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REVIEW 3 major objections 5 minor 43 references

Shots-to-Approximate-Solution Scaling in Neutral-Atom Quantum Optimization

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper establishes that postprocessed Rydberg annealing outputs follow a one-parameter shell distribution and that annealing beats an excitation-matched random baseline, yielding exponential shot-cost reduction for near-exact targets…

desk verdict A serious, unusually honest benchmarking paper whose two-regime conclusion survives direct counting, but whose headline near-exact exponential advantage is a shell-model extrapolation, not a measurement. read the letter →

arxiv 2608.12858 v1 pith:CPTSCELE submitted 2026-08-13 quant-ph physics.atom-ph

Junwoo Jung , Jaewook Ahn This is my paper · ORCID
classification quant-phphysics.atom-ph
keywords Rydbergatomarraysmaximumindependentsetquantumannealingshots-to-approximate-solutionshelldistributionapproximationratioexcitation-matchedbaselinelargedeviations
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper tries to establish an operational measure of how many experimental shots a Rydberg-atom optimizer needs to reach a solution of a given approximation quality, and to determine whether quantum annealing genuinely concentrates probability near optimal solutions. The authors model postprocessed outputs as a degeneracy-weighted exponential shell distribution with one effective quality parameter β, and compare annealing against a random baseline matched to the same excitation density. On King's-lattice maximum-independent-set instances up to 125 sites, the residual advantage Δβ_ann is positive in 86 of 96 instances (0.23–0.40), which they interpret as genuine concentration beyond density effects. The payoff is a two-regime answer: exact targets need exponentially many shots in system size, with annealing reducing that cost at the same exponential level within the model, while relaxed targets need only order-unity shots where classical greedy already succeeds.

What carries the argument

The load-bearing object is the STS metric, STS(r;N) = ⌈ln(1−p_req)/ln(1−p_r)⌉, defined via the per-shot probability p_r of landing in shells j ≤ J(r)=α−⌈rα⌉. The distribution of postprocessed outputs is summarized by the degeneracy-weighted shell model π_j = d_{α−j} $e^{{−βj}}$ / Σ_u d_{α−u} $e^{{−βu}}$, where d_{α−j} are exact near-optimal independent-set counts from a transfer-matrix dynamic program and β is the effective quality parameter. The shell form is motivated by maximum entropy and derived from algorithmic locality: for product-measure inputs and local postprocessing the same exponential form appears with corrections O(j²/N), so β_rand(p_exc) is the quality attainable by any spatially uncorrelated input at the measured excitation density. The combination of the fitted β_ann, the matched baseline β_rand, and the residual Δβ_ann = β_ann − β_rand is what turns raw shot data into the two-regime shot-cost scaling.

What would settle it

Run N≈120–125 instances with enough annealing shots, say 5000 or more, that the direct count of exact-optimum hits is statistically solid, and compare the directly counted STS(r=1) with the shell-model value; if the direct STS remains systematically about three times the shell-model estimate, the near-exact exponential shot-cost reduction would not be directly established. A second check is to extend exact degeneracy counts and measurements to N≈260 and see whether the rate function I(δ_c) develops the predicted non-analytic kink at δ_c=δ^⋆, whose absence would undercut the large-deviation derivation of the two regimes.

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Extended reading notes

Core claim

The central claim is that on site-diluted King's-lattice MIS instances with up to 125 sites, the postprocessed outputs of Rydberg quantum annealing are well described by a degeneracy-weighted exponential shell distribution, π_j ∝ d_{α−j} $e^{{−βj}}$, with a single effective parameter β, and that the fitted annealing parameter exceeds the excitation-matched random baseline by Δβ_ann = 0.23–0.40 (positive in 86 of 96 instances). Because the same postprocessing maps any product-measure input to the same shell form, this residual certifies correlations in the quantum output, beyond one-point statistics, that suppress postprocessing-irreparable defects. Translating β into a shots-to-approximate-solution cost yields two regimes: for near-exact targets (r≈1) the shot count grows exponentially with N with an intensive rate I≈0.039, and annealing reduces the prefactor at the same exponential level within the shell model; for relaxed targets (r=0.9) the shot cost is order unity, and the classical randomized greedy baseline alone reaches the target in one or two passes. The paper explicitly frames the shot counts as a diagnostic of probability concentration, not as evidence of an end-to-end quantum speedup, and reports exact classical solves in 0.6–97 ms per instance.

Load-bearing premise

The load-bearing premise is that one fitted value of β describes the whole postprocessed shell distribution, in particular the probability of hitting an exact optimum, so that shot counts near r=1 can be extrapolated from the model; the paper's own direct counts show this model overestimates the exact-hit probability by up to roughly a factor of three.

Editorial extensions

If this is right

  • For near-exact targets the required number of shots grows exponentially with system size, at a measured intensive rate I≈0.039 per site, and annealing lowers the prefactor within the shell model without removing the exponential growth.
  • For relaxed targets such as r=0.9, the shot cost saturates near order unity over the whole size range, and the excitation-matched random baseline alone reaches the target in one to two greedy passes, so this target has little discriminatory power.
  • A positive excitation-matched advantage Δβ_ann = 0.23–0.40 (86 of 96 instances) indicates that Rydberg annealing concentrates probability toward the MIS manifold beyond what the raw excitation density alone explains.
  • The classical reference is cheap: exact transfer-matrix solves run in 0.6–97 ms per instance and are subexponential, 2^Θ(√N), so the paper's shot counts are a diagnostic of concentration, not an end-to-end speedup claim.
  • The rate function at the exact target is size-independent to within 8%, implying NI grows linearly with N and the sharp two-regime kink should become resolvable near N≈260 with larger arrays.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: because the shell model overestimates the exact-hit probability by up to a factor of about three, the near-exact shot-cost reduction should be read as a model-based lower bound, and direct counting with several thousand shots per instance at N≈120–125 would test whether the hardware's j=0 concentration matches the fitted β.
  • Editorial connection: the locality derivation implies the same degeneracy-weighted exponential form for any product-measure input and any local postprocessor, so the two-regime STS structure is likely a generic property of local postprocessing plus sharp concentration; testing it on other unit-disk graph families would separate what is special to Rydberg annealing from what is generic.
  • Editorial testable extension: replacing the independent-set degeneracy d_{α−j} in Eq. (5) with the count of 1-swap-stable independent sets actually returned by the pipeline should remove most of the j=0 overestimate; this is computable by extending the transfer-matrix dynamic program to track pipeline stability, and would give an exact-target shot-cost prediction not requiring the fitted β.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper introduces a shots-to-approximate-solution metric, STS(r), for evaluating neutral-atom quantum optimization. Postprocessed bitstrings from Rydberg annealing on King's-lattice MIS instances are modeled by a one-parameter degeneracy-weighted shell distribution, Eq. (5), with an effective quality parameter β. An excitation-matched random baseline is constructed using Bernoulli(pexc) inputs put through the same postprocessing pipeline, and a positive residual Δβ_ann = β_ann − β_rand is reported in 86 of 96 instances (bins 1–4). From the fitted β, the paper derives two regimes: near-exact targets (r ≈ 1) show an exponential-in-N shot cost that is reduced by annealing, while relaxed targets (r = 0.9) require order-unity shots. The authors provide direct count checks at both targets, exact degeneracy computations, a classical reference cost, and open data/code.

Significance. The paper is valuable for proposing an operational, target-dependent benchmark and for explicitly separating excitation-density effects from genuine structural concentration. It is commendably transparent: direct counts are reported alongside shell-model values, the classical tractability of the graph family is acknowledged, and no end-to-end quantum speedup is claimed. If the shell model were validated at the exact shell, the near-exact exponential shot-cost reduction would be a meaningful physics statement. As it stands, the central near-exact claim relies on a model that the paper itself shows is inaccurate at j = 0, so the significance of the headline result is currently limited by that gap.

major comments (3)
  1. [Sec. IIIE and Appendix D, Eq. (5)] The near-exact STS claim rests on a shell model that is not validated at the exact target. The paper reports that the model overestimates π0 by up to a factor of ≈3, giving shell-model STS(r=1) medians of 11/27/63/140 versus direct-count values 14/49/190/459, and that no single β reproduces both the bulk shells and the j=0 population (Appendix D). Because the claimed exponential shot-cost reduction by annealing at r≈1 is computed from Eq. (5) rather than from direct counts, that central claim is an extrapolation from a model known to fail at the exact shell. The paper should either replace this part of the claim with direct-count comparisons between annealing and the matched random baseline, or supply the 1-swap-stable degeneracy counts that the pipeline actually samples.
  2. [Sec. IIIE and Fig. 4] The validation narrative in the main text is misleading. The text states that 'over 97% of tested instances satisfy D_KL < 0.1', but Figs. 4(e)–(h) display mock data only; Appendix D reports that for the 96 annealing instances the median D_KL is 0.05 and only 78% fall below the same 0.1 threshold. The experimental fit quality should be stated in Sec. IIIE alongside the mock result, and the implications of the 22% failure rate for the shell-model conversion of measured outputs into STS(r) should be discussed.
  3. [Sec. IIB and Appendix C] The statement that the shell model is 'expected to be most accurate precisely in the low-j region that controls STS(r) for near-exact targets' (Sec. IIB) is contradicted by the empirical finding in Sec. IIIE that the largest model discrepancy occurs at j=0. The O(j²/N) correction derived in Appendix C does not capture the systematic overcounting of maximum independent sets versus 1-swap-stable sets, which is the dominant error at the exact shell. The text should reconcile the locality-based expectation with the observed j=0 failure and state clearly that Eq. (5) is reliable only for j≥1.
minor comments (5)
  1. [Sec. IIIE] The direct-count median at the exact target for the small group is reported as 146.5 per 500 shots; this non-integer median should be defined more precisely, e.g., as the average of the 24th and 25th order statistics.
  2. [Sec. IIB] The maximum-entropy motivation for Eq. (5) is described as 'maximizing the entropy of π relative to the degeneracy measured', which is slightly imprecise; the quantity being maximized is the negative relative entropy S[π∥d] with the sign convention shown in Eq. (6).
  3. [Fig. 5] In panel (b), the filled diamonds and open diamonds are distinguished only by color in the legend; adding different marker shapes or a clearer caption would improve accessibility.
  4. [Sec. IVC] The statement that a fixed ratio r=0.9 'admits a one-atom deficit in the small group but four in xlarge' is an important caveat and should be repeated in the caption of Fig. 5(b) to avoid over-generalizing the constant-cost regime.
  5. [Appendix D] The sentence 'the paired points are slightly offset horizontally for visibility' in the Fig. 8 caption should specify which points are paired and offset, as it is not obvious from the figure.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the shell model is fit to the measured distributions, but the shot-cost claims are transparently derived quantities that the paper also checks by direct counting, and no load-bearing conclusion rests on a self-citation.

full rationale

The paper's derivation chain is self-contained. STS(r) is defined directly from the per-shot success probability p_r (Eqs. 1-4), and p_r is either counted directly from the experimental shots or modeled through the degeneracy-weighted shell distribution of Eq. (5). The parameter beta is estimated from the measured postprocessed shell distributions, and the STS values obtained by inserting that beta into Eq. (5) are openly model-based summaries, not independent predictions presented as new evidence. The paper explicitly supplies model-free checks: at the exact target, direct counts yield STS(r=1) = 14, 49, 190, and 459 for the four size groups, while the per-instance shell model gives 11, 27, 63, and 140, and the text states that shell-model STS(r=1) should be read as a lower bound because the model overestimates pi_0 by up to a factor of about 3. At the relaxed target, direct counting alone gives STS(r=0.9)=2 in every group, so the two-regime structure is supported independently of Eq. (5). The claimed quantum reduction in near-exact shot cost relative to the excitation-matched random baseline is derived from the measured positive Delta_beta_ann via the monotone dependence of Eq. (5) on beta, and the paper consistently qualifies this as 'within the shell-model description'; this is a model-based inference rather than a definitional identity. The one real caveat, namely that the shell model is least accurate precisely at the exact target that controls near-exact STS, is a validation limitation that the authors flag explicitly, not a circular step. There is also no load-bearing self-citation: references to prior work by the same group (e.g., Ref. [24]) are used only for background on swap-based local improvement, and the hardness proxy H(G) is credited to the external Ref. [14]. No uniqueness theorem is imported from the authors' own prior work, and no known result is merely renamed. The central experimental content, including the raw shot counts, the excitation-matched Bernoulli baseline, and the direct-count rate function of Fig. 6, stands independently of the fitted shell model.

Assumptions & free parameters 1 free parameters · 6 assumptions · 0 invented entities

No new physical entities are introduced. STS(r) and beta are operational quantities defined from measured outputs, not independent degrees of freedom. The central claim rests on the fitted parameter beta plus several asymptotic and algorithmic assumptions that the paper itself flags as approximations.

free parameters (1)
  • beta (effective quality parameter) = beta_ann approximately 3.79 to 4.06 per group; beta_rand from Bernoulli(p_exc) baseline
    Single free parameter in Eq. (5). Fitted by maximum likelihood to postprocessed shell distributions for each instance or group, then used in Eqs. (1)-(4) to compute all STS(r) values and the claimed Delta_beta_ann advantage.
assumptions (6)
  • standard math Maximum entropy / Gibbs form for shell distribution (Eq. 5)
    Unique distribution maximizing relative entropy subject to fixed mean shell depth (Jaynes). Standard inference but does not by itself guarantee empirical validity.
  • standard math Laplace principle / large-deviation approximation for shell sum
    Used in Sec. IVB to derive the exponential form p_r approximately exp[-N I(delta_c)] and the two-regime prediction. Standard asymptotic tool, applied where measured NI = 1.3 to 4.5, below the regime where the Laplace step is sharp.
  • domain assumption Entropy-density description of shell degeneracies
    Sec. IVB assumes d_{alpha-j} approximately exp[N s(delta)] with s concave. Appendix A shows collapse for N >= 60 over a narrow window delta <= 0.12, but the authors state the window is too narrow for definitive verification.
  • domain assumption Algorithmic locality: finite propagation radius, defect sparsity, type uniformity (Appendix C)
    These three assumptions justify the exponential shell form Eq. (5). The authors explicitly call (i) and (iii) approximations whose adequacy is reflected in fit quality, and (ii) holds only at low j.
  • domain assumption Bernoulli excitation-matched null model suffices to isolate structural correlations
    Sec. IIC matches only mean excitation density p_exc. The claim that positive Delta_beta_ann certifies correlations beyond one-point statistics depends on this minimal null-model choice; the authors argue that matching edge statistics would build in the blockade physics under test.
  • domain assumption Degeneracy d_{alpha-j} in Eq. (5) can be the count of all independent sets rather than only 1-swap-stable outputs
    Sec. IV states outputs are 1-swap-stable maximal independent sets, so the degeneracy should be stable-set counts; the paper absorbs this distinction into the fitted beta, contributing to the j=0 discrepancy and making beta less physically interpretable.

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Pith. "Pith review of Shots-to-Approximate-Solution Scaling in Neutral-Atom Quantum Optimization." pith.science (2026). https://pith.science/paper/CPTSCELE

@misc{pith2026260812858,
  author       = {Pith},
  title        = {Pith review of: Shots-to-Approximate-Solution Scaling in Neutral-Atom Quantum Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CPTSCELE}},
  note         = {Machine review of arXiv:2608.12858}
}
abstract

Whether neutral-atom quantum optimization protocols exhibit genuine concentration toward low-energy solution structure remains an open question. Here, we introduce a shots-to-approximate-solution metric, STS(r), where r denotes the approximation ratio, and evaluate it using postprocessed outputs modeled by a degeneracy-weighted shell distribution governed by a single effective parameter, $\beta$, that quantifies concentration toward near-optimal independent sets. To extract the genuine concentration effect in the quantum data, we apply identical postprocessing to both experimental bitstrings and randomly generated bitstrings with matched excitation density, thereby constructing an excitation-matched random baseline. Experiments on programmable Rydberg-atom arrays with system sizes up to 125 sites show that quantum annealing consistently exceeds the random baseline, demonstrating enhanced concentration toward low-energy solution structure beyond what can be attributed solely to excitation density. The results further reveal two distinct target-dependent regimes. For near-exact targets with $r \approx 1$, the required shot count grows exponentially with system size and is reduced at the same exponential level by quantum annealing within the shell-model description. By contrast, for relaxed targets, the shot cost becomes effectively constant, and the corresponding quantum enhancement diminishes, with the classical postprocessing heuristic alone reaching the target in order-unity attempts. Together, these results establish an operational method for quantifying quantum optimization performance and clarify the regimes under which quantum approaches can yield practical benefits.

Figures

Figures reproduced from arXiv: 2608.12858 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
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Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
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Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
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Figure 7. Figure 7: FIG. 7 [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
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Figure 8. Figure 8: FIG. 8 [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]

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Works this paper leans on

43 extracted references · 32 canonical work pages

  1. [1]

    Exactly, πj = X S:|S|=α−j W(S), W(S) = Pr z∼µ [PP(z) =S]

    Pushforward identity Let the input bitstringz∈{0,1} N be drawn from a product measureµ(independent coordinates), and let S= PP(z)denote the output of Algorithm 1. Exactly, πj = X S:|S|=α−j W(S), W(S) = Pr z∼µ [PP(z) =S]. (C1) For the homogeneous Bernoulli measureµ= Bern(p)⊗N, W(S) = (1−p)NGS p 1−p , G S(x) = X z∈PP−1(S) x|z|, (C2) 14 whereGS is the weight...

    work page

  2. [2]

    Defect factorization The pipeline is local: each of the three phases makes accept/reject decisions based on graph neighborhoods of bounded radius, so there is an effective propagation ra- diusR=O(1)such that whether a given local defect survives postprocessing is determined by the input re- stricted to its distance-Rneighborhood [assumption (i)]. The iter...

    work page

  3. [3]

    (C3) depends on the graph but not on the placement of the defects, and on homo- geneous regions of the King’s lattice the local weights c(p)are position-independent

    Within-shell exchangeability The bulk factorPbulk in Eq. (C3) depends on the graph but not on the placement of the defects, and on homo- geneous regions of the King’s lattice the local weights c(p)are position-independent. Two residual sources of position dependence remain: boundary effects, which in- volve a vanishing fraction of sites at largeN, and the...

    work page

  4. [4]

    Exactly solvable case and corrections The structure above is exact when the blockade graph decomposes into disjoint clusters, each contributing one MIS slot. The pipeline then factorizes over clusters, each slot is resolved independently with some probabilityq(p), and πj = α j (1−q) jqα−j ∝d α−je−βj, β= ln q 1−q , (C5) withd α−j = α j the exact shell dege...

    work page

  5. [5]

    Consequences Three consequences are used in the main text. First, for any product-measure input,βis fixed entirely by the one-point statistics throughc(p); the excitation-matched baselineβ rand(pexc)therefore represents the quality pa- rameter attainable by an arbitrary spatially uncorrelated ensemble at the given excitation density, and∆βann >0 certifies...

    work page

  6. [6]

    Albash and D

    T. Albash and D. A. Lidar, Adiabatic quantum compu- tation, Rev. Mod. Phys.90, 015002 (2018)

    2018

  7. [7]

    Lucas, Ising formulations of many NP problems, Front

    A. Lucas, Ising formulations of many NP problems, Front. Phys.2, 5 (2014)

    2014

  8. [8]

    Farhi, J

    E. Farhi, J. Goldstone, S. Gutmann, and J. Sipser, Quan- tum computation by adiabatic evolution, arXiv:quant- ph/0001106 (2000)

    arXiv 2000

Show all 43 references
  1. [9]

    Kadowaki and H

    T. Kadowaki and H. Nishimori, Quantum annealing in the transverse Ising model, Phys. Rev. E58, 5355 (1998)

    1998

  2. [10]

    Hauke, H

    P. Hauke, H. G. Katzgraber, W. Lechner, H. Nishimori, and W. D. Oliver, Perspectives of quantum annealing: Methods and implementations, Rep. Prog. Phys.83, 054401 (2020)

    2020

  3. [11]

    M. R. Garey and D. S. Johnson,Computers and In- tractability: A Guide to the Theory of NP-Completeness (Freeman, New York, 1979)

    1979

  4. [12]

    Zuckerman, Linear degree extractors and the inap- proximability of max clique and chromatic number, The- ory Comput.3, 103 (2007)

    D. Zuckerman, Linear degree extractors and the inap- proximability of max clique and chromatic number, The- ory Comput.3, 103 (2007)

    2007

  5. [13]

    Håstad, Clique is hard to approximate withinn1−ϵ, in Proc

    J. Håstad, Clique is hard to approximate withinn1−ϵ, in Proc. 37th Annual Symposium on Foundations of Com- puter Science, pp. 627–636 (IEEE, 1996)

    1996

  6. [14]

    H. B. Hunt III, M. V. Marathe, V. Radhakrishnan, S. S. Ravi, D. J. Rosenkrantz, and R. E. Stearns, NC- approximation schemes for NP- and PSPACE-hard prob- lems for geometric graphs, J. Algorithms26, 238 (1998)

    1998

  7. [15]

    Nieberg and J

    T. Nieberg and J. Hurink, A PTAS for the minimum dominating set problem in unit disk graphs, inApprox- imation and Online Algorithms, edited by T. Erlebach and G. Persiano, Lecture Notes in Computer Science Vol. 3879, pp. 296–306 (Springer, Berlin, 2006)

    2006

  8. [16]

    Erlebach, K

    T. Erlebach, K. Jansen, and E. Seidel, Polynomial-time approximationschemesforgeometricintersectiongraphs, SIAM J. Comput.34, 1302 (2005)

    2005

  9. [17]

    Saffman, T

    M. Saffman, T. G. Walker, and K. Mølmer, Quantum information with Rydberg atoms, Rev. Mod. Phys.82, 2313 (2010)

    2010

  10. [18]

    Browaeys and T

    A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nat. Phys.16, 132 (2020)

    2020

  11. [19]

    Ebadiet al., Quantum optimization of maximum in- dependent set using Rydberg atom arrays, Science376, 1209 (2022)

    S. Ebadiet al., Quantum optimization of maximum in- dependent set using Rydberg atom arrays, Science376, 1209 (2022)

    2022

  12. [20]

    Nguyenet al., Quantum optimization with ar- bitrary connectivity using Rydberg atom arrays, PRX Quantum4, 010316 (2023)

    M.-T. Nguyenet al., Quantum optimization with ar- bitrary connectivity using Rydberg atom arrays, PRX Quantum4, 010316 (2023)

    2023

  13. [21]

    Y. Song, M. Kim, H. Hwang, W. Lee, and J. Ahn, Quan- tum simulation of Cayley-tree Ising Hamiltonians with three-dimensional Rydberg atoms, Phys. Rev. Res.3, 013286 (2021)

    2021

  14. [22]

    A. Byun, M. Kim, and J. Ahn, Finding the maximum in- dependent sets of Platonic graphs using Rydberg atoms, PRX Quantum3, 030305 (2022)

    2022

  15. [23]

    M. Kim, K. Kim, J. Hwang, E.-G. Moon, and J. Ahn, Rydberg quantum wires for maximum independent set problems, Nat. Phys.18, 755 (2022)

    2022

  16. [24]

    R. S. Andristet al., Hardness of the maximum indepen- dent set problem on unit-disk graphs and prospects for quantum speedups, Phys. Rev. Res.5, 043277 (2023)

    2023

  17. [25]

    Wurtzet al., Aquila: QuEra’s 256-qubit neutral-atom quantum computer, arXiv:2205.08500 (2022)

    J. Wurtzet al., Aquila: QuEra’s 256-qubit neutral-atom quantum computer, arXiv:2205.08500 (2022)

    2022 arXiv

  18. [26]

    Dupontet al., Quantum annealing for maximum in- dependent set using Rydberg atom arrays, Phys

    M. Dupontet al., Quantum annealing for maximum in- dependent set using Rydberg atom arrays, Phys. Rev. Res.5, 043220 (2023)

    2023

  19. [27]

    Larkin, M

    J. Larkin, M. Jonsson, D. Justice, and G. G. Guerreschi, Evaluation of QAOA based on the approximation ratio of individual samples, Quantum Sci. Technol.7, 045014 (2022)

    2022

  20. [28]

    A. Yu. Chernyavskiyet al., Approximation-ratio de- pendent sampling cost in quantum optimization, arXiv:2509.19035 (2025)

    2025

  21. [29]

    Jeong, J

    S. Jeong, J. Park, and J. Ahn, Quantum-enhanced sim- ulated annealing using Rydberg atoms, Adv. Quantum Technol.8, e2500070 (2025)

    2025

  22. [30]

    E. T. Jaynes, Information theory and statistical mechan- ics, Phys. Rev.106, 620 (1957);108, 171 (1957)

    1957

  23. [31]

    M. H. Amin, Searching for quantum speedup in qua- sistatic quantum annealers, Phys. Rev. A92, 052323 (2015)

    2015

  24. [32]

    Benedetti, J

    M. Benedetti, J. Realpe-Gómez, R. Biswas, and A. Perdomo-Ortiz, Estimation of effective temperatures in quantum annealers for sampling applications: A case study with possible applications in deep learning, Phys. Rev. A94, 022308 (2016)

    2016

  25. [33]

    Marshall, E

    J. Marshall, E. G. Rieffel, and I. Hen, Thermalization, freeze-out, and noise: Deciphering experimental quan- tum annealers, Phys. Rev. Applied8, 064025 (2017)

    2017

  26. [34]

    Vuffray, C

    M. Vuffray, C. Coffrin, Y. A. Kharkov, and A. Y. Lokhov, Programmable quantum annealers as noisy Gibbs sam- plers, PRX Quantum3, 020317 (2022)

    2022

  27. [35]

    Weidemüller, Suppression of excitation and spec- tral broadening induced by interactions in a cold gas of Rydberg atoms, J

    K.Singer, M.Reetz-Lamour, T.Amthor, L.G.Marcassa, and M. Weidemüller, Suppression of excitation and spec- tral broadening induced by interactions in a cold gas of Rydberg atoms, J. Phys. B38, S295 (2005)

    2005

  28. [36]

    Pichler, S.-T

    H. Pichler, S.-T. Wang, L. Zhou, S. Choi, and M. D. Lukin, Quantum optimization for maxi- mum independent set using Rydberg atom arrays, arXiv:1808.10816 (2018)

    2018 arXiv

  29. [37]

    com/aquila(accessed 2026)

    QuEra,Aquila quantum computer,https://www.quera. com/aquila(accessed 2026)

    2026

  30. [38]

    Shots-to- Approximate-Solution Scaling in Neutral-Atom Quan- tum Optimization

    J. Jung and J. Ahn, Data and code for “Shots-to- Approximate-Solution Scaling in Neutral-Atom Quan- tum Optimization”, figshare, Dataset (2026),https:// doi.org/10.6084/m9.figshare.33205122

    2026 doi

  31. [39]

    den Hollander,Large Deviations(American Mathe- matical Society, Providence, RI, 2000)

    F. den Hollander,Large Deviations(American Mathe- matical Society, Providence, RI, 2000)

    2000

  32. [40]

    M.deBerg, H.L.Bodlaender, S.Kisfaludi-Bak, D.Marx, and T. C. van der Zanden, A framework for exponential- time-hypothesis–tightalgorithmsandlowerboundsinge- ometric intersection graphs, SIAM J. Comput.49, 1291 (2020)

    2020

  33. [41]

    T. W. B. Kibble, Topology of cosmic domains and strings, J. Phys. A9, 1387 (1976)

    1976

  34. [42]

    W. H. Zurek, Cosmological experiments in superfluid he- lium?, Nature317, 505 (1985)

    1985

  35. [43]

    Keeslinget al., Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg sim- ulator, Nature568, 207 (2019)

    A. Keeslinget al., Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg sim- ulator, Nature568, 207 (2019)

    2019

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Reviewed August 15, 2026 · model on record in the stance chip above.