{"id":"636a8e34-d24b-4a78-a9d0-cc9cb110d09f","arxiv_id":"2510.14533","paper_version":2,"verdict":"REJECT","confidence":"LOW","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"Abstract claims zero-shot 5-to-10-city EQC transfer beats target-size training only in exact simulation, degrading by 31.3% under sampling noise and 45.3% on hardware; the supplied body omits these experiments.","lead":"This preprint's abstract reports end-to-end measurements of zero-shot cross-size transfer for equivariant quantum reinforcement-learning policies on TSP, finding finite-shot and hardware barriers. The supplied full text, however, is a different paper on a theoretical transfer bound with state-vector simulations, and contains none of the abstract's hardware or MPS results.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Assumption (A2) is not satisfied by the paper's online QRL training loop, so the G_n term in Theorem 1 is not a valid bound; without G_n, the transfer lower bound and the claimed diagnostic barrier are unproven.","rationale":"The reader's weakest_assumption identifies A2 as the load-bearing bridge, and I agree. The transfer bound has three terms: empirical source performance, generalization error G_n, and transfer penalty D. Only G_n connects the measured training reward to the true source performance; if the QRL episode stream is not i.i.d. or if the mixing time is unknown, the probabilistic guarantee collapses. This is a correctness risk, not a disagreement with consensus: even under the authors' assumptions about D, Theorem 1 is unproven. The abstract/body mismatch (hardware, MPS, 31.3%/45.3%, n^{-2.1}) is also a serious missing-support objection, but the A2 flaw is technical and independently load-bearing; it would invalidate the theoretical vehicle even if the missing experiments were supplied. Therefore the existing REJECT verdict is appropriate; I do not adjust it.","tokens_in":25247,"tokens_out":12129,"duration_ms":108959,"concrete_test":"Inspect the training code/algorithm block used in Section 5.1 and count the number of distinct source instances and the policy-update schedule. If episodes are produced on a single graph with an evolving epsilon-greedy policy, then A2-i and A2-ii are inapplicable; estimate the beta-mixing coefficient tau_beta of the return sequence (or use a delayed online-to-PAC conversion) and recompute G_n. If tau_beta is unestimated or the resulting G_n is substantially larger than reported, Theorem 1 cannot be instantiated and the validation in Section 5.3/Appendix G does not test the stated bound.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The transfer bound rests on Assumption (A2) in Appendix C, which maps Schatzki et al.'s supervised, i.i.d. QML generalization theorem onto QRL training. Three options are offered: (A2-i) fresh i.i.d. instances with a fixed exploratory policy; (A2-ii) i.i.d. per-instance averages from a finite pool; (A2-iii) beta-mixing with mixing time tau_beta. The manuscript never establishes that the actual training loop falls into any of these regimes. Section 5.1 describes training on a graph with epsilon decay; if episodes are generated on a single fixed instance while the policy updates, the return sequence is neither i.i.d. nor stationary, so (A2-i) and (A2-ii) do not apply. (A2-iii) would require an estimate of tau_beta, and none is provided. Since G_n(delta) is the only term separating empirical source performance P-hat_n from true source performance P_n, Theorem 1's P_m(theta*_n) >= P-hat_n - G_n(delta) - D_{n->m} has no proven foundation. The abstract's 'conditional diagnostic bound' is therefore not established by the supplied text.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a theoretical framework for zero-shot cross-size transfer of equivariant quantum circuits (EQCs) used as reinforcement-learning policies for the Traveling Salesman Problem. It derives a lower bound P_m(θ*_n) ≥ P̂_n(θ*_n) − G_n(δ) − D_{n→m}, where G_n is a source-task generalization term adapted from Schatzki et al. and D_{n→m} is a task-dissimilarity penalty decomposed into a parametric-mismatch term and a structural term based on the Beardwood–Halton–Hammersley theorem. Empirically, the body reports state-vector simulations on 4- to 15-city Euclidean TSPs, comparing a permutation-equivariant circuit against an Efficient SU(2) circuit and claiming that the equivariant architecture transfers better and that fine-tuning improves performance. The arXiv abstract, however, claims additional results: finite-shot execution inflates the transfer gap from ~5% to 31.3% from sampling noise and to 45.3% on hardware, action margins collapse as n^{-2.1}, a four-vendor hardware campaign was performed, and MPS bond-dimension truncation destroys policy quality. None of these abstract-level claims appear in the supplied full text.","tokens_in":25558,"tokens_out":3091,"duration_ms":30417,"significance":"If the abstract's claims were supported, the paper would provide a valuable diagnostic standard for evaluating whether equivariant QRL policies retain cross-size transfer under realistic execution, with quantitative finite-shot and hardware penalties. The theoretical decomposition into a generalization term and a transfer-penalty term is a useful conceptual contribution, and extending permutation-equivariant QML generalization bounds to a cross-size transfer setting is a reasonable research direction. However, the significance as presented is substantially undermined: the quantitative empirical claims in the abstract are not present in the body, and the central theorem relies on assumptions that are not satisfied by the described training protocol and on constants that are fitted to the same data used for validation. The manuscript does not ship code or datasets, so the claimed empirical results are not independently checkable.","major_comments":[{"comment":"The abstract states that finite-shot execution inflates the transfer gap from ~5% to 31.3% (sampling noise) and 45.3% (hardware), that action margins collapse as n^{-2.1}, that a four-vendor hardware campaign confirms the penalty is set by native two-qubit gate count, and that MPS bond-dimension truncation destroys policy quality. Section 5.1 describes only state-vector simulation on graphs with n∈{4,6,8,10,12,15}; no finite-shot execution, no hardware runs, no MPS results, and no shot-count analysis appear anywhere in the supplied full text. These are the central quantitative claims of the abstract, and they are unsupported by the manuscript body.","section":"Abstract vs. §5"},{"comment":"Theorem 1's G_n(δ) is inherited from Schatzki et al.'s supervised generalization theorem, but the manuscript does not establish that the QRL training loop satisfies any of the three regimes in (A2). Section 5.1 trains on graphs with epsilon decay and online updates; episodes are not fresh i.i.d. instances from a fixed exploratory policy, and the finite-pool replay option is not described in the experiments. Option (A2-iii) would require an estimate of the mixing time τ_β, and none is provided. Since G_n is the only term separating empirical from true source performance, the lower bound in Theorem 1 has no proven foundation for the actual training procedure.","section":"Appendix C, Assumption (A2); Theorem 1"},{"comment":"The validation of the theoretical bound is circular. The coefficient of the parametric term is consolidated into an empirically measured strength α_n 'for a given source model' (G.1.1), and the structural constant C' is estimated from the experimental normalization constants (G.1.2). Figure 3 then shows data lying above a bound that uses these fitted constants. A bound whose constants are fitted to the data it purports to validate does not provide independent evidence for the bound; this is a load-bearing issue because the empirical validation is the main support for the transfer-penalty decomposition.","section":"Appendix G.1.1, G.1.2; Figure 3; §5.3"},{"comment":"The structural term D_{n→m}^{(struct)} ≤ C'(m−n)/√n is used as a deterministic-looking bound, but the text itself states that the Beardwood–Halton–Hammersley theorem makes no formal statement for finite k and that the non-asymptotic bound is 'conjectured' (Appendix C, A6). The derivation in Appendix E then treats this conjecture as an established inequality. For the small sizes n,m∈{4,...,15} used in the experiments, asymptotic BHH scaling is not a demonstrated guarantee, and the affine rescaling with fixed L_max and L_opt introduces additional finite-size issues. This makes the structural component of D_{n→m} unproven.","section":"Assumption (A6)/(A7-4); Appendix C, Appendix E"},{"comment":"The body claims that zero-shot transfer beats target-size training in 'all six evaluations' per the abstract, but the results section does not report quantitative comparisons against the 'Training from Scratch' baseline. It shows equivariant vs. Efficient SU(2) tour costs and mentions a classical baseline, but there is no table or plot of scratch-trained target-size policies. The stated advantage over target-size training is therefore not supported by the reported data.","section":"§5.2; Figure 2"}],"minor_comments":[{"comment":"The definition of G_n(δ) uses the notation T_en+1 without redefining it; it is earlier defined in Appendix A as T_en+1 = \\binom{n+3}{3}. Also the displayed formula has a formatting artifact ('s' before the square-root terms) that should be corrected.","section":"§3.4"},{"comment":"The subsection title 'Prook Sketch' is a typo for 'Proof Sketch.'","section":"Appendix A.3"},{"comment":"Figure 2 is described as comparing transfer performance, but the caption lacks axis labels, units, and error-bar definitions; the classical baseline is referred to as 'e.g., a greedy or MST-based solver' without specifying which one.","section":"§5.2, Figure 2"},{"comment":"The contribution list says 'zero-shot five-to-ten-city transfer beats target-size training in all six evaluations,' but this claim is not in the body's experimental section and should be either stated with data or removed.","section":"§1, Contributions"},{"comment":"The limitation paragraph correctly admits that the constants in D_{n→m} 'remain abstract,' but this conflicts with the stronger validation language in §5.3; the authors should reconcile these statements.","section":"§6.1"},{"comment":"Reference [9] is a preprint by the same authors on capacitated vehicle routing that is not cited in the text; please check whether it is needed.","section":"References"}],"recommendation":"reject","confidential_remarks":"The supplied manuscript appears to be internally inconsistent: the arXiv abstract advertises finite-shot, hardware, MPS, and four-vendor results that the full text does not contain. Even if the abstract were disregarded, the central theorem's proof depends on an unsatisfied generalization assumption and a transfer-penalty coefficient fitted to the data used for validation. These are not merely presentation issues, and they cannot be fixed without substantial new proof and experimental reporting. I would encourage the authors to resubmit a revised version that either matches the abstract with complete supporting data or narrows the claims to the theoretical and state-vector results, with a rigorous treatment of the assumptions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe first thing you should know: the abstract and the supplied full text do not describe the same work. The abstract promises an end-to-end hardware and shot-noise diagnostic — 31.3% sampling gap, 45.3% hardware gap, n^{-2.1} margin collapse, four hardware vendors. The full text is a state-vector simulation study that derives a transfer bound and reports no hardware results, no shot-noise analysis, no MPS experiments, and no vendor campaign. Nothing in the text supports the abstract's quantitative claims. If the arXiv metadata is meant to be accurate, that is a desk-reject-level mismatch.\n\nOn the body's own merits, there is something worth engaging with. Extending Schatzki et al.'s single-task generalization bound to zero-shot cross-size transfer by adding a task dissimilarity term D_{n→m} is a legitimate extension. The decomposition into parametric mismatch (from rescaling generators 1/n to 1/m) and structural shift (via the Beardwood–Halton–Hammersley asymptotics) is sensible. The empirical comparison of equivariant versus Efficient SU(2) transfer shows the expected advantage for symmetry, and the MPS/MPO scalability discussion in Appendix H is honest and useful.\n\nThe soft spots are substantial, though. The stress-test note lands: Section 5.1 describes training on a graph with epsilon decay, so episode returns are neither i.i.d. (A2-i) nor per-instance averages (A2-ii). Option (A2-iii) requires an unestimated mixing time. Therefore the term G_n(δ) — the only quantity separating empirical from true source performance — is not justified, and Theorem 1 loses its foundation. On top of that, Appendix G fits α_n per source size before using the same data to validate the bound. The red dashed line in Figure 3 is a fitted curve, not a prediction. Appendix A also flags A6 as a conjectured non-asymptotic bound, yet the theorem treats it as rigorous. These are not minor blemishes; together they turn “validated bound” into “assumptions tuned to match observations.”\n\nThe math and the citation pattern are otherwise fine — the citations to Schatzki, Skolik, and BHH are appropriate and the derivation is careful, given its stated assumptions. The problem is that the central claim, as presented in the abstract, is unsupported by this text.\n\nWho gets value? Researchers working on equivariant QRL transfer might extract the D_{n→m} decomposition as a starting point, but they should not cite this as a proof. The hardware and barrier claims should not be cited at all from this manuscript.\n\nIf the full text is the submission, I would send it to a referee with instructions to focus on whether A2 can be satisfied by an online QRL loop and whether the fitted α_n amount to post-hoc validation. Expect major revision or reject. If the abstract is the actual paper, the supplied text is simply the wrong manuscript.","headline":"The abstract and the supplied full text are two different papers; the body's transfer bound is a real idea but rests on an assumption its own training loop violates.","tokens_in":26065,"tokens_out":3386,"would_cite":false,"duration_ms":31759,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["03.67.-a"],"model":"deepseek-v4-flash","headline":"Zero-shot transfer of equivariant quantum policies from 5- to 10-city TSPs works in exact simulation but is obstructed by finite-shot execution and hardware noise, raising the transfer gap from ~5% to 31.3% and then 45.3%.","keywords":["equivariant quantum circuits","quantum reinforcement learning","zero-shot transfer","traveling salesman problem","finite-shot noise","hardware noise","generalization bound","combinatorial optimization"],"falsifier":"Run the same transferred EQC checkpoint on TSP sizes n=4..10 under exact state-vector simulation and under finite-shot execution with, say, 10^3 and 10^4 shots each. The paper predicts the action margin (probability gap between the top-two choices) falls below the 1/√K shot-noise floor and scales as n^{-2.1}, and that the transfer gap jumps from ~5% to ~31%. Observing margins well above the shot-noise floor, an exponent clearly different from -2.1, or a transfer gap that shrinks substantially with more shots would overturn the finite-shot barrier and thus the paper's main empirical claim.","tokens_in":25063,"feed_emoji":"⚛️","tokens_out":10571,"duration_ms":78505,"temperature":0.7,"pith_summary":"This paper asks whether quantum reinforcement-learning policies built from equivariant quantum circuits and trained on small traveling-salesman instances can be reused on larger instances without retraining. In exact simulation, within the validated regime, the answer is yes: zero-shot transfer from five to ten cities beats training directly on the target size in all six evaluations. The central result, however, is that the transfer is systematically obstructed under realistic execution. Finite sampling noise alone widens the performance gap from about 5% to 31.3%, and running on trapped-ion hardware widens it to 45.3%, because the policy's action margins fall below the shot-noise floor and collapse roughly as n^{-2.1}. The paper claims no quantum advantage; it offers a diagnostic standard that future cross-size transfer claims should meet.","feed_headline":"45% transfer gap: quantum TSP policies break on real hardware","feed_subtitle":"Exact simulation sees the transfer work; finite shots and hardware push the gap to 45%.","key_machinery":"The carrying object is the equivariant quantum circuit (EQC), a parameterized circuit whose layers are generated by permutation-averaged operators (for example, sums like (1/k)Σ_j X_j and (2/k(k-1))Σ_{j<k} Z_jZ_k), so the same trained parameters can be plugged into a larger k-qubit circuit without changing the parameter count. The theoretical workhorse is the decomposition P_m(θ*_n) ≥ P̂_n − G_n(δ) − D_{n→m}: G_n is the finite-sample generalization error on the source size, and D_{n→m} bounds the transfer penalty from scaled generators plus structural task shift. The empirical workhorse is the shot-noise floor: actions are chosen from probabilities estimated with finitely many measurements,","core_discovery":"The paper's central claim is that zero-shot cross-size transfer of equivariant quantum circuit policies works in exact state-vector simulation but fails to survive finite-shot execution and hardware noise. The transfer gap grows from roughly 5% in simulation to 31.3% under sampling noise alone and to 45.3% on hardware, because the action-choice margins of the trained policy lie below the shot-noise floor and decay as n^{-2.1}. A cross-platform campaign across four hardware vendors shows the hardware penalty is set by native two-qubit gate count and error-mitigation overhead, not by shot budget. The paper also derives a theoretical performance bound separating source generalization error from","pith_inferences":["Editorial extension: the same shot-noise obstruction should appear in any equivariant quantum policy whose action distribution concentrates with problem size, not just TSP; the n^{-2.1} exponent is a measurable quantity that could be reported alongside approximation-ratio curves for other combinatorial problems.","Editorial extension: the margin-collapse diagnostic could be used predictively—measuring action margins at a small source size and extrapolating the transfer gap to a target size and shot budget before running hardware, which would tell a practitioner whether fine-tuning or error mitigation is worth doing.","Editorial extension: because the hardware penalty tracks native two-qubit gate count, an architecture search over EQC generator orderings or a compilation pass aimed at minimizing two-qubit gates might restore a large fraction of the lost transfer; the paper stops at diagnosing the obstacle rather than testing that fix."],"forward_implications":["Zero-shot transfer of EQC policies across TSP sizes is only trustworthy under exact simulation; with finite measurement shots, a transfer gap floor is set by shot noise, and no amount of additional training on the source size removes it.","The n^{-2.1} collapse of action margins means the obstruction worsens as target size grows, so scaling claims need to report margin-versus-shot statistics, not just average tour quality.","The hardware penalty tracks native two-qubit gate count and error-mitigation overhead; reducing that penalty means compiling EQC layers to fewer native two-qubit gates rather than increasing the shot budget.","The bound P_m(θ*_n) ≥ P̂_n − G_n(δ) − D_{n→m} gives a diagnosis: a transfer failure can be apportioned between source-side generalization error, generator/parameter mismatch, and structural task shift, and each component points to a different remedy (more episodes, smaller size jumps, fine-tuning).","If the central claims hold, the paper's measurement protocol becomes the standard by which future claims of cross-size quantum transfer should be judged."],"fun_headline_variants":["Simulation-to-hardware gap: 5% to 45% in quantum TSP","Finite shots alone inflate quantum transfer gap to 31%","Action margins below shot noise: why quantum transfer fails","Zero-shot transfer works in sim, dies on hardware: 45% gap","Quantum TSP transfer gap scales as n^-2.1 on real chips"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The entire bound rests on the assumption that the small-instance training episodes are independent draws from a fixed distribution (or mix quickly enough for statistical generalization bounds to apply); if the agent is trained online on a single instance with an evolving policy, the generalization term G_n(δ) is not the quantity the bound needs it to be.","fun_headline_variants_meta":{"raw":{"variants":["Simulation-to-hardware gap: 5% to 45% in quantum TSP","Finite shots alone inflate quantum transfer gap to 31%","Action margins below shot noise: why quantum transfer fails","Zero-shot transfer works in sim, dies on hardware: 45% gap","Quantum TSP transfer gap scales as n^-2.1 on real chips"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000264,"raw_usage":{"total_tokens":1446,"prompt_tokens":757,"completion_tokens":689,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":501,"completion_tokens_details":{"reasoning_tokens":592}},"tokens_in":501,"tokens_out":689,"duration_ms":5963,"temperature":1.0,"reasoning_tokens":592,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T09:33:44.992453+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same transferred EQC checkpoint on TSP sizes n=4..10 under exact state-vector simulation and under finite-shot execution with, say, 10^3 and 10^4 shots each. The paper predicts the action margin (probability gap between the top-two choices) falls below the 1/√K shot-noise floor and scales as n^{-2.1}, and that the transfer gap jumps from ~5% to ~31%. Observing margins well above the shot-noise floor, an exponent clearly different from -2.1, or a transfer gap that shrinks substantially with more shots would overturn the finite-shot barrier and thus the paper's main empirical claim.","supporting_citations":[],"review_version":1}