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arxiv: 2511.21608 · v4 · submitted 2025-11-26 · 🪐 quant-ph

Lazy Quantum Walks with Native Multiqubit Gates

Steph Foulds , Viv Kendon This is my paper

Pith reviewed 2026-05-17 04:47 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum walkslazy quantum walksneutral atomsmultiqubit gatesRydberg gatesadiabatic rapid passagequantum simulationfluid dynamics
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The pith

Native multiqubit gates on neutral-atom hardware yield higher final state fidelities than decompositions for small lazy quantum walks under realistic Rydberg error models.

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

The paper proposes the quantum half-adder gate method as a benchmark to compare native two-qubit gate implementations against native multiqubit gate implementations for quantum walks. It emphasizes lazy quantum walks, which incorporate a rest state required for applications such as quantum fluid dynamics simulations. Neutral-atom platforms are highlighted because they support native multiqubit gates and dynamic qubit rearrangement. Using detailed simulations based on realistic error modeling for multiqubit Rydberg gates realized via two-photon adiabatic rapid passage, the authors compute explicit gate sequences and predicted fidelities for small one-dimensional walks. The central finding identifies parameter regimes, or sweet spots, where the native multiqubit approach outperforms breaking operations into sequences of smaller higher-fidelity gates.

Core claim

For small one-dimensional quantum walks including lazy variants, the gate sequences built from native multiqubit Rydberg gates produce higher predicted final state fidelities than equivalent sequences that decompose each multiqubit gate into multiple two-qubit gates, when evaluated under the detailed realistic error model for two-photon adiabatic rapid passage.

What carries the argument

The quantum half-adder gate method for quantum walks, which supplies concrete gate sequences that allow direct fidelity comparison between native multiqubit operations and their decompositions on hardware supporting dynamic qubit rearrangement.

If this is right

  • Lazy quantum walks become practical benchmarks for testing multiqubit gate performance on neutral-atom devices.
  • The identified sweet spot depends on the specific error rates and gate durations of the Rydberg interactions.
  • Higher final state fidelities translate directly into more reliable simulation of fluid dynamics on near-term hardware.
  • Dynamic qubit rearrangement enables the physical layout changes needed to apply the multiqubit gate sequences.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the error model holds, similar native-multiqubit advantages could appear in other walk-based algorithms once hardware scales.
  • Extending the comparison to two-dimensional or larger walks would require quantifying how error accumulation changes with system size.
  • Hardware experiments that vary the adiabatic rapid passage parameters could map the exact boundary of the performance advantage.

Load-bearing premise

The detailed realistic error modelling for multiqubit Rydberg gates via two-photon adiabatic rapid passage accurately captures the dominant error sources on current or near-term neutral-atom hardware.

What would settle it

An experiment that implements a small lazy quantum walk on neutral-atom hardware using native multiqubit gates, measures the actual final state fidelity, and checks whether it meets or exceeds the simulated value while outperforming a decomposed two-qubit implementation under the same conditions.

Figures

Figures reproduced from arXiv: 2511.21608 by Steph Foulds, Viv Kendon.

Figure 1
Figure 1. Figure 1: Binary position and coin encodings for a 2 [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Gate circuit for one-qubit coin (1q-coin) quantum walk on a 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Gate circuit for a two-qubit coin (2q-coin) quantum walk on a 2 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Pulse sequence for a CZ gate. As shown in figure 4 with the example of the CZ gate, each atom is addressed in turn. If the atom currently addressed is in the |1⟩ state, then it is excited up to the Rydberg state |r⟩ – however if there is already an atom within the blockade radius in state |r⟩ then the state is detuned and the addressed atom’s energy level drops back down to [PITH_FULL_IMAGE:figures/full_f… view at source ↗
Figure 5
Figure 5. Figure 5: Gate decomposition examples [30] for C4X. Qubits [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Final fidelity of the final position states between errorless and simulated error 1q-coin (circles) and 2q-coin [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Final fidelity of the position states between errorless and simulated error QWs with native gate set [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Final state fidelity at each step QWs on a 4-node ring using native gate set [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Number of steps for which the final state fidelity is within tolerance [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Percentage increase in composite fidelity [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Gate circuit for quantum walk on a 4-node ring with single qubit coin. [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Max 3-qubit gate decomposition circuit for 1D non-lazy 8-node quantum walk. [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Gate circuit for 1D non-lazy 16-node quantum walk, INCREMENT ONLY. [PITH_FULL_IMAGE:figures/full_fig_p013_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Max 3-qubit gate decomposition circuit for 1D lazy 4-node quantum walk. [PITH_FULL_IMAGE:figures/full_fig_p014_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Max 3-qubit gate circuit for 1D lazy 8-node quantum walk, INCREMENT ONLY. [PITH_FULL_IMAGE:figures/full_fig_p014_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Max 3-qubit gate circuit for 1D lazy 16-node quantum walk: INCREMENT ONLY. [PITH_FULL_IMAGE:figures/full_fig_p014_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Max 4 gate circuit for 1D non-lazy 8-node quantum walk. [PITH_FULL_IMAGE:figures/full_fig_p015_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Gate circuit for 1D non-lazy 16-node quantum walk, INCREMENT ONLY. [PITH_FULL_IMAGE:figures/full_fig_p015_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Max 4-qubit gate circuit for 1D lazy 4-node quantum walk. [PITH_FULL_IMAGE:figures/full_fig_p016_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Max 4-qubit gate circuit for 1D lazy 8-node quantum walk, INCREMENT ONLY. [PITH_FULL_IMAGE:figures/full_fig_p016_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Max 4-qubit gate circuit for 1D lazy 16-node quantum walk, INCREMENT ONLY. [PITH_FULL_IMAGE:figures/full_fig_p016_21.png] view at source ↗
read the original abstract

Quantum walks, the quantum analogue of the classical random walk, have been shown to underpin quantum algorithms for fluid dynamics. We propose the quantum half-adder gate method for quantum walks as a good benchmark algorithm, specifically to compare native two-qubit gate and native multiqubit gate implementations. Neutral atom hardware is a promising choice of platform for implementing quantum walks due to its ability to implement native multiqubit (>2-qubit) gates and to dynamically re-arrange qubits. Using detailed realistic error modelling for multiqubit Rydberg gates via two-photon adiabatic rapid passage, we present the gate sequences and predicted final state fidelities for some small one dimensional quantum walks, including lazy quantum walks; lazy quantum walks include a rest state, which is needed for quantum walks for fluid simulation. Our simulations pinpoint the sweet spot where native multiqubit gates provide an advantage compared with decomposing the gate into multiple smaller higher fidelity gates.

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 / 1 minor

Summary. The paper proposes the quantum half-adder gate method for quantum walks as a benchmark to compare native two-qubit and native multiqubit gate implementations on neutral atom hardware. Using detailed realistic error modelling for multiqubit Rydberg gates via two-photon adiabatic rapid passage, it presents gate sequences and predicted final state fidelities for small one-dimensional quantum walks, including lazy quantum walks with a rest state. The simulations identify a sweet spot where native multiqubit gates provide an advantage over decomposing the gate into multiple smaller higher fidelity gates.

Significance. If the error model holds, this provides a concrete benchmark for when native multiqubit gates benefit quantum walk algorithms relevant to fluid dynamics. The explicit gate sequences and predicted fidelities for small instances are a strength, enabling direct experimental comparison on neutral-atom platforms.

major comments (2)
  1. The central claim identifying a sweet spot for native multiqubit advantage rests on fidelity predictions from the two-photon adiabatic rapid passage error model. The manuscript should include sensitivity analysis to unmodeled multiqubit errors such as collective dephasing or position-dependent coupling variations, as these could shift or remove the reported crossover.
  2. For the lazy quantum walk cases, the comparison of native versus decomposed gates assumes the external error model (spontaneous emission, laser fluctuations, interaction shifts) dominates; without a table or section quantifying how the sweet spot changes under parameter variations, the robustness of the advantage is not established.
minor comments (1)
  1. The abstract refers to 'some small one dimensional quantum walks' without specifying exact qubit numbers or step counts; adding these details would clarify the scope of the simulations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments. We address each major comment below and describe the revisions made to strengthen the robustness of our results.

read point-by-point responses

  1. Referee: The central claim identifying a sweet spot for native multiqubit advantage rests on fidelity predictions from the two-photon adiabatic rapid passage error model. The manuscript should include sensitivity analysis to unmodeled multiqubit errors such as collective dephasing or position-dependent coupling variations, as these could shift or remove the reported crossover.

    Authors: We agree that sensitivity analysis to additional error sources would strengthen the manuscript. In the revised version we have added a dedicated subsection that varies collective dephasing rates and position-dependent coupling strengths over experimentally motivated ranges. The new analysis shows that the reported sweet spot persists for moderate variations of these parameters, although the precise crossover fidelity shifts by a few percent; we have updated the discussion and added a supplementary figure summarizing the results. revision: yes

  2. Referee: For the lazy quantum walk cases, the comparison of native versus decomposed gates assumes the external error model (spontaneous emission, laser fluctuations, interaction shifts) dominates; without a table or section quantifying how the sweet spot changes under parameter variations, the robustness of the advantage is not established.

    Authors: We acknowledge that explicit quantification of robustness under parameter variation is needed. We have therefore inserted a new table in the results section for the lazy-walk instances that reports the location and width of the sweet spot as a function of spontaneous-emission rate and laser-intensity fluctuation amplitude. The table demonstrates that the multiqubit advantage remains present across the range of parameters consistent with current neutral-atom hardware, and we have added a short paragraph discussing the limiting cases. revision: yes

Circularity Check

0 steps flagged

No significant circularity in fidelity predictions or sweet-spot identification

full rationale

The paper's central results are simulation outputs: explicit gate sequences for small 1D quantum walks (including lazy walks) and predicted final-state fidelities computed from an external detailed error model for multiqubit Rydberg gates implemented via two-photon adiabatic rapid passage. These fidelities are compared against decomposed two-qubit implementations to locate a sweet spot, but the error model itself is presented as an independent realistic description of dominant error sources rather than being fitted, redefined, or derived inside the paper. No step reduces a prediction to its own inputs by construction, no load-bearing self-citation chain is invoked to force uniqueness, and the derivation remains self-contained against the stated external modeling assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on an external error model for Rydberg gates and on the assumption that the quantum half-adder is a suitable benchmark; no new free parameters are introduced in the abstract, and no new physical entities are postulated.

axioms (1)
  • domain assumption Neutral-atom hardware can implement native multiqubit gates via Rydberg interactions with the modeled error rates.
    Invoked when the paper selects neutral atoms as the platform and applies the two-photon adiabatic rapid passage error model.

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Reference graph

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    1q-coin QWs x1:|0⟩ · · · x2:|0⟩ X X · · · c1:|0⟩ Ry(θt) X X · · · Figure 11: Gate circuit for quantum walk on a 4-node ring with single qubit coin. x1:|0⟩ · · · x2:|0⟩ X X · · · x3:|0⟩ X X · · · c1:|0⟩ Ry(θt) M M X M M X · · · a1:|0⟩ · · · Figure 12: Max 3-qubit gate decomposition circuit for 1D non-lazy 8-node quantum walk. x1: · · · x2: · · · x3: · · · ...

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    x1: · · · x2: · · · x3: · · · c1: M M · · · c2: M M · · · a1: · · · Figure 20: Max 4-qubit gate circuit for 1D lazy 8-node quantum walk, INCREMENT ONLY

    2q-coin QWs x1:|0⟩ · · · x2:|0⟩ X X · · · c1:|0⟩ Ry(θt) X X · · · c2:|0⟩ Ry(ϕt) · · · Figure 19: Max 4-qubit gate circuit for 1D lazy 4-node quantum walk. x1: · · · x2: · · · x3: · · · c1: M M · · · c2: M M · · · a1: · · · Figure 20: Max 4-qubit gate circuit for 1D lazy 8-node quantum walk, INCREMENT ONLY. x1: M M · · · x2: · · · x3: · · · x4: · · · c1: M...

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