{"id":"349e27d1-35e8-4af2-88ca-f0661089eaca","arxiv_id":"2507.15544","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"For fully-connected random Ising models of 240 to 640 spins, solving a spin-reduced subproblem on a quantum annealer improves on preprocessing simulated annealing, and the optimal subproblem size grows with quantum annealing accuracy.","lead":"A hybrid optimizer runs a classical annealer many times, freezes the spins it consistently agrees on, and hands only the remaining unstable spins to a quantum annealer. The paper shows this finds lower-energy solutions on random Ising models too large for current D-Wave hardware, with the best number of unfrozen spins shifting with the annealer's accuracy.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The gap-widening mechanism is computed under ground-state-fixed spins (Sec. V-B), but the realized hybrid fixes spins from tentative SA solutions; the link from wider gaps to the headline improvement is unverified.","rationale":"The central empirical claim is that the hybrid method improves upon preprocessing SA on unembeddable sizes, and the paper's supporting mechanism is that sub-Ising models have wider minimum gaps, so QA solves them more accurately, with the best sub-Ising size set by a trade-off between unstable-spin coverage and QA accuracy. The mechanism analysis in Sec. V-B and Appendix A fixes excluded spins to their ground-state values, whereas the actual hybrid algorithm fixes spins from tentative SA solutions. The paper itself flags in Sec. V-C that wrong fixing prevents reaching the ground state, so the concern is not hidden, but the consequence is that the gap-widening evidence does not directly support the realized algorithm. This is the most load-bearing concern because the paper's explanatory claim, not just the raw improvement, rests on it. The proposed test reuses the paper's own simulation components and solution pools, so it can settle the question without new hardware. Other weaknesses such as one instance per size, absent error bars, and no resource-fair classical baseline affect the strength of the empirical claim, but they do not undermine the logical link between mechanism and result as directly. The reader's CONDITIONAL verdict is therefore appropriate, and my read does not change it.","tokens_in":19321,"tokens_out":6808,"duration_ms":73359,"concrete_test":"Rerun the Sec. V-B minimum-gap computation on the n=8 instances, but fix the excluded spins to the values from the actual tentative SA solution pools used in Sec. V-C (100 pools excluding the ground state) instead of the ground-state values. Compare the average minimum gaps of sub-Ising models with and without unstable spins against the ground-state-fixed results in Fig. 5 and Appendix A. If the average gap is no longer wider than the original model when wrong-fixed spins occur, the mechanism explanation does not transfer to the realized algorithm; if the gap remains wider, the idealization is benign.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's mechanistic explanation for why sub-Ising solving improves over preprocessing SA rests on Sec. V-B, where excluded spins are fixed to ground-state values. The actual hybrid algorithm (Sec. II-B) fixes spins according to a tentative SA solution, and Sec. V-C deliberately uses solution pools that exclude the ground state. Section V-C itself concedes that wrong fixing prevents the hybrid method from reaching the ground state. Therefore, the measured gap-widening of sub-Ising models (Fig. 5, Appendix A) may not transfer to the realized algorithm: wrong fixation changes the effective Hamiltonian, and the sub-Ising ground state can lie above the original ground state. The empirical improvement in Sec. IV is reported directly in Fig. 3, but the paper uses the V-B idealization to explain that improvement and to predict the sub-Ising size dependency via unstable-spin count and QA accuracy. Without checking gap statistics under tentative-fixed spins, the causal story connecting wider gaps to the headline result remains unsupported. This is load-bearing because the paper's contribution is not just a numerical observation but a claimed mechanism for when and why hybrid QA helps.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper evaluates a hybrid optimization method for Ising machines that combines simulated-annealing-based preprocessing (solution pooling and sample-persistence spin fixing) with quantum annealing on the resulting sub-Ising model. Section IV reports D-Wave Advantage experiments on fully connected random Ising models of sizes 240, 320, 480, and 640 that cannot be embedded in the device, and observes that the hybrid method lowers the energy density relative to preprocessing SA. Section V uses small fully connected models (n = 8, 6, 10) with exact master-equation and Schrödinger-equation dynamics to analyze the separation of spins into stable and unstable groups, the minimum energy gaps of sub-Ising models, and the dependence of solution accuracy on sub-Ising size and annealing time. The paper concludes that the hybrid method remains effective for non-embeddable sizes, that sub-Ising models with unstable spins have wider gaps than the original model but narrower gaps than sub-Ising models without unstable spins, and that the optimal sub-Ising size is controlled by the number of unstable spins and the accuracy of the quantum annealer.","tokens_in":19481,"tokens_out":10449,"duration_ms":105768,"significance":"The paper addresses a practically relevant question: how to use a limited-size quantum annealer through spin reduction, and it offers a falsifiable qualitative prediction that increasing annealing time shifts the optimal sub-Ising size upward. The small-system analysis is a strength: the master-equation spin-expectation calculations, exhaustive enumeration of spin states, and Schrödinger-equation QA simulations are carefully specified and reproducible in principle. The empirical D-Wave results, however, rest on a very small number of instances, and the mechanism proposed in Section V is not yet connected to the realized algorithm in a fully supported way.","major_comments":[{"comment":"The minimum-energy-gap analysis in Section V-B is performed under the assumption that 'the fixed spins took the values corresponding to the ground state.' In the actual hybrid algorithm (Section II-B, Eqs. (2)-(4)), the fixed spins take values from tentative SA solutions, and Section V-C deliberately uses solution pools 'that did not include the ground state' and concedes that 'if the fixed spins are different from the ground state, solving the sub-Ising model will not reach the ground state of the original Ising model.' The mechanistic claim that QA is more accurate on sub-Ising models because their gaps are wider is therefore established only in an idealized setting and does not, as written, transfer to the realized algorithm. Please provide a gap analysis (or an analytic argument) for sub-Ising models generated with tentatively fixed spins, or restrict the mechanism claim to the ground-state-fixing regime.","section":"Section V-B and Section V-C"},{"comment":"The headline empirical claim that the hybrid method improves over preprocessing SA for models that cannot be embedded in the quantum annealer rests on a single random fully connected Ising model instance for each size (n = 240, 320, 480, 640), as stated in Section IV-A ('One instance was prepared for each model'). Figure 3 shows ten simulations, but these are repeated runs on the same instance, so they do not quantify instance variability. The same limitation applies to Figure 11. Please add multiple random instances per size, or at minimum report error bars or instance-by-instance results, before claiming a general improvement for this class of models.","section":"Section IV-A and Figure 3"},{"comment":"The counts of sub-Ising models given in the caption of Figure 8 are not consistent with the stated unstable-spin sets. For Ising model A with unstable spins {sigma_1, sigma_2, sigma_5, sigma_6}, the numbers of sub-Ising models containing all four unstable spins would be 1, 4, 6, 4 for sizes m = 4, 5, 6, 7 and zero for m < 4, while the caption reports 1, 6, 15, 20, 15, 6 for sizes m = 2, ..., 7; the reported values also do not match the counts for 'at least one unstable spin.' The same issue occurs for model B (reported counts 1, 4, 6, 4 for m = 4, ..., 7). Since Figure 8 is used to support the size-dependency explanation in Section V-C, please clarify exactly which sub-Ising models enter the average and verify the counts; error bars should be added.","section":"Appendix A and Figure 8"},{"comment":"The text states that '100 sets of solution pools that did not include the ground state were prepared,' but it does not state whether the same 100 pools are used for every sub-Ising size m and annealing time tau. If the pools differ across conditions, the comparisons in Figure 7 mix algorithmic effects with sampling variability, and no error bars are shown for the averages. Please specify the experimental design (shared versus independent pools) and report the spread across the 100 sets.","section":"Section V-C and Figure 7"}],"minor_comments":[{"comment":"There is a typographical spacing error in 'D-Wave Advantage has5, 627 qubits'; it should read 'has 5,627 qubits.'","section":"Section IV-A"},{"comment":"The statement 'Error bars are not shown in the figure' should be replaced by actual error bars or a clear explanation of why they are omitted; as written it weakens the comparison in Figure 8.","section":"Appendix B, Figure 8"},{"comment":"The inference that 'the number of unstable spins' controls the size dependency is based on only two 8-spin instances; a sentence acknowledging this limited basis would help the reader calibrate the strength of the claim.","section":"Section V-C"},{"comment":"The paper does not state whether code or data are available; depositing the instance-generation and analysis scripts would improve reproducibility.","section":"Reproducibility"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is potentially publishable after major revision. The exact small-system numerics are a genuine strength, and the annealing-time prediction is falsifiable. The main risk is not the numerics themselves but the gap between the idealized gap analysis and the realized hybrid algorithm; the Appendix A count inconsistencies should also be checked carefully before resubmission."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a solid, plainly written extension of the authors' previous hybrid method [72]. The genuinely new material is the evaluation on fully connected Ising models too large to embed on D-Wave (n=240–640) and a small-scale exact analysis distinguishing sub-Ising models that contain unstable spins from those that don't. The latter observation—unstable-spin sub-Ising models have smaller minimum gaps and larger constants than stable-only ones, while still larger-gap than the original—is a real and useful numerical finding.\n\nThe paper does a number of things well. The master-equation integration and exhaustive diagonalization are done carefully. The authors state their parameters and their limitations plainly: one instance per size, solution pools that deliberately exclude the ground state in Section V-C, and the explicit admission that fixing spins to wrong values prevents reaching the ground state. This transparency makes the work easy to evaluate.\n\nThe soft spots are the usual ones for this kind of hardware paper, and they matter here because the abstract makes a fairly strong claim. First, one random instance per size (n=240, 320, 480, 640) is very thin. Figures 3, 8 and 11 show no error bars. Second, the comparison is only against preprocessing SA; a resource-fair baseline—SA run for the same total wall-clock time on the full model—is missing. So part of the observed 'improvement' could be a time-allocation effect. Third, and this is the stress-test point, the mechanism story is built on Section V-B, where excluded spins are fixed to their ground-state values. The realized algorithm fixes spins from tentative SA solutions, and the gap-widening under correct fixing does not guarantee gap-widening under wrong fixing. The paper concedes the risk in V-C, but the causal link from 'wider gaps' to the headline improvement remains unverified. That doesn't kill the paper; it does mean the mechanism section overreaches a little relative to what is actually computed.\n\nBottom line: this is not a breakthrough, but it is a careful, honest contribution that deserves a serious referee. Publishability hinges on the requested major revision: multiple instances per size, error bars, a resource-fair classical baseline, and ideally gap statistics under tentative-fixed spins. I'd bring it to a reading group with those caveats.","headline":"A careful but thin extension of the authors' hybrid annealing method to unembeddable sizes; the headline claim is plausible, the mechanism analysis is idealized, and the empirical support needs more instances and a fair baseline.","tokens_in":20097,"tokens_out":2718,"would_cite":true,"duration_ms":28540,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A hybrid method that fixes stable spins with simulated annealing and sends only the unstable core to a quantum annealer improves solutions even when the full Ising model cannot be embedded.","keywords":["hybrid optimization method","quantum annealing","simulated annealing","sample persistence","spin fixing","sub-Ising model","minimum energy gap","Ising machine"],"falsifier":"Compare, on a small fully connected Ising model with a known ground state, the minimum energy gaps of sub-Ising models with spins fixed to ground-state values versus fixed to tentative simulated-annealing values, and run the hybrid method across sub-Ising sizes and annealing times; the central claim fails if wrong-fixed submodels do not show wider gaps than the original or if longer annealing time does not shift the best sub-Ising size upward.","tokens_in":19041,"feed_emoji":"⚛️","tokens_out":10417,"duration_ms":106271,"temperature":0.7,"pith_summary":"This paper aims to establish that a hybrid optimization method, which preprocesses an Ising model with simulated annealing (SA) and then solves a smaller spin-fixed sub-Ising model on a quantum annealing machine, delivers lower-energy solutions than SA alone even when the original model is too large to fit on the quantum device. That matters because quantum annealing hardware currently has far fewer usable spins than classical Ising machines, and a reliable preprocessing scheme would extend its reach to larger combinatorial problems. The paper supports the claim with runs on fully connected random Ising models of 240 to 640 spins, beyond the size embeddable in the quantum annealing hardware, and with exact small-scale simulations of SA and quantum annealing dynamics. It also identifies the trade-off that sets the best subproblem size: the number of unstable spins that must be included versus the accuracy of the quantum annealer on larger submodels.","feed_headline":"Hybrid annealing beats preprocessing even on models too big to embed","feed_subtitle":"Preprocessing finds the hard spins, so quantum annealers can attack problems larger than their hardware.","key_machinery":"The load-bearing object is the spin-fixed sub-Ising model generated from multiple SA solutions by sample persistence. A spin is deemed stable when it takes the same value in many tentative solutions and unstable when its disagreement count is high; the $m$ most unstable spins form the subproblem, while the rest are fixed to values from a tentative solution, producing an effective field $R_i$ and a constant $C$ in $H_{\\mathrm{sub}}$. The argument then runs through the minimum energy gap of this sub-Hamiltonian: fixing stable spins compresses the spectrum so the low-energy part survives, and sub-Ising models with unstable spins have large constants but wider minimum gaps than the original, making QA more accurate on them. The paper uses exact master-equation SA and time-dependent Schr\\\"odinger-equation QA on eight-spin fully connected models to watch how this gap behavior and the choice of submodel size interact.","core_discovery":"On the paper's own terms, the central discovery is that spin-fixed sub-Ising models are systematically easier for quantum annealing than the original Ising model, but only if the fixed spins are chosen well. Preprocessing SA separates spins into stable ones, whose expectation values sit near $\\pm 1$, and unstable ones with expectation values near zero; sub-Ising models are built by fixing stable spins to tentative solution values and leaving unstable spins in the subproblem. Computing minimum energy gaps shows that sub-Ising models containing unstable spins have smaller gaps than models without them, yet still larger gaps than the original full model, and that the average gap widens as the submodel shrinks. The hybrid method therefore profits in two stages: QA is more accurate on the smaller, wider-gap submodel, while removing stable spins keeps the low-energy spectrum intact. The remaining size dependence is governed by the number of unstable spins and by QA accuracy: if the submodel is too small, some unstable spins get fixed wrongly and the ground state becomes unreachable; if it is too large, QA loses accuracy. Increasing annealing time shifts the best sub-Ising size upward, which the paper verifies in simulations and on hardware with short versus long annealing.","pith_inferences":["The same trade-off should appear for other spin-fixing preprocessing schemes, so the paper's mechanism can be tested by substituting a different non-quantum solver and re-checking the gap-widening signature.","The benefit of the hybrid method may be largest on instances with many near-degenerate low-energy states, where sample persistence isolates a genuinely hard core; on easy instances the gain could vanish.","An adaptive variant could grow the sub-Ising model until the unstable-spin condition is satisfied, removing the need to know the number of unstable spins in advance.","Because the mechanism is gap-based, it suggests a tuning recipe: choose the sub-Ising size in proportion to the number of unstable spins and increase it as the quantum annealer's accuracy improves."],"forward_implications":["Even when the original Ising model cannot be embedded in the quantum annealing machine, the hybrid method can return lower-energy solutions than preprocessing simulated annealing alone, as shown for fully connected models of 240 to 640 spins.","The useful sub-Ising size is set by a trade-off: it must include all unstable spins so none are fixed wrongly, but it must stay small enough that the quantum annealer remains accurate.","Longer annealing times improve quantum-annealer accuracy and therefore move the best sub-Ising size upward, as verified both in Schr\\\"odinger-equation simulations and in hardware with short versus long annealing.","Minimum energy gaps provide a practical diagnostic: sub-Ising models containing unstable spins have wider gaps than the original model, which is why solving them with QA gives higher solution accuracy.","As quantum annealing hardware accuracy improves, the hybrid method should handle effectively larger problems, because the optimal subproblem size grows with annealing accuracy."],"supporting_citations":[{"why":"Defines the hybrid optimization method being evaluated and supplies the earlier embeddable-model results that this paper extends to large non-embeddable models.","marker":"[72]"},{"why":"Introduces sample persistence, the spin-fixing principle used to generate sub-Ising models from multiple solutions.","marker":"[67]"},{"why":"Extends sample persistence to quantum annealers and Monte Carlo optimizers, supporting the choice of stable-spin fixing.","marker":"[68]"},{"why":"Cited for the observation that fixing spins in a random fully connected Ising model widens the minimum energy gap.","marker":"[75]"},{"why":"Reports an optimal sub-Ising size when fixed spins differ from the ground state and that this optimum grows with annealing time, providing the comparison for the annealing-time analysis.","marker":"[95]"},{"why":"Cited for the quantum annealing device showing improved accuracy as problem size decreases for fully connected Ising models.","marker":"[98]"},{"why":"Cited to justify that longer annealing time improves quantum-annealer accuracy, which is used to vary QA accuracy in the hardware experiment.","marker":"[99]"}],"fun_headline_variants":["Hybrid method extends quantum annealing to non-embeddable models","Spin-fixing preprocessing shrinks subproblems for better QA accuracy","Sub-Ising models improve quantum annealer accuracy even beyond embeddability","Hybrid optimization: preprocessing then QA beats isolated preprocessing","Quantum annealers get a leg up from hybrid preprocessing on large Ising models"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the gap-widening effect seen when excluded spins are fixed to their ground-state values also holds when they are fixed to tentative simulated-annealing solutions, even though the paper concedes that wrong fixing prevents the sub-Ising solve from reaching the ground state.","fun_headline_variants_meta":{"raw":{"variants":["Hybrid method extends quantum annealing to non-embeddable models","Spin-fixing preprocessing shrinks subproblems for better QA accuracy","Sub-Ising models improve quantum annealer accuracy even beyond embeddability","Hybrid optimization: preprocessing then QA beats isolated preprocessing","Quantum annealers get a leg up from hybrid preprocessing on large Ising models"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000184,"raw_usage":{"total_tokens":1334,"prompt_tokens":976,"completion_tokens":358,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":592,"completion_tokens_details":{"reasoning_tokens":267}},"tokens_in":592,"tokens_out":358,"duration_ms":4985,"temperature":1.0,"reasoning_tokens":267,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T15:30:30.912135+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compare, on a small fully connected Ising model with a known ground state, the minimum energy gaps of sub-Ising models with spins fixed to ground-state values versus fixed to tentative simulated-annealing values, and run the hybrid method across sub-Ising sizes and annealing times; the central claim fails if wrong-fixed submodels do not show wider gaps than the original or if longer annealing time does not shift the best sub-Ising size upward.","supporting_citations":[{"cited_title":"Hybrid optimization method using simulated-annealing-based Ising machine and quantum annealer,","cited_arxiv_id":null,"evidence_quote":"Defines the hybrid optimization method being evaluated and supplies the earlier embeddable-model results that this paper extends to large non-embeddable models."},{"cited_title":"Boosting quantum annealer performance via sample persistence,","cited_arxiv_id":null,"evidence_quote":"Introduces sample persistence, the spin-fixing principle used to generate sub-Ising models from multiple solutions."},{"cited_title":"Effective optimization using sample persistence: A case study on quantum annealers and various Monte Carlo optimization methods,","cited_arxiv_id":null,"evidence_quote":"Extends sample persistence to quantum annealers and Monte Carlo optimizers, supporting the choice of stable-spin fixing."},{"cited_title":"Statistical Qubit Freezing Extending Physical Limit of Quantum Annealers","cited_arxiv_id":"2405.12594","evidence_quote":"Cited for the observation that fixing spins in a random fully connected Ising model widens the minimum energy gap."},{"cited_title":"Advantages of fixing spins in quantum annealing,","cited_arxiv_id":null,"evidence_quote":"Reports an optimal sub-Ising size when fixed spins differ from the ground state and that this optimum grows with annealing time, providing the comparison for the annealing-time analysis."},{"cited_title":"Experimental investigation of performance differences between coherent Ising machines and a quantum annealer,","cited_arxiv_id":null,"evidence_quote":"Cited for the quantum annealing device showing improved accuracy as problem size decreases for fully connected Ising models."},{"cited_title":"Quantum critical VOLUME 4, 2016 15 Kikuchi et al.: Effectiveness of Hybrid Optimization Method for Quantum Annealing Machines dynamics in a 5,000-qubit programmable spin glass,","cited_arxiv_id":null,"evidence_quote":"Cited to justify that longer annealing time improves quantum-annealer accuracy, which is used to vary QA accuracy in the hardware experiment."}],"review_version":1}