{"id":"0ace8c9f-02f4-47d8-97ee-d8c4e2639148","arxiv_id":"2608.02041","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"For the tested Max-3-SAT instances, the native PUBO encoding beats the quadratized QUBO encoding, and simulated annealing matches or outperforms DMRG everywhere.","lead":"Researchers compared two ways of encoding Max-3-SAT problems into physics models, then solved them with tensor-network and simulated annealing algorithms. They found the quadratic encoding performs much worse than the native higher-order encoding, and classical annealing wins on both speed and accuracy.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Quadrization-harmfulness conclusion rests on a single LSR parameter point (p=1); without testing other p values or quadratisation methods, the claim is not robust.","rationale":"The reader's weakest assumption precisely identifies the p=1 dependence, and I agree this is the most load-bearing concern. The paper's novelty is the empirical demonstration that quadratisation is not neutral and that encoding choice dominates solver behavior. If that demonstration is only valid for one parameterization of one quadratisation algorithm, the general claim is overstated. The proposed concrete test directly addresses this by checking whether the degradation persists across the quadratisation design space. Other concerns, such as the missing instance counts or reproduction link, are secondary because they affect reproducibility rather than the core inference. The reader's CONDITIONAL verdict already conditions on sensitivity analysis, so my recommendation is UNCHANGED: the concern reinforces the need for the condition, but does not move the verdict further.","tokens_in":6417,"tokens_out":4662,"duration_ms":48186,"concrete_test":"Repeat the Max-3-SAT benchmarks on the same generated instances and with the same DMRG/SA hyperparameter protocol, but vary the quadratisation: (a) LSR with p=0 and p=0.5, and (b) a structurally different quadratisation (e.g., Rosenberg reduction or Biamonte's k-body-to-2-body commuting conversion). Record the median deviation from the exact ground state for each QUBO encoding. If any variant produces deviations close to the PUBO baseline (within the PUBO interquartile range), the conclusion that quadratisation is inherently harmful is falsified. Only if all variants show the same degradation can the claim be considered robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central empirical claim that quadratisation degrades solution quality relies exclusively on the LSR algorithm with p=1 (Section IV-C). The paper itself states that p governs a trade-off: higher p minimizes auxiliary variables but yields a denser interaction graph. p=1 thus produces QUBOs with maximal connectivity among auxiliary variables, which is arguably the worst case for DMRG: high connectivity inflates MPO bond dimensions and complicates variational optimization. If p=0 (more auxiliaries, sparser graph) or an alternative quadratisation method yields QUBO deviations comparable to the PUBO baseline, the headline conclusion—'quadratisation is not a neutral transformation step'—would be an artifact of this single configuration, not a general property. The abstract and discussion generalize beyond LSR p=1, making this a load-bearing gap. No sensitivity analysis or alternative reduction is presented.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper addresses hybrid HPC/QC system design by evaluating classical tensor-network surrogates for quantum optimisation tasks. It compares two pipelines for solving Max-3-SAT: a native PUBO-to-Ising encoding and a QUBO-to-Ising encoding produced by the LSR quadratisation algorithm with parameter p=1. Both are represented as MPOs and optimised with a vanilla two-site DMRG, with simulated annealing as a classical baseline. Across random instances with 4-22 variables and 30-150 clauses, the authors measure deviation from the exact ground state and runtime over 100 randomised solver trials. The results show that the QUBO encoding leads to markedly larger median deviations that grow with instance size, while the PUBO encoding remains near zero; SA is consistently faster and at least as accurate as DMRG. The authors conclude that quadratisation is not a neutral transformation step and that surrogate selection in HPC/QC runtimes must be encoding- and instance-aware.","tokens_in":6638,"tokens_out":7239,"duration_ms":63856,"significance":"If robust, the empirical finding that quadratisation harms solution quality in tensor-network solvers would be practically important: it would caution against blind use of QUBO transformations in hybrid quantum-classical workflows and would justify encoding-aware runtime decisions. The paper is commendable for providing a reproduction package, using exact ground states for small n, and running 100 randomised trials per instance with both encodings corrected for Ising constants. The main weakness is that the generality of the conclusion rests on a single quadratisation parameter (p=1) and on unstated instance counts, which limits the strength of the claims as they currently stand.","major_comments":[{"comment":"The central claim that quadratisation degrades solution quality is based exclusively on LSR with p=1. The paper itself notes that p trades off the number of auxiliary variables against interaction-graph density; p=1 produces the densest QUBO interaction graph, which is the most unfavourable configuration for MPO bond dimensions and DMRG convergence. Without testing p=0 or intermediate values, or an independent quadratisation method, the headline conclusion may be an artifact of this parameter choice rather than a general property of quadratisation. Please add a sensitivity analysis over p (or at least p=0) and, if the degradation persists, report it; if not, restrict the conclusion to LSR p=1.","section":"Section IV-C"},{"comment":"The number of independently generated Max-3-SAT instances per (n,m) configuration is not stated. Figure 2 reports medians, interquartile ranges, and outliers, but no sample size is given. Since the empirical comparison is the core contribution, this information is essential to judge statistical reliability and reproducibility. Please specify the number of instances per configuration and, if feasible, release the instance set.","section":"Section IV-A/Figure 2"},{"comment":"The manuscript does not state whether the LSR quadratisation is exact (i.e., whether penalty terms are introduced to enforce consistency between auxiliary and original variables) or how the 'Ising constant' correction accounts for the added auxiliary variables. If the QUBO Hamiltonian admits spurious states with energies below the legal-assignment optimum, the reported deviation against the PUBO ground state is not a valid measure of solver quality. Please clarify the equivalence proof or reference and describe the correction in detail.","section":"Section IV-C/IV-E"}],"minor_comments":[{"comment":"Typo: 'DMRGs advantages dont' should read 'DMRG's advantages don't'.","section":"Abstract"},{"comment":"Grammar: 'Our notations follows' should be 'Our notation follows'.","section":"Section II"},{"comment":"The sentence 'As each additional introduced variable doubles the search space, we fix p=1 in our automated pipeline used in our experiments' is redundant; consider simplifying to 'we fix p=1'.","section":"Section IV-C"},{"comment":"The PUBO and QUBO panels use different y-axis scales (e.g., [0,2] vs [0,20]), which may visually exaggerate the difference. Please use a consistent scale or note the change in the caption.","section":"Figure 2"},{"comment":"Reference [8] is formatted as 'L. Schmidbauer et al.' with a missing space after the author name in the text; also check other references for formatting consistency.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the scope of the journal and the experimental design is thoughtful. The main barrier to acceptance is the lack of sensitivity analysis for the LSR parameter; this should be fixable with additional experiments. I would not raise concerns about novelty or citation practices."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nUseful empirical baseline, and the central negative result for DMRG on SAT-derived product states is credible. But the quadratisation-harm conclusion is overgeneralised from a single LSR parameter point, and the missing instance metadata and reproduction link need fixing before I'd trust the broader claims.\n\nWhat's new: they actually benchmark native PUBO against quadratised QUBO for Max-3-SAT under DMRG, with simulated annealing as baseline, across a range of n and m. I don't recall that exact comparison in the literature. The experimental design is decent: 100 independent trials per instance, exact ground states computed for small n, and both encodings corrected for Ising constants. The claim that SA matches or outperforms DMRG on this problem class is well supported. And the point that quadratisation changes the problem structure in ways that matter for the solver is a fair one, even if the current evidence is narrower than the abstract suggests.\n\nThe soft spots: LSR parameter p=1 is fixed without sensitivity analysis. Since higher p means fewer auxiliary variables but a denser interaction graph, p=1 is precisely the configuration most likely to inflate MPO bond dimensions and hurt DMRG. So the paper demonstrates a problem for this particular quadratisation, not for quadratisation in general. The title and abstract should say that. Also, the number of random instances per (n,m) cell is never stated—only the number of trials per instance—so the medians and whiskers in Fig. 2 lack a clearly defined sample size. And the promised reproduction package link is absent from the text I read, which is a reproducibility red flag for an empirical paper.\n\nThe reliance on the authors' own LSR method doesn't bother me—it's a published algorithm, not a result fitted to this data. The stress-test note is right, though: it's a load-bearing gap because the conclusion is stated without the caveat.\n\nWho should read this: people designing hybrid HPC/QC runtimes and anyone tempted to use DMRG for classical combinatorial optimisation. It's a serious empirical contribution that deserves peer review. I'd send it out, with a strong request for sensitivity analysis and a full instance table.","headline":"Useful empirical baseline, but the quadratisation-harm conclusion needs sensitivity analysis and metadata before the broader claims can hold.","tokens_in":7093,"tokens_out":3294,"would_cite":true,"duration_ms":32879,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that quadratisation from PUBO to QUBO is not a neutral transformation: auxiliary variables and pairwise couplings substantially degrade Max-3-SAT solution quality, while simulated annealing matches or outperforms DMRG acros","keywords":["Max-3-SAT","DMRG","tensor networks","QUBO","PUBO","quadratisation","simulated annealing","HPC/QC integration"],"falsifier":"Run the identical benchmark on the same Max-3-SAT instances using LSR with p=0 or a different quadratisation scheme; if median QUBO deviation drops to near-zero and matches PUBO, then the encoding-degradation claim fails as stated.","tokens_in":6343,"feed_emoji":"⚛️","tokens_out":3967,"duration_ms":40195,"temperature":0.7,"pith_summary":"Integrated HPC/QC systems need classical surrogates for quantum tasks, and this paper asks whether tensor-network ground-state search can serve as one for combinatorial optimisation. Using Max-3-SAT as a benchmark, it compares two compilation paths: a native higher-order Ising Hamiltonian (PUBO) and a quadratised quadratic Ising Hamiltonian (QUBO), both optimised by DMRG with simulated annealing as baseline. The paper claims that quadratisation is not a neutral step: the auxiliary variables and pairwise couplings it introduces substantially degrade solution quality and reliability relative to the native representation, while SA matches or outperforms DMRG on every tested instance. The reason offered is that SAT optima are classical product states, so DMRG's ability to capture entanglement gives no advantage here. The upshot is that surrogate selection in hybrid runtimes must be encoding- and instance-aware.","feed_headline":"Quadratisation degrades SAT quality; simulated annealing wins","feed_subtitle":"Native higher-order encoding stays near zero deviation, while quadratised form exceeds 10% on large instances; SA matches DMRG.","key_machinery":"The two-site DMRG algorithm optimises a matrix product state ansatz to minimise the energy of a matrix product operator encoded Ising Hamiltonian. The comparison hinges on two MPO constructions: one from the native degree-3 PUBO polynomial of Max-3-SAT and one from the degree-2 QUBO obtained by LSR quadratisation, which inserts auxiliary variables and pairwise couplings. The benchmark's control is a classical simulated-annealing baseline run on the same Ising models.","core_discovery":"The central discovery is that the end-to-end transformation path matters more than the solver. On uniform random Max-3-SAT instances, converting the problem to QUBO via LSR with p=1 yields median ground-state deviations that grow from below 1% to 10-15% as the variable count grows past 12, whereas the PUBO encoding keeps deviations near zero across the entire tested range. SA matches or slightly beats DMRG in the quadratic encoding, and the gap widens with instance size; DMRG never exploits entanglement because the ground states are product states. The paper concludes that representing SAT as a quadratic Ising model is a poor surrogate choice when a native higher-order Ising formulation is a","pith_inferences":["The paper does not test this, but the encoding-dependence result suggests that compiler pipelines for quantum optimisation should expose representation choice as a tunable parameter for schedulers, not as a hidden implementation detail.","A direct extension would be Max-4-SAT or weighted Max-3-SAT, where quadratisation overhead grows and might either amplify or reverse the observed gap; the paper leaves that open.","Because the tested optima are classical product states, genuinely entangled ground-state problems remain a plausible regime where DMRG's bond-dimension advantage could reappear; the paper does not establish that.","If the result transfers to other NP-hard optimisation problems, it argues for benchmarking entire transformation chains before committing HPC/QC runtimes to one encoding."],"forward_implications":["In a hybrid HPC/QC runtime, fallback and surrogate decisions should be made per encoding and per instance, not by solver type alone.","For Max-3-SAT, the native PUBO/Ising pipeline should be preferred over the quadratised QUBO pipeline when tensor-network solvers are used.","Simulated annealing, not DMRG, is the empirically better classical surrogate for this problem class.","Quadratisation overhead, not solver weakness, dominates the observed quality loss; improving DMRG implementations will not remove it."],"fun_headline_variants":["DMRG loses to annealing on SAT when quadratised","Quadratising SAT harms DMRG; annealing wins","Why DMRG fails on SAT: quadratisation's cost","Annealing beats DMRG for Max-3-SAT surrogates","Encoding choice trumps solver for SAT surrogates"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The entire QUBO-degradation conclusion rests on one quadratisation algorithm (LSR) at one parameter value (p=1); if other reductions produce better-conditioned quadratic forms, the observed gap may not be intrinsic to quadratisation.","fun_headline_variants_meta":{"raw":{"variants":["DMRG loses to annealing on SAT when quadratised","Quadratising SAT harms DMRG; annealing wins","Why DMRG fails on SAT: quadratisation's cost","Annealing beats DMRG for Max-3-SAT surrogates","Encoding choice trumps solver for SAT surrogates"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000408,"raw_usage":{"total_tokens":2007,"prompt_tokens":847,"completion_tokens":1160,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":591,"completion_tokens_details":{"reasoning_tokens":1073}},"tokens_in":591,"tokens_out":1160,"duration_ms":9725,"temperature":1.0,"reasoning_tokens":1073,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T16:09:21.751540+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the identical benchmark on the same Max-3-SAT instances using LSR with p=0 or a different quadratisation scheme; if median QUBO deviation drops to near-zero and matches PUBO, then the encoding-degradation claim fails as stated.","supporting_citations":[],"review_version":1}