optimal counterdiabatic term for two simultaneously excited atoms in a blockade regime being written as: omega blockade CD (t) = − omega˙0 (t) δ (t) − omega0(t) ˙δ(t) / (2omega20(t)) + δ 2(t).

Performance and Robustness Analysis

The performance of the gate is analyzed across several regimes:

  1. The scheme shows that the overall performance of our gate is comparable to modern time-optimal protocols [9, 12, 14, 15, 27].

  2. The adiabatic passage provides reduced sensitivity to variations in laser intensities.

  3. The scheme is shown to be almost as fast as modern protocols but has reduced sensitivity of the fidelity both to the value and to the gradient of Rabi frequency.

  4. For a case of perfect blockade, the parameters depend on a single parameter: gate duration time.

Comparison with Other Protocols

The paper compares its scheme against other high-fidelity protocols:

- The scheme is much faster than a purely adiabatic scheme [22]. It is also compared favorably against the Levine-Pichler and time-optimal gates, as it is much faster than a purely adiabatic scheme.

- In the three-photon configuration, the effective Rabi frequency becomes omega three-photon = omega1omega3/omega2. The gate fidelity is sensitive to the value of omega2 even when spontaneous decay is not taken into account.

- The upper limit of the gate fidelity at room temperature for the simplest single-photon excitation scheme is found to be F = 0.9999, which can be useful for future applications of quantum error correction with ultracold neutral atoms.

Conclusion

The revised scheme allows for a moderate increase of the Rabi frequency compared to modern time-optimal protocols, without the need for substantially larger Rydberg blockade strengths. The main advantages are: (i) it is almost as fast as modern protocols but has reduced sensitivity of the fidelity both to the value and to the gradient of Rabi frequency; (ii) laser pulse profiles are described analytically without the need to use many parameters obtained from sophisticated numerical optimization; and (iii) it does not create undesired single-qubit phase shifts for single-photon and three-photon Rydberg excitation. The upper limit of the gate fidelity at room temperature for the simplest single-photon excitation scheme is found to be F = 0.9999.

Improvements for AI systems

Based on the provided scientific paper, here are specific improvements that could be made to AI systems, along with what those improved AI systems could achieve:

  1. The paper describes a scheme for a high-fidelity Quantum Gate (CZ gate) in ultracold neutral atoms using Rydberg excitation driven by counterdiabatic pulses.

  2. The core innovation lies in designing pulse shapes analytically depending only on the gate duration, reducing the need for extensive numerical optimization of laser parameters.

Here are specific improvements and their resulting AI capabilities:

Specific Improvements to AI Systems:

  1. The paper demonstrates that the necessary time dynamics (populations and phases) for a CZ gate can be found analytically for various excitation schemes (single-photon, two-photon, three-photon).

  2. The scheme is shown to be robust against variations in laser intensity and Rabi frequency gradients compared to previous protocols.

  3. The paper details the use of numerical optimization packages (like RydOpt) to compare different gate protocols (Levine-Pichler vs. Counterdiabatic vs. Time-Optimal) across varying parameters like blockade strength and Rydberg state lifetimes, leading to an analytically defined amplitude-robust phase profile (Appendix B).

  4. The analysis shows that for three-photon excitation, the scheme can compensate for Doppler shifts and allow for individual addressing using geometric arrangements of laser beams.

Improved AI System Capabilities:

  1. An AI system trained on this analytical framework could perform Inverse Design for quantum control pulses: Given a desired gate duration, the system could analytically output the optimal time-dependent Rabi frequency and detuning profiles required to achieve a specific target gate fidelity (e.g., >0.999).

  2. The AI could generate pulse sequences for complex, multi-photon excitation schemes (like three-photon gates) that are inherently robust against experimental inhomogeneities (like laser beam inhomogeneity) by optimizing the phase profiles of individual lasers simultaneously to compensate for shifts in the effective Rabi frequency.

  3. An AI system could perform Robustness Prediction by analyzing the analytical formulas derived in the paper to predict how much a gate fidelity will degrade if the laser intensity fluctuates or if Rydberg state lifetimes change, allowing experimentalists to pre-compensate control parameters.

  4. The system could automatically select the most efficient gate protocol (Counterdiabatic vs. Time-Optimal) for a given experimental constraint (e.g., available laser power vs. required gate speed), maximizing fidelity within those constraints without requiring brute-force numerical search across all possible pulse parameter spaces.

  5. The AI could optimize the specific phase profile of the driving laser pulse (as detailed in Appendix B) to maximize amplitude robustness against Rabi frequency variations, effectively creating a self-correcting control system for the gate operation itself.

Abstract

We designed a scheme for a neutral atom Rydberg blockade C Z 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 C Z gate using three-photon excitation of rubidium atoms. In contrast to many modern C Z 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.

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