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arxiv: 2502.17188 · v2 · submitted 2025-02-24 · 🪐 quant-ph

Holonomic quantum computation: a scalable adiabatic architecture

Clara Wassner , Tommaso Guaita , Jens Eisert , Jose Carrasco This is my paper

Pith reviewed 2026-05-23 02:30 UTC · model grok-4.3

classification 🪐 quant-ph
keywords holonomic quantum computationadiabatic gatesRydberg atomsgeometric phasesquantum error robustnessscalable quantum computingdifferential geometryquantum gates
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The pith

The paper introduces a framework for scalable quantum computation in atom experiments using a universal set of fully holonomic adiabatic gates.

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

The paper develops a framework to achieve scalable quantum computation in experiments with atoms by relying on a universal set of fully holonomic adiabatic gates. These gates use the geometric evolution of quantum states to perform operations, analyzed through differential geometry to demonstrate built-in resistance to control errors and noise. This approach is situated within advancements in Rydberg atom systems for quantum computing. A reader would care if true because it provides a method for more reliable quantum gates that could scale without perfect hardware control. The geometric insights are positioned as useful for designing robust holonomic protocols more broadly.

Core claim

We introduce a framework for performing scalable quantum computation in atom experiments through a universal set of fully holonomic adiabatic gates. Through a detailed differential geometric analysis, we elucidate the geometric nature of these gates and their inherent robustness against classical control errors and other noise sources. The concepts are expected to be widely applicable to the understanding and design of error robustness in generic holonomic protocols, and the gate design is contextualized within recent advancements in Rydberg-based quantum computing and simulation.

What carries the argument

Fully holonomic adiabatic gates whose evolution depends only on geometric phases, analyzed via differential geometry to establish robustness.

If this is right

  • A universal set of gates enables full quantum computation in the adiabatic holonomic regime for atom experiments.
  • The gates provide inherent robustness against classical control errors and noise due to their geometric character.
  • The differential geometric analysis supplies tools for designing error robustness in other holonomic protocols.
  • The gate designs fit within current Rydberg atom hardware capabilities for quantum computing and simulation.

Where Pith is reading between the lines

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

  • Similar geometric gate constructions could be adapted to other physical systems such as trapped ions or superconducting qubits.
  • If the robustness holds in practice, it could reduce the resources needed for early-stage quantum error correction.
  • Concrete pulse sequences or Hamiltonian parameters from the analysis could be directly tested in existing Rydberg platforms.

Load-bearing premise

The differential geometric analysis of the gates translates directly to practical robustness in Rydberg atom experiments without additional unmodeled decoherence or control limitations.

What would settle it

An experiment that implements the proposed gates in a Rydberg atom system and checks whether observed error rates and decoherence match the geometric predictions or reveal extra unmodeled effects.

Figures

Figures reproduced from arXiv: 2502.17188 by Clara Wassner, Jens Eisert, Jose Carrasco, Tommaso Guaita.

Figure 1
Figure 1. Figure 1: (a) For an arbitrary loop f(t) in the complex plane, as for example depicted here, we set the transition amplitudes (our Hamiltonian parameters) to be Ω(t) = |Ωd|f(t)ω, with ω ∈ C d an arbitrary, constant unit￾vector. This allows us to analytically determine the unitary implemented by an adiabatic evolution along this loop. (b) The analytic expressions for the implemented unitaries depend on two phases whe… view at source ↗
Figure 2
Figure 2. Figure 2: The difference surface (red) between the original loop [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: A particular choice for the loop f(t) (Eq. (47)) in the complex plane implementing our phase gate. We linearly parametrise every of the three segments and have a total protocol time T = 2t1 +t2. At a constant radius R we can reach any phase α2 for our gate by appropriate choice of the angle β. subspaces of our proposal are in general not error correction code spaces, as required in Ref. [29]: so holonomic … view at source ↗
Figure 4
Figure 4. Figure 4: For the case d = 2 we computed the gate fidelity for a constant multiplicative error ϵ. The analytically found scaling 1 − C · ϵ 2 is apparent. We see as well how the coefficient in the leading-order error term can be decreased by choosing higher values of R for R > 3. the complex loop f(t). Due to the rapid decay of c(R) already slightly increasing R makes our gate significantly more robust. This is a dir… view at source ↗
Figure 5
Figure 5. Figure 5: We compute the gate fidelity F between the target controlled-Z gate and the effectively implemented gate resulting from a near-adiabatic evolution along f(t) with R = 5 for different partial protocol times t1 and t2. The gate is determined by numerically solving the time-dependent Schrödinger equation. A non-Hermitian term proportional to the decay rate Γ of the state vector |d⟩, usually some Rydberg level… view at source ↗
Figure 6
Figure 6. Figure 6: a) The closest eigenvalue of the Hamiltonian to the zero-energy computation subspace when evolving [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: a) Dependence of the gap ∆ of the two-qubit Hamiltonian on the Rydberg interaction strength W along the path from [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗
read the original abstract

Holonomic quantum computation exploits the geometric evolution of eigenspaces of a degenerate Hamiltonian to implement unitary evolution of computational states. In this work we introduce a framework for performing scalable quantum computation in atom experiments through a universal set of fully holonomic adiabatic gates. Through a detailed differential geometric analysis, we elucidate the geometric nature of these gates and their inherent robustness against classical control errors and other noise sources. The concepts that we introduce here are expected to be widely applicable to the understanding and design of error robustness in generic holonomic protocols. To underscore the practical feasibility of our approach, we contextualize our gate design within recent advancements in Rydberg-based quantum computing and simulation.

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 introduces a framework for scalable holonomic quantum computation in atom arrays via a universal set of fully holonomic adiabatic gates. It performs a differential-geometric analysis to establish that the gates are purely geometric (dynamic phase zero, evolution in degenerate subspace) and therefore robust to classical control errors, then situates the construction in recent Rydberg-atom hardware.

Significance. If the geometric analysis survives experimental decoherence channels, the work would supply an explicit, parameter-light route to adiabatic holonomic gates whose error robustness is derived rather than fitted, directly addressing a central obstacle to scaling neutral-atom processors.

major comments (2)
  1. [§3] §3 (differential-geometric analysis of the gates): the claim that the holonomy is fully robust rests on the assumption that the evolution remains strictly within the degenerate subspace for the entire gate duration. No quantitative bound is given on non-adiabatic leakage or on the size of the gap relative to the Rydberg decay rates at the gate times needed for scalability.
  2. [§5] §5 (contextualization with Rydberg hardware): the translation from abstract holonomy to experimental fidelity is asserted without explicit modeling of Lindblad operators for spontaneous emission, blackbody radiation, or motional dephasing. These channels are known to be present at the relevant timescales and are not covered by the classical-control-error analysis.
minor comments (1)
  1. Notation for the control functions and the instantaneous eigenbasis is introduced without a consolidated table; a single reference table would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive feedback on our manuscript. We address each major comment below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [§3] §3 (differential-geometric analysis of the gates): the claim that the holonomy is fully robust rests on the assumption that the evolution remains strictly within the degenerate subspace for the entire gate duration. No quantitative bound is given on non-adiabatic leakage or on the size of the gap relative to the Rydberg decay rates at the gate times needed for scalability.

    Authors: We agree that the robustness claims rely on the adiabatic approximation keeping the evolution within the degenerate subspace. Our differential-geometric analysis establishes that the gates are purely geometric when this holds, providing robustness to classical control errors. However, the manuscript does not supply explicit quantitative bounds on non-adiabatic leakage or gap-to-decay-rate ratios. In the revision we will add an estimate of the adiabaticity parameter for the proposed gate times using typical Rydberg parameters, including a bound on leakage probability. revision: yes

  2. Referee: [§5] §5 (contextualization with Rydberg hardware): the translation from abstract holonomy to experimental fidelity is asserted without explicit modeling of Lindblad operators for spontaneous emission, blackbody radiation, or motional dephasing. These channels are known to be present at the relevant timescales and are not covered by the classical-control-error analysis.

    Authors: The referee is correct that our analysis centers on geometric robustness to classical control errors and does not include explicit Lindblad master-equation modeling of spontaneous emission, blackbody radiation, or motional dephasing. Section 5 provides hardware context but does not simulate these quantum channels. We will revise the section to explicitly state this scope limitation, discuss qualitatively how such channels may interact with the holonomic structure, and note that quantitative open-system simulations remain future work. revision: partial

Circularity Check

0 steps flagged

No significant circularity; geometric derivation of holonomic gates is self-contained

full rationale

The manuscript derives its universal set of holonomic adiabatic gates and their robustness properties from standard differential-geometric analysis of degenerate Hamiltonians and their eigenspace evolution. No equations or claims reduce by construction to fitted parameters renamed as predictions, self-definitional loops, or load-bearing self-citations whose supporting results themselves depend on the present work. The contextualization to Rydberg platforms is presented as an application rather than a derivation that collapses into its own inputs. The central claims therefore remain independent of the patterns that would indicate circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; no specific free parameters, invented entities, or ad-hoc axioms identifiable. Relies on standard quantum mechanics and adiabatic theorem.

axioms (1)
  • standard math Adiabatic theorem holds for the degenerate Hamiltonian evolution in the proposed gates
    Invoked implicitly for holonomic gate operation in atom experiments.

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Forward citations

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