{"id":"56d34d88-4998-4a37-96f6-7068169308f0","arxiv_id":"2501.15865","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Reverse annealing benefits from reusing solutions of similar knapsack instances, and Hamming distance to the target solution predicts success better than energy difference.","lead":"This paper tests whether a reverse quantum annealer can solve a new optimization problem by reusing the best solution from a similar, already solved problem. The authors report initial evidence that this knowledge transfer works on small knapsack instances, with the number of differing bits between solutions as the main success factor.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The RQ2 conclusion that Hamming distance—not energy—drives reverse-annealing success is not de-confounded from the descendant-instance construction variables (X and modification direction), so the claimed 'only Hamming distance' result is over-stated.","rationale":"The reader's weakest-assumption analysis identifies the same load-bearing concern that I do: the descendant-instance construction confounds Hamming distance with X and modification direction, and the paper does not de-correlate these factors before drawing the categorical RQ2 conclusion. This concern is central because the paper's strongest claim is precisely that Hamming distance is the relevant selection metric and energy closeness is irrelevant. If the observed Hamming trend is actually a proxy for how much the source instance was modified, then the 'what to share' guidance collapses. The paper is honest about being preliminary and provides open data, which is a real positive, but the evidence as presented supports only a tentative association, not the strong 'only Hamming distance' statement in Sections 3.2 and 4. Since the reader already issued a CONDITIONAL verdict for essentially this reason, my analysis does not move the verdict; it reinforces the need for the stated condition: de-confounding or a softened conclusion.","tokens_in":11634,"tokens_out":4300,"duration_ms":46708,"concrete_test":"Re-analyze the archived Mendeley dataset by computing partial Spearman correlations between RA success (best energy, mean energy, or probability of matching the optimal solution) and both Hamming distance and energy difference, controlling for X and modification direction (L2L, L2H, H2L, H2H). If the Hamming-distance correlation loses significance once X and direction are controlled, while energy difference remains insignificant, the RQ2 claim must be weakened. As a complementary check, generate additional descendant instances with fixed X but systematically varied Hamming distances; if performance no longer tracks Hamming distance within a fixed X, the claimed causal role of Hamming distance is not supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3.2's categorical conclusion that 'only the closeness with respect to the Hamming distance is [related]' rests on an uncontrolled observational comparison. The descendant-instance generator described in Section 2 varies the percentage X of modified items and the direction of the energy modification (L2L, L2H, H2L, H2H). Both variables plausibly determine how far the descendant optimum lies from the parent optimum, and they are correlated with the measured Hamming distance h in Table 1: changing more items tends to produce larger Hamming distances, and the direction of energy change affects which solutions become optimal. With only 16 source instances per target, no partial-correlation or multivariate analysis is presented, so the apparent trend in Figures 1b and 2b could be driven by X or by the specific way items were modified, rather than by bitstring overlap per se. The conclusion in Section 4 that 'the neighborhood must be based on solution codification and not energy' is therefore not yet established by the data; the evidence is consistent with Hamming distance being a proxy for the degree of instance modification rather than the causal selection criterion.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper experimentally investigates whether reverse annealing (RA) on a D-Wave quantum annealer can benefit from transferring solutions from similar but distinct knapsack problem instances (RQ1), and what characteristics of the input solution determine success (RQ2). Two parent instances of 14 and 16 items are used, each accompanied by 16 descendant instances generated by modifying a fraction X of item profits/weights in four energy-direction categories. RA is applied with the best descendant solutions as initial states, and results are compared with forward annealing under equal annealing time. The paper reports that RA with transferred knowledge improves robustness and, for the larger instance, optimality, and concludes that performance is driven by Hamming distance between source and target solutions rather than by energy closeness.","tokens_in":11918,"tokens_out":4866,"duration_ms":44423,"significance":"If the conclusions hold, the work would offer a practical guideline for warm-starting quantum annealers: use solutions from neighboring instances and select them by bitstring overlap rather than by energy. The paper is among the first to address knowledge transfer for reverse annealing and makes its dataset openly available. The study is explicitly preliminary, based on very small instances (14 and 16 items) and a limited number of runs, but the research questions are relevant to the quantum annealing community and the experimental design is systematic, with clearly described instance generation and a fixed RA schedule. The main claims are, however, stated more strongly than the evidence supports, primarily because the observed Hamming-distance trend is not de-confounded from the instance-generation variables.","major_comments":[{"comment":"The conclusion that \"only the closeness with respect to the Hamming distance is [related]\" to RA performance is confounded. The descendant-instance construction in Section 2 simultaneously varies the percentage X of modified items and the direction of energy modification (L2L, L2H, H2L, H2H); both variables plausibly influence the location of the descendant optimum and are correlated with the measured Hamming distance h. The paper presents no partial correlation, multivariate analysis, or stratification that would separate the effect of h from these construction variables, so the apparent trend could be driven by X or by the direction of modification rather than by bitstring overlap per se. For example, in Table 2, s160.2H2H (h=12) achieves a best energy of -10714 while s160.4H2L (h=8) achieves -10716, so h alone does not cleanly separate the outcomes. The authors should de-confound these variables (for instance, by stratifying the data by X and direction, or by reporting partial correlations) before claiming causal or exclusive relevance of Hamming distance.","section":"Section 3.2, Figures 1b and 2b, Table 1"},{"comment":"The RA schedule used in all experiments was selected as the best among 25 schedules tested on the same two target instances (s14 and s16), each solved 10 times with a random input. This selection bias can inflate the performance of RA relative to the forward-annealing baseline, which uses a standard schedule without similar tuning. The comparison in Table 2 may therefore overstate the benefit of knowledge transfer. The authors should either choose the schedule on a hold-out set, report the spread of results across the 25 schedules, or demonstrate that the selected schedule is not anomalously favorable to the targets.","section":"Section 3.1, RA schedule selection"},{"comment":"All conclusions rest on 10 independent runs per condition and only 16 source instances per target, with no significance tests, confidence intervals, or effect sizes. The \"clear trend\" in Hamming distance is assessed visually from boxplots. For claims as strong as those in Section 4 (\"only the closeness with respect to the Hamming distance is\"), the authors should provide quantitative evidence, such as correlation coefficients, significance tests, or at least a scatter plot with a fitted trend line and its uncertainty. Without this, the strength of the conclusions is not statistically justified.","section":"General statistical support, Table 2 and Figures 1-2"},{"comment":"The Hamming distance h used in the RQ2 analysis includes contributions from slack variables (sh), but the descendant-instance construction modifies only the first n items; the slack variables are artifacts of the QUBO mapping and the solver, not of the intended instance similarity. Table 1 shows that sh varies across descendants (e.g., s160.2L2L has sh=2 while s160.8L2H has sh=3). Since the construction does not control slack bits, the reported correlation between total h and RA performance may be partly driven by solver-dependent slack differences rather than by meaningful overlap in the item decisions. The authors should repeat the analysis using only the item Hamming distance nh, or provide a justification for including slacks.","section":"Section 2 and Table 1, slack variables in Hamming distance"}],"minor_comments":[{"comment":"The phrase \"probability of succeeding in a RA process\" is imprecise; in the experiments it is operationalized as the best energy found over 10 runs, not as a probability of reaching the optimum. Please clarify the success metric.","section":"Introduction, RQ2 phrasing"},{"comment":"The optimal results are reported as positive numbers (12422 and 10718), while all energies in the table are negative. This sign inversion is confusing; please state explicitly that energies are minimized or use a consistent sign convention.","section":"Table 2 caption"},{"comment":"The notation H0 and H1 is introduced, but the role of the initial Hamiltonian in the reverse-annealing process is not explained; a brief description of how the initial state is encoded as an eigenstate of H1 would help the reader.","section":"Section 2, Eq. (1)"},{"comment":"The boxplots mentioned in the text are not displayed in the manuscript version; ensure that the figures are reproducible and that the captions fully explain the color scheme, the meaning of \"baseline,\" and the exact quantity plotted on the x-axis.","section":"Figures 1 and 2"},{"comment":"The connection to partial overlap in the unified search space is relevant, but the authors do not cite any work that specifically uses Hamming distance as a similarity metric in transfer optimization; adding such a reference would strengthen the argument.","section":"Section 3.2, ref. (37)"},{"comment":"There are several typos and grammar issues, including \"permiting\" in Section 2, \"st.\" for standard deviation in Table 2's header, and inconsistent spacing in author initial. A thorough proofread is needed.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The paper addresses a genuine and timely question for quantum annealing, and the authors are commendably transparent about the preliminary nature of the study and about their data availability. My main reservation is that the two central conclusions (knowledge transfer helps, and Hamming distance is the sole predictor of RA success) are stated too strongly for the scale and design of the experiments. The Hamming-distance conclusion is particularly vulnerable because of the unaddressed confounding with the descendant-instance construction variables. These issues are fixable with additional analysis rather than requiring new hardware experiments, so I see this as a major revision rather than a rejection. I would also encourage the editor to weigh whether the journal's standards expect statistical rigor for empirical claims of this strength; the current manuscript may be better suited as a preliminary report if the statistical concerns are not fully resolved."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is a preliminary empirical study of whether reverse annealing on a D-Wave machine can use the optimal solution of one knapsack instance to warm-start a similar instance, and what property of the input matters. The headline is that the paper is genuinely new in testing cross-instance transfer in RA, but its main categorical conclusion about Hamming distance is not actually de-confounded from how the instances were built.\n\nWhat's new: it is the first systematic test of transfer between different problem instances under reverse annealing. The dataset and results are openly available, the two research questions are clear, and the framing is honestly preliminary. The practical angle is useful: if the effect is real, it gives a simple rule (pick the input whose bitstring is closest in Hamming distance to the target optimum) for warm-starting industrial QA tasks.\n\nWhat's good: the experiment is transparent and reproducible, and the hypothesis that Hamming distance matters more than energy is worth testing. The paper also connects to the classical transfer-optimization literature, which is appropriate.\n\nWhere it's soft: (1) only 34 tiny instances, 10 runs per condition, and no statistical tests, so the apparent trends in Figures 1 and 2 are largely eyeballed; (2) the RA schedule was selected as the best of 25 schedules tested on the same target instances, while the forward-annealing baseline was not tuned this way. That asymmetry can inflate RA's apparent advantage independently of knowledge transfer; (3) the RQ2 conclusion is the weakest part. Descendant instances vary in the percentage X of modified items and the direction of energy change, and both variables are correlated with Hamming distance. In fact, X is a direct determinant of how much the instance is modified, so the observation that RA does better when Hamming distance is small could simply mean that less-modified instances are easier, not that Hamming distance itself is the causal selection criterion. The paper's conclusion says \"only\" Hamming distance matters, which is too strong for this data.\n\nThe stress-test note lands. The RQ1 direction is plausible and worth pursuing, but the evidence does not support the categorical RQ2 claim. A same-instance RA control (warm start with the parent's own best solution) is missing, and that is needed to separate the benefit of transfer from the benefit of RA itself.\n\nWho this is for: practitioners using D-Wave for recurring optimization problems and researchers in transfer optimization for quantum algorithms. It is not a theory paper; it is a preliminary empirical report. A serious referee should engage because the question is important and the data are open, but the paper needs substantial revision before the central claims are accepted.\n\nMy recommendation: send to peer review with the expectation of major revision. The core experiment is worth repeating with more instances, proper controls, and at least basic significance testing.","headline":"A genuinely new but statistically thin empirical study of cross-instance transfer in reverse annealing; the Hamming-distance conclusion is over-stated because it is confounded with the instance-generation variables.","tokens_in":12378,"tokens_out":3325,"would_cite":false,"duration_ms":34453,"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":"This paper claims that reverse annealing on a quantum annealer is a viable mechanism for transferring knowledge between similar optimization problems, and that a transferred solution helps precisely when it is close to the target optimum…","keywords":["Quantum Annealing","Reverse Annealing","D-Wave","Quantum Optimization","Transfer Optimization","Hamming distance","Knapsack Problem"],"falsifier":"A control experiment would fix one target instance and feed reverse annealing two input bitstrings with identical Hamming distance from the target optimum but very different energies, plus two with identical energy but different Hamming distances; if performance tracks energy rather than Hamming distance in either comparison, the paper's claim breaks.","tokens_in":11429,"feed_emoji":"🔁","tokens_out":7083,"duration_ms":61391,"temperature":0.7,"pith_summary":"The paper asks whether reverse annealing, a quantum-annealing schedule that starts from a supplied solution and refines it locally, can reuse a solution found for one optimization problem when solving a similar but different problem. It answers yes, based on experiments on small knapsack instances: feeding the annealer a solution from a neighboring instance matches or improves on forward annealing, and markedly stabilizes the results. The paper also asks what makes a transferred solution useful, and concludes that the deciding property is Hamming distance to the target's optimum, not energy closeness. This matters because in industrial settings problems recur with small variations, so reusing previous solutions could save quantum resources and improve reliability.","feed_headline":"Hamming closeness, not energy, predicts reverse-annealing success","feed_subtitle":"Warm-starting a quantum annealer with a similar problem's solution works when the bitstrings overlap.","key_machinery":"The machinery is reverse annealing with a piecewise-linear schedule: the annealer runs backward to a pause point, then quenches forward, so the evolution starts from a supplied classical bitstring and explores its local neighborhood. The paper pairs this with a transfer experiment design: each descendant instance is created by changing a percentage X of the parent's items (X = 0.2 to 0.8) in one of four energy directions (low-to-low, low-to-high, high-to-low, high-to-high). The quantity that carries the argument is the Hamming distance h, the number of differing bits between the source solution and the target optimum, decomposed into item bits and slack bits, which is used to rank the transferred solutions against measured reverse-annealing performance.","core_discovery":"The paper's central claim is that the closeness that matters for reverse annealing is closeness in the solution bitstring, not in objective value. In the authors' experiments, a descendant knapsack instance's best solution, when used as the input state for reverse annealing on the parent instance, performs well when its Hamming distance to the parent's optimum is small, and poorly when that distance grows; source solutions that are energy-close but Hamming-distant do not reliably help. The paper states this directly: 'the closeness in terms of energy is not related to the performance of RA, and only the closeness with respect to the Hamming distance is.' The intended practical reading is that transfer of knowledge between similar quantum-optimization tasks works, and the right criterion for choosing what to transfer is overlap of the encoded bitstrings.","pith_inferences":["Editorial extension: the Hamming-distance result suggests a practical pre-filter for transfer pipelines: before spending annealer time, estimate the bitstring overlap between each candidate source solution and a cheap classical approximation of the target optimum, and feed reverse annealing only the sources with the largest overlap.","Editorial extension: the paper's own observation that iterative biased quantum annealing sees a reduced Hamming-distance effect on large instances implies the same attenuation may appear for reverse annealing as instance sizes grow; this is a testable prediction rather than something the experiments here support.","Editorial extension: if the Hamming-distance rule transfers beyond knapsack, the same principle could organize warm-started QAOA or other warm-start quantum heuristics, where the initial circuit state is also judged by state overlap; this is a cross-paradigm conjecture, not the paper's claim."],"forward_implications":["Warm-starting a quantum annealer with a solution from a previously solved, similar instance is a workable knowledge-transfer strategy, and for the harder 16-item target it improved the probability of finding the optimum relative to forward annealing.","When building this kind of transfer, practitioners should rank candidate source solutions by bitstring overlap with the target's optimum, not by their energy gap, because Hamming distance is the observable that tracks reverse-annealing success.","Problem encoding becomes part of the transfer strategy: solutions should be coded so that similar problems live close to one another in a unified search space, since the refinement neighborhood is defined by solution codification.","In repetitive real-world settings with a pool of past solutions, reverse annealing can act as a low-cost refinement of a previously known good state, reducing the need to solve each new instance from scratch with forward annealing."],"supporting_citations":[{"why":"defines reverse annealing and its local-refinement mechanism, the central object under study","marker":"[15]"},{"why":"supplies the reverse-annealing schedule formulation and parameterization used to fix the schedule","marker":"[18]"},{"why":"introduces transfer optimization and knowledge reuse between similar tasks, framing research question 1","marker":"[20]"},{"why":"represents the energy-based interpretation of a good initial state that the paper tests and rejects","marker":"[24]"},{"why":"proposes Hamming distance as the relevant closeness measure, contradicting energy-based views and supporting the paper's conclusion","marker":"[25]"},{"why":"shows that biased quantum annealing depends on Hamming distance between driver and ground state, lending coherence to the RQ2 result","marker":"[10]"},{"why":"defines problem similarity as overlap of energy landscapes in a unified search space, used to justify the transfer setup","marker":"[36]"},{"why":"supplies the partial-overlap condition on optima in transfer optimization, which the Hamming-distance result echoes","marker":"[37]"}],"fun_headline_variants":["Reverse annealing: bitstring overlap, not energy, predicts success","Share solutions, not energies, for reverse annealing transfer","Hamming distance rules reverse annealing knowledge transfer","Quantum annealing transfer: choose bitstring closeness","Reverse annealing benefits from Hamming-close warm starts"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The conclusion that Hamming distance, and not energy, drives reverse-annealing success assumes that the descendant-instance construction does not confound Hamming distance with the percentage of modified items or the direction of their energy change, since those variables rise together.","fun_headline_variants_meta":{"raw":{"variants":["Reverse annealing: bitstring overlap, not energy, predicts success","Share solutions, not energies, for reverse annealing transfer","Hamming distance rules reverse annealing knowledge transfer","Quantum annealing transfer: choose bitstring closeness","Reverse annealing benefits from Hamming-close warm starts"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000153,"raw_usage":{"total_tokens":1166,"prompt_tokens":860,"completion_tokens":306,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":476,"completion_tokens_details":{"reasoning_tokens":233}},"tokens_in":476,"tokens_out":306,"duration_ms":3566,"temperature":1.0,"reasoning_tokens":233,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T13:49:55.151039+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A control experiment would fix one target instance and feed reverse annealing two input bitstrings with identical Hamming distance from the target optimum but very different energies, plus two with identical energy but different Hamming distances; if performance tracks energy rather than Hamming distance in either comparison, the paper's claim breaks.","supporting_citations":[{"cited_title":"Reverse annealing for the fully connected p-spin model","cited_arxiv_id":null,"evidence_quote":"defines reverse annealing and its local-refinement mechanism, the central object under study"},{"cited_title":"Warm-started qaoa with custom mixers provably converges and computationally beats goemans-williamson's max-cut at low circuit depths","cited_arxiv_id":null,"evidence_quote":"supplies the reverse-annealing schedule formulation and parameterization used to fix the schedule"},{"cited_title":"Travel time optimization on multi-agv routing by reverse annealing","cited_arxiv_id":null,"evidence_quote":"introduces transfer optimization and knowledge reuse between similar tasks, framing research question 1"},{"cited_title":"Insights on transfer optimization: Because experience is the best teacher","cited_arxiv_id":null,"evidence_quote":"represents the energy-based interpretation of a good initial state that the paper tests and rejects"},{"cited_title":"Initial state encoding via reverse quantum annealing and h-gain features","cited_arxiv_id":null,"evidence_quote":"proposes Hamming distance as the relevant closeness measure, contradicting energy-based views and supporting the paper's conclusion"},{"cited_title":"Adiabatic Quantum Optimization Fails to Solve the Knapsack Problem","cited_arxiv_id":"2008.07456","evidence_quote":"defines problem similarity as overlap of energy landscapes in a unified search space, used to justify the transfer setup"},{"cited_title":"Quantum optimization heuristics with an application to knapsack problems","cited_arxiv_id":null,"evidence_quote":"supplies the partial-overlap condition on optima in transfer optimization, which the Hamming-distance result echoes"}],"review_version":1}