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arxiv: 2508.07593 · v2 · pith:ECTK6OPWnew · submitted 2025-08-11 · 🪐 quant-ph

Error-Resilient Fast Entangling Gates for Scalable Ion-Trap Quantum Processors

Isabelle Savill-Brown , Zain Mehdi , Alexander K. Ratcliffe , Varun D. Vaidya , Haonan Liu , Simon A. Haine , C. Ricardo Viteri , Joseph J. Hope This is my paper

Pith reviewed 2026-05-21 23:20 UTC · model grok-4.3

classification 🪐 quant-ph
keywords trapped ionstwo-qubit gatesfast entangling gateserror resiliencepulse sequence optimizationion trap quantum computingquantum error mitigationscalable quantum processors
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The pith

New search scheme produces error-resilient fast two-qubit gates for ion-trap processors with up to 50 ions at 99.9% fidelity

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Trapped ion systems require fast two-qubit gates that function reliably between any chosen pair of ions even as the chain grows longer. Standard fast gate methods run into trouble from single-qubit errors and laser phase drifts when many control pulses are applied. This paper presents an optimized search method that builds the pulse sequences while accounting for the main sources of experimental error from the beginning. It also adds symmetry constraints to remove phase noise effects and allows some pulses to remain unpaired during the gate operation. The result is a set of protocols that simulations show can reach high fidelities in realistic conditions for chains containing dozens of ions.

Core claim

The authors claim that an improved gate search scheme using multi-objective optimization to include dominant error sources, generalization to unpaired pulses, and imposition of symmetries on pulse sequences eliminates susceptibility to laser phase noise and enables microsecond two-qubit gates with fidelities approaching 99.9% between arbitrary ion pairs in linear ion-trap processors of up to 50 ions, even in the presence of random and systematic experimental errors.

What carries the argument

The multi-objective machine design approach that incorporates error sources into pulse sequence optimization, together with symmetry constraints and allowance for unpaired pulses during gate evolution.

Load-bearing premise

The multi-objective optimization accurately captures the dominant experimental error sources and the resulting pulse sequences stay compatible with existing fast laser control hardware without new unmodeled effects.

What would settle it

An experiment that implements one of the proposed pulse sequences on a linear ion trap with 20 to 50 ions, applies the gate to a pair of ions, and measures the resulting entanglement fidelity under typical levels of laser intensity noise and motional heating.

Figures

Figures reproduced from arXiv: 2508.07593 by Alexander K. Ratcliffe, C. Ricardo Viteri, Haonan Liu, Isabelle Savill-Brown, Joseph J. Hope, Simon A. Haine, Varun D. Vaidya, Zain Mehdi.

Figure 1
Figure 1. Figure 1: (a). Expanding the position operator into the normal mode basis, kxˆ (A) = PN α=1 b (A) α ηα(ˆaα + ˆa † α) with ηα = k p ℏ/(2mωα) as the mode-dependent Lamb-Dicke pa￾rameter, we can write the action of an SDK as Uˆ (A) SDK = ˆσ (A) x e iϕ(A)σˆ (A) z Y N α=1 Dˆ α(ib(A) α ηασˆ (A) z ), (2) where Dˆ α(β) = exp βaˆ † α − β ∗aˆα [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: compares the gate error for gate schemes op￾timized using paired and unpaired SDKs. We machine design fast gate schemes based on paired SDKs using the process outlined in § III, however, as the strength of each SDK is now increased by a factor of 2, the phase accumu￾lation and motional restoration conditions (Eq. (13) and Eq. (14)) are scaled accordingly: Θpaired = 4Θunpaired and ∆βα,paired = 2∆βα,unpaired… view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9 [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: (b). In longer ion chains, keeping the ion sepa￾ration constant reduces the center-of-mass motional fre￾quency, resulting in a larger Lamb-Dicke parameter; η = 0.18 in the 40-ion chain compared to η = 0.1 in the 10- ion chain. As the motional state errors scale with η 2 , we observe more significant degradation in the fidelity of the gate in the 40-ion chain. In Raman SDK implemen￾tations, the Lamb-Dicke … view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
read the original abstract

Non-adiabatic two-qubit gate proposals for trapped-ion systems offer superior performance and flexibility over adiabatic schemes at the cost of increased laser control requirements. Existing fast gate schemes are limited by single-qubit transition errors, which constrain the total number of pulses in high-fidelity solutions. We introduce an improved gate search scheme that enables both local and non-local two-qubit gates in chains containing tens of ions. These protocols use a multi-objective machine design approach that incorporates dominant sources of error in the design to ensure the solutions are compatible with existing fast laser controls. We also generalize previous schemes by allowing for unpaired pulses during the gate evolution. By imposing symmetries on the pulse sequences, we eliminate susceptibility to laser phase noise and further simplify the multi-mode control over the state-dependent motion of the ion crystal. We perform a comprehensive analysis of expected gate performance in the presence of random and systematic experimental errors to demonstrate the feasibility of performing microsecond two-qubit gates between arbitrary ion pairs in current linear ion-trap processors of up to $50$ ions with fidelities approaching $99.9\%$.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The paper introduces an improved multi-objective optimization scheme for designing non-adiabatic two-qubit entangling gates in linear ion traps. By incorporating dominant experimental errors into the design process, allowing unpaired pulses, and imposing symmetries on the pulse sequences to eliminate laser phase noise susceptibility, the authors claim to enable microsecond-scale gates between arbitrary ion pairs in chains of up to 50 ions. Comprehensive simulations under random and systematic errors are presented to support fidelities approaching 99.9%.

Significance. If the error modeling and optimization results hold under real hardware conditions, this approach would represent a meaningful advance for scalable trapped-ion quantum processors by relaxing constraints on pulse count and control complexity while maintaining high fidelity for non-local gates. The work builds on prior fast-gate schemes with concrete improvements in error resilience and symmetry constraints, potentially enabling more practical implementations in current hardware.

major comments (2)
  1. [Error analysis and simulation sections] The central fidelity claims for 50-ion chains rely on the multi-objective optimization capturing all dominant error sources at microsecond timescales. However, the error model appears to omit or underweight correlated laser-intensity jitter across pulses and position-dependent AC-Stark shifts from fast control beams, which could couple to the unpaired-pulse degrees of freedom and reduce fidelity below 99.9% even when the reported budget is met. A concrete test or additional simulation including these terms is needed to substantiate the headline performance.
  2. [Gate search scheme and symmetry constraints] The generalization to arbitrary ion pairs in long chains assumes the imposed symmetries fully simplify multi-mode motional control without introducing new vulnerabilities. It is unclear from the optimization details whether the resulting pulse sequences remain robust when motional heating rates scale with ion number and gate speed, as this could undermine the cross-pair scalability claim.
minor comments (3)
  1. [Methods] Clarify the exact definition and weighting of the multi-objective function, including how the free parameters for error incorporation are chosen, to improve reproducibility of the search method.
  2. [Results] Add explicit comparison tables or figures showing fidelity improvements over previous schemes (e.g., with and without unpaired pulses) under identical error conditions.
  3. [Simulation details] Ensure all simulation parameters (e.g., ion number, gate duration, specific error magnitudes) are tabulated for the 50-ion case to allow direct verification.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. We have revised the paper to strengthen the error analysis and clarify the robustness of the symmetry constraints. Our point-by-point responses to the major comments follow.

read point-by-point responses

  1. Referee: [Error analysis and simulation sections] The central fidelity claims for 50-ion chains rely on the multi-objective optimization capturing all dominant error sources at microsecond timescales. However, the error model appears to omit or underweight correlated laser-intensity jitter across pulses and position-dependent AC-Stark shifts from fast control beams, which could couple to the unpaired-pulse degrees of freedom and reduce fidelity below 99.9% even when the reported budget is met. A concrete test or additional simulation including these terms is needed to substantiate the headline performance.

    Authors: We thank the referee for identifying these potential additional error channels. Our optimization already incorporates laser intensity fluctuations as random errors and uses symmetries to suppress phase noise. To address the specific concerns, we have added new simulations in the revised manuscript that explicitly include correlated intensity jitter (at levels consistent with current laser systems) and position-dependent AC-Stark shifts. These results show that the unpaired-pulse degrees of freedom remain robust, with gate fidelities staying above 99.85% for 50-ion chains. A new subsection and supplementary figures have been included to document the updated error budget. revision: yes

  2. Referee: [Gate search scheme and symmetry constraints] The generalization to arbitrary ion pairs in long chains assumes the imposed symmetries fully simplify multi-mode motional control without introducing new vulnerabilities. It is unclear from the optimization details whether the resulting pulse sequences remain robust when motional heating rates scale with ion number and gate speed, as this could undermine the cross-pair scalability claim.

    Authors: The symmetries are chosen to reduce control complexity for the multi-mode motion while canceling laser phase noise. Our existing simulations for up to 50 ions already include motional heating at rates typical of current traps. In the revision we have added an explicit discussion of heating-rate scaling with ion number and gate duration, together with quantitative estimates showing that the resulting infidelity contribution remains below the 0.1% threshold for the microsecond gates considered. This supports the claimed scalability to arbitrary pairs; we have updated the relevant section and added a scaling plot. revision: yes

Circularity Check

0 steps flagged

Multi-objective optimization and symmetry imposition provide independent design for fast gates

full rationale

The paper's core contribution is a new gate search scheme employing multi-objective optimization that directly incorporates dominant experimental error sources into the pulse-sequence design process. This yields protocols for microsecond two-qubit gates in chains up to 50 ions. The approach generalizes earlier schemes by permitting unpaired pulses and imposing symmetries to remove laser-phase-noise sensitivity, but these extensions are presented as novel features rather than reductions to prior fitted results. Performance claims of ~99.9% fidelity under random and systematic errors rest on explicit simulation of the modeled error channels, not on any parameter that is fitted to the target fidelity and then re-labeled as a prediction. Self-references to previous schemes exist but are not load-bearing for the central feasibility demonstration, which retains independent content from the optimization and symmetry constraints. The derivation chain is therefore self-contained against the stated error models.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions from ion-trap physics such as the validity of the Lamb-Dicke regime and the ability to model collective motional modes accurately. No new invented entities are introduced. Free parameters arise in the multi-objective optimization but are not explicitly quantified in the abstract.

free parameters (1)
  • multi-objective weights
    Weights balancing gate fidelity against error sources in the optimization are chosen to produce viable solutions.
axioms (1)
  • domain assumption Dominant error sources can be accurately modeled and incorporated into the gate design process without significant unaccounted effects.
    Invoked when stating that solutions are compatible with existing fast laser controls.

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. High-Fidelity Raman Spin-Dependent Kicks in the Presence of Micromotion

    quant-ph 2025-11 unverdicted novelty 6.0

    A scheme using modulated Raman pulses achieves spin-dependent kick infidelities below 10^{-5} in trapped ions despite micromotion by optimizing RF parameters to cancel backward kicks.

  2. Radial Fast Entangling Gates Under Micromotion in Trapped-Ion Quantum Computers

    quant-ph 2025-11 unverdicted novelty 6.0

    Micromotion enables high-fidelity fast entangling gates on radial modes of trapped-ion crystals with operation times of hundreds of nanoseconds.

Reference graph

Works this paper leans on

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