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REVIEW 4 major objections 6 minor 43 references

Transfer of Knowledge through Reverse Annealing: A Preliminary Analysis of the Benefits and What to Share

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read 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…

desk verdict 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. read the letter →

arxiv 2501.15865 v2 pith:SB743QWQ submitted 2025-01-27 quant-ph cs.AIcs.ET

Eneko Osaba , Esther Villar-Rodriguez This is my paper · ORCID
classification quant-phcs.AIcs.ET
keywords QuantumAnnealingReverseD-WaveOptimizationTransferHammingdistanceKnapsackProblem
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

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

  • 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.

Reading between the lines

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

  • 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.
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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

4 major / 6 minor

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.

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 (4)
  1. [Section 3.2, Figures 1b and 2b, Table 1] 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.
  2. [Section 3.1, RA schedule selection] 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.
  3. [General statistical support, Table 2 and Figures 1-2] 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.
  4. [Section 2 and Table 1, slack variables in Hamming distance] 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.
minor comments (6)
  1. [Introduction, RQ2 phrasing] 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.
  2. [Table 2 caption] 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.
  3. [Section 2, Eq. (1)] 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.
  4. [Figures 1 and 2] 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.
  5. [Section 3.2, ref. (37)] 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.
  6. [Throughout] 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.

Circularity Check

1 steps flagged · score 2.0 of 10

No definitional circularity; small leakage from tuning the RA schedule on the same target instances used to claim RA benefit.

  1. fitted input called prediction [Section 3.1, reverse-annealing schedule selection (paragraph before Table 2)]
    "A fixed RA schedule has been used for all the tests, [(0.0, 1.0), (2.5, 0.5), (102.5, 0.5), (102.75, 1.0)], which has been obtained through an empirical procedure performed in lab. More precisely, an experimentation was carried out in which 25 different RA schedule were tested. ... each one was used to solve the two target-instance 10 times each, using one random solution for the problem as input. The aforementioned schedule was selected due to its superior performance compared to the others."

    The RA schedule is a control parameter fitted by maximizing performance on the two target instances that are subsequently used in Table 2 to conclude that knowledge transfer through RA is promising. The favorable comparison of RA with forward annealing is therefore not fully independent: the schedule was selected because it performed well on those exact instances. This does not invalidate the internal RQ2 ranking across sources under one fixed schedule, and it does not force the Hamming-distance result by construction, so the circularity is limited and partial.

full rationale

The paper contains no mathematical derivation in which a quantity is defined in terms of the target result, and no fitted model is used to generate the RQ2 conclusion. The Hamming-distance result is an empirical correlation measured on D-Wave hardware; Hamming distance is not defined in terms of RA success, so no self-definitional reduction is present. The only mild circularity/leakage is the RA-schedule selection: 25 schedules were tested on the same two target instances and the best one was then used to produce the RQ1 evidence, making the RA-versus-forward comparison partly an artifact of tuning. The self-citation (ref. 26) is used only to name source/target tasks and is not load-bearing. The confound between Hamming distance and the descendant-instance modification percentage (X) is a validity threat but not a circularity, because the paper never equates the two by construction. Overall, the central empirical claims retain independent content, so the score is low.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The experimental claims rest on a handful of practical assumptions: the QUBO is correct, the D-Wave results are representative, Hamming distance is the right similarity measure, and the tuned RA schedule is fair across all inputs. There are no discovered entities, and the only tuned quantity is the RA schedule; the QUBO penalty weight is an unstated parameter.

free parameters (3)
  • Reverse annealing schedule (sp, t1, t2, T) = sp=0.5, t1=2.5, t2=102.5, T=102.75 (in the schedule coordinate units)
    Selected empirically as the best among 25 tested schedules using the target instances s14 and s16 (Section 3.1); a fixed schedule is then used for all RA runs.
  • QUBO penalty coefficient for knapsack capacity constraint = Not stated (Qiskit Knapsack default)
    The QUBO is generated with Qiskit's Knapsack class but the penalty weight is not reported; it changes the energy landscape and therefore affects which bitstrings are low-energy.
  • Instance-generation random values (v, w in {1,2,3,4}) = Not fixed; no seed reported
    Parent instances are generated ad hoc with profits and weights randomly drawn from {1,2,3,4}; the choice of distribution and absence of a seed makes exact reproduction of the instances dependent on the authors' dataset rather than the description.
assumptions (4)
  • domain assumption The QUBO formulation of the knapsack problem used by Qiskit correctly encodes the optimization objective and capacity constraint.
    The paper relies on the correctness of the QUBO generated by Qiskit v0.6.0 without re-deriving or testing the encoding (Section 3).
  • domain assumption D-Wave Advantage 6.4 samples are high enough quality that the best solution found over 10 forward-annealing runs is a meaningful reference solution for both ancestor and descendant instances.
    The entire transfer experiment treats the best forward-annealing solution as the 'knowledge' to transfer and as the baseline for comparison; if these solutions are noisy or not representative, the conclusions about RA improvement do not hold (Section 3).
  • ad hoc to paper Hamming distance is an appropriate and sufficient measure of solution similarity for reverse annealing.
    The paper chooses Hamming distance for its simplicity and uses it to draw the main conclusion in RQ2, but this is an assumption embedded in the analysis rather than a derived or validated metric for RA (Section 3.2).
  • ad hoc to paper The fixed RA schedule, tuned on the target instances, remains appropriate for all source-target combinations.
    The schedule was selected once using the target instances and random inputs, but no sensitivity analysis is provided to show it does not bias performance for particular source inputs (Section 3.1).

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Cite this review

Pith. "Pith review of Transfer of Knowledge through Reverse Annealing: A Preliminary Analysis of the Benefits and What to Share." pith.science (2026). https://pith.science/paper/SB743QWQ

@misc{pith2026250115865,
  author       = {Pith},
  title        = {Pith review of: Transfer of Knowledge through Reverse Annealing: A Preliminary Analysis of the Benefits and What to Share},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SB743QWQ}},
  note         = {Machine review of arXiv:2501.15865}
}
read the original abstract

Being immersed in the NISQ-era, current quantum annealers present limitations for solving optimization problems efficiently. To mitigate these limitations, D-Wave Systems developed a mechanism called Reverse Annealing, a specific type of quantum annealing designed to perform local refinement of good states found elsewhere. Despite the research activity around Reverse Annealing, none has theorized about the possible benefits related to the transfer of knowledge under this paradigm. This work moves in that direction and is driven by experimentation focused on answering two key research questions: i) is reverse annealing a paradigm that can benefit from knowledge transfer between similar problems? and ii) can we infer the characteristics that an input solution should meet to help increase the probability of success? To properly guide the tests in this paper, the well-known Knapsack Problem has been chosen for benchmarking purposes, using a total of 34 instances composed of 14 and 16 items.

Figures

Figures reproduced from arXiv: 2501.15865 by the authors.

Figure 1
Figure 1. Results related to the resolution of s14 using as input the best solution found for each descendant￾instance over 10 independent runs. The blue colored boxplots represent the baseline results obtained through forward annealing. The less the energy value, the better the solution. Regarding s16 0.6 L2H, its performance has proven to be poor even being near the reference solution (-10709 vs. -10716, +7). Finally, the o… view at source ↗
Figure 2
Figure 2. Results related to the resolution of s16 using as input the best solution found for each descendant￾instance over 10 independent runs. The blue colored boxplots represent the baseline results obtained through forward annealing. The less the energy value, the better the solution. Furthermore, conclusions related to RQ2 are also coherent with the work proposed in (10). That paper is focused on a specific kind of quant… view at source ↗

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