{"id":"f3e9db6d-842e-4844-91c5-b289304b06e7","arxiv_id":"2507.20570","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"The new PEDT threshold for EMICoRe VQE optimization yields modest average energy improvements over the original EMICoRe baseline on the off-critical 10-qubit Ising model and comparable results on more complex Hamiltonians.","lead":"A tweak to the EMICoRe Bayesian optimizer's confidence threshold, one that scales with the Gaussian process prior and recent energy changes, is tested on 10-qubit Ising and Heisenberg Hamiltonians. It reaches slightly lower energies than EMICoRe on the off-critical Ising benchmark and similar energies elsewhere, though without error bars and with constants chosen on the same tests.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The off-critical improvement is in-sample: c=3 is tuned on the same benchmark and no error bars are given, so the claimed gain over EMICoRe may be a selection or seed-noise artifact.","rationale":"The reader's CONDITIONAL verdict already identifies the core risk: the constant c=3 is tuned on the same benchmark used to demonstrate improvement, making the headline result in-sample. My stress-test agrees and sharpens the point: even setting aside selection, the paper reports only averaged curves without error bars, so the small final-energy gap on the off-critical Ising system could be seed noise. This is load-bearing because the entire novel contribution is an empirical claim of improved or comparable performance; without out-of-sample validation or uncertainty quantification, the claim is not yet established. I do not see an internal inconsistency in Eq. (1) or a flaw in the GP variance bound in Appendix B; the paper is honest in its hedging and explicitly acknowledges unoptimized constants. The proposed fix—testing the fixed c=3 on a held-out system and reporting per-seed differences with bootstrap intervals—directly settles whether the improvement generalizes or is an artifact of in-sample tuning and seed noise. Since the reader already conditioned acceptance on exactly this kind of evidence, the verdict remains CONDITIONAL rather than being strengthened or weakened by this pass.","tokens_in":7847,"tokens_out":5654,"duration_ms":66460,"concrete_test":"Hold c=3 fixed and run PEDT versus EMICoRe on a held-out off-critical Ising Hamiltonian (e.g., 12 qubits or a different transverse-field strength) for 310 iterations and 10 seeds; report per-seed final energies and a bootstrap 95% confidence interval for the mean final-energy difference. The central claim is supported only if PEDT's mean final energy is lower on this held-out system and the confidence interval excludes zero.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that PEDT outperforms EMICoRe on the 10-qubit off-critical Ising Hamiltonian—rests on a threshold constant c=3 that is selected on that exact benchmark in Appendix A (comparing c=1, 3, and 5 on the same 10-qubit off-critical system) and then reported in Section 5/Fig. 3a on the same system. Because the comparison is in-sample, the reported edge may be a selection artifact. Moreover, Fig. 3a and Fig. 5 show only seed-averaged energy curves without per-seed variance or confidence intervals; with 10 seeds, a final-energy gap of the size shown could easily lie within seed noise. The at-critical Ising and Heisenberg cases are described qualitatively as 'similar' or 'slightly closer,' with no quantitative significance test. Thus the empirical support for the headline improvement is not yet established out-of-sample or statistically.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes an alternative threshold function, PEDT (Prior and Energy Dependent Threshold), for the EMICoRe acquisition function used in Bayesian optimization of variational quantum circuits. The proposed threshold, Eq. (1), is κ_PEDT = (σ0/2) · min(δE, 1/(3 + exp(−δE))), where σ0 is the GP prior standard deviation and δE is the absolute average energy change over TAvg iterations. The authors argue that this threshold avoids the κ = 0 events that occur in EMICoRe's threshold and that it better matches the scale of posterior variance. They compare EMICoRe and PEDT on 10-qubit Ising Hamiltonians off and at criticality, and on a 10-qubit Heisenberg Hamiltonian, each run for 310 iterations over 10 independent seeds. The paper reports that PEDT reaches a lower final average energy than EMICoRe on the off-critical Ising system, similar performance at criticality, and practically identical performance on the Heisenberg system. Appendix A justifies the constant c = 3 in the denominator by comparing c = 1, 3, and 5 on the off-critical Ising benchmark, and Appendix B gives a standard bound showing that the posterior variance is bounded by the prior variance.","tokens_in":8119,"tokens_out":3001,"duration_ms":34249,"significance":"If the empirical claims hold, the contribution is a modest but potentially useful heuristic improvement to a specific acquisition function for VQE optimization. The paper is honest in its language, explicitly stating that the criticality and Heisenberg results are not claimed as improvements, and Appendix B correctly reproduces the standard GP variance bound. The proposed threshold is simple, interpretable, and could be of interest to practitioners using EMICoRe. However, the central claim of improvement over EMICoRe rests entirely on a small, in-sample empirical comparison: the key constant c = 3 is selected on the very benchmark used to demonstrate the improvement, and no uncertainty quantification or significance testing is provided for the reported energy differences. As a result, the significance of the result is currently limited, although the proposed framework does offer a plausible direction for further study.","major_comments":[{"comment":"The constant c = 3 in Eq. (1) is selected by comparing c = 1, 3, and 5 on the same 10-qubit off-critical Ising Hamiltonian that is later presented as the main success case (Figs. 6–8 in Appendix A, then Fig. 3a in Section 5). This makes the reported improvement over EMICoRe an in-sample comparison: the advantage may be a selection artifact rather than a general property of the PEDT threshold. To support the headline claim, the paper should either evaluate the threshold on a benchmark not used for tuning, use a nested or cross-validation procedure, or demonstrate that the final-energy ordering is insensitive to c across a range of values.","section":"Appendix A / §5, Fig. 3a"},{"comment":"The empirical comparison is based on seed-averaged energy curves over only 10 seeds, with no error bars, confidence intervals, or significance tests. The off-critical gap at iteration 310 appears small relative to the fluctuations visible in the trajectories, so it could easily arise from seed noise. The claims of \"similar\" or \"slightly closer\" performance for the at-critical Ising and Heisenberg systems are likewise purely qualitative. The authors should report per-seed final energies, the mean and standard deviation (or a confidence interval), and a paired significance test (e.g., a paired t-test or Wilcoxon signed-rank test across seeds) for each benchmark.","section":"§5, Figs. 3a, 3b, 5"},{"comment":"The mechanism proposed for PEDT's advantage—that EMICoRe's κ = 0 events hinder convergence—is demonstrated with a specific example at iterations 280–290 in Fig. 3a and with a single-seed threshold trace in Fig. 4. Since κ = 0 events are seed-dependent, the causal story needs quantitative support: the authors should report, across all 10 seeds, how often EMICoRe's κ hits zero, when those events occur, and whether their frequency correlates with the average energy gap between the two methods. Without this, the explanation remains anecdotal.","section":"§5, Fig. 3a and Fig. 4"}],"minor_comments":[{"comment":"The denominator in Eq. (1) is written inline as 1/(3 + e^{−δE}), but the surrounding text and Fig. 2 refer to f(δE) = 1/(3 + e^{−δE}); please add parentheses consistently and explicitly write the fraction to avoid ambiguity, e.g., κ_PEDT = (σ0/2) · min(δE, 1/(3 + exp(−δE))).","section":"Eq. (1)"},{"comment":"The caption says the run is for 300 iterations, while the main text and other figure captions state 310 iterations; please correct the inconsistency.","section":"Fig. 4 caption"},{"comment":"The caption says \"2 points for which κ = 0 between them are shown in green,\" but the green dotted line also denotes the analytically computed ground state energy; using the same color for both makes the figure confusing. Use distinct markers or colors for these two elements.","section":"Fig. 3a caption and text"},{"comment":"The general form κ_PEDT = (a·σ0) · min(δE, b/(c + d·e^{−f·δE})) introduces constants a through f without naming them as hyperparameters or providing guidance on how they should be chosen in practice; a brief discussion of plausible ranges would be helpful.","section":"Section 6"},{"comment":"There are several typographical and grammatical issues, such as \"VQE's\" in the abstract, missing spaces before references, and inconsistent use of \"EMICoRe\" versus \"EMICoRe model\"; a careful proofread would improve readability.","section":"Throughout"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a short empirical study of a small heuristic modification to an existing acquisition function. The central idea is defensible and the GP variance bound in Appendix B is correct, but the empirical support for the main claim is currently too weak: the tuning constant is selected on the same benchmark used for the headline result, and no statistical significance or uncertainty quantification is provided. A revision that addresses the out-of-sample concern and adds proper error reporting would make the contribution publishable. I would not support rejection on scientific grounds, but the current evidence is not sufficient for acceptance."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a small, honest heuristic paper with one real empirical claim and one real empirical weakness. The claim—that replacing EMICoRe's zero-clamped threshold with sigma0/2 * min(deltaE, 1/(3+exp(-deltaE))) gives slightly better VQE convergence on a 10-qubit off-critical Ising chain—is plausible but not established, because the constant c=3 was picked on that same benchmark in Appendix A and the comparison shows no error bars.\n\nWhat's genuinely new: the PEDT formula does not appear in the EMICoRe paper or code, and the motivation (avoiding kappa=0 stalls, tying threshold scale to GP prior variance) is clearly argued. The paper is also unusually transparent: Appendix A shows the constant selection, the text repeatedly hedges with 'suggest' and 'similar,' and the general parametric form is stated for future work. Appendix B correctly proves the posterior variance bound. That is real epistemic hygiene and should be credited.\n\nSoft spots, in order of importance. First, the headline improvement is in-sample. Appendix A chooses c=3 by comparing c=1, 3, 5 on the 10-qubit off-critical Ising system, and the main result in Fig. 3a is that same system. That makes the advantage over EMICoRe vulnerable to selection bias; the comparison is not out-of-sample. Second, all figures show seed-averaged curves only. With 10 seeds and no variance bands or significance test, a final gap of the size shown could easily be seed noise. The at-critical and Heisenberg cases are described qualitatively, which is appropriately cautious but adds no statistical weight. Third, this is one pipeline on three small Hamiltonians; even if the gain is real, it is an incremental improvement in a heuristic, not a new class of results. I don't think these flaws sink the paper—the author labels the regime correctly—but they cap the strength of the conclusion.\n\nWho should read it: anyone actively working on Bayesian optimization of VQEs, especially on EMICoRe variants. For that reader it's a useful data point and a clearly stated research direction. A serious referee should see it, with the main request being a proper out-of-sample evaluation: fix the constants on one system, then test on others, and report per-seed statistics. I'd accept it for peer review, and I'd hope the revision adds those numbers. I would not cite the off-critical improvement as established.","headline":"Small, honest heuristic paper on a new EMICoRe threshold; the idea is plausible but the headline gain is in-sample and lacks error bars, so it needs a revision, not a desk reject.","tokens_in":8594,"tokens_out":1875,"would_cite":false,"duration_ms":20311,"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 threshold that stays positive when energy stalls reaches lower ground-state energies than EMICoRe on the off-critical 10-qubit Ising model and matches it on harder benchmarks.","keywords":["variational quantum eigensolver","Bayesian optimization","EMICoRe","confident region","Gaussian process surrogate","Ising Hamiltonian","Heisenberg Hamiltonian","threshold function"],"falsifier":"Run PEDT and EMICoRe on a held-out set of 10-qubit Ising Hamiltonians at several transverse-field values, none of which were used to set $c=3$, and check whether PEDT still ends at a lower average energy. If the advantage disappears outside the benchmark that chose $c$, the central claim is in-sample tuning; if it persists, the threshold is doing genuine work.","tokens_in":7670,"feed_emoji":"⚛️","tokens_out":10156,"duration_ms":86315,"temperature":0.7,"pith_summary":"EMICoRe is a Bayesian optimization routine for variational quantum eigensolvers that keeps a Confident Region of low-variance points open for exploration, but its threshold collapses to zero whenever the predicted energy stops decreasing over the averaging window. This paper proposes a Prior and Energy Dependent Threshold (PEDT), $\\kappa_{\\mathrm{PEDT}} = (\\sigma_0/2)\\min(\\delta E, 1/(3+e^{-\\delta E}))$ with $\\delta E = |\\mu_{t-T_{\\mathrm{Avg}}}-\\mu_t|/T_{\\mathrm{Avg}}$, which never collapses and scales with the Gaussian process prior variance. The paper reports that PEDT reaches a lower average energy than EMICoRe on the 10-qubit off-critical Ising Hamiltonian over 310 iterations with 10 seeds, and matches EMICoRe on the critical Ising and Heisenberg Hamiltonians. A sympathetic reader would take the contribution to be a simple, variance-aware threshold that keeps EMICoRe's exploration alive exactly when energy stagnation would otherwise kill it.","feed_headline":"PEDT threshold lowers Ising VQE energy below EMICoRe","feed_subtitle":"The new threshold never collapses to zero, letting the confident region keep exploring through late optimization.","key_machinery":"The load-bearing object is Eq. (1), the PEDT threshold function, together with the Gaussian process posterior-variance bound that justifies its scale. With $\\sigma_0$ the GP prior standard deviation and $\\delta E = |\\mu_{t-T_{\\mathrm{Avg}}}-\\mu_t|/T_{\\mathrm{Avg}}$ the absolute average energy change, Eq. (1) sets the threshold as the smaller of $\\delta E$ and the saturating curve $1/(3+e^{-\\delta E})$, all scaled by $\\sigma_0/2$. The first factor imports the observation that posterior variance never exceeds the prior variance (Appendix B), so the threshold is always on the same order as the system's variance; the second factor keeps early optimization controlled while preventing later thresholds from growing linearly with $\\delta E$. The absolute value is what removes the EMICoRe failure mode $\\kappa=0$ that the paper identifies in Fig. 4 and in the green points of Fig. 3a. The mechanism carries the argument because every reported improvement is attributed to keeping the Confident Region non-empty when EMICoRe's would vanish.","core_discovery":"The central claim is that the Confident Region threshold in EMICoRe should depend on the Gaussian process prior variance and on the absolute value of the recent average energy change, not on the signed energy decrease. PEDT sets $\\kappa_{\\mathrm{PEDT}} = \\frac{\\sigma_0}{2}\\min(\\delta E, \\frac{1}{3+e^{-\\delta E}})$, where $\\delta E$ is the absolute average energy change over the last $T_{\\mathrm{Avg}}$ iterations. Taking the absolute value keeps the threshold positive during the natural upward fluctuations that make EMICoRe's threshold $\\kappa = \\max(0, (\\mu_{t-T_{\\mathrm{Avg}}}-\\mu_t)/T_{\\mathrm{Avg}})$ equal to zero, and the $\\min$ with the logistic-like term keeps the threshold from growing without bound when $\\delta E$ is large. The paper argues that the zero-threshold episodes are actively harmful, because they restrict the Confident Region to exactly observed points and slow convergence at the start and end of optimization. On the off-critical 10-qubit Ising model, PEDT's average energy after 310 iterations is closer to the analytic ground state than EMICoRe's; on the critical Ising and Heisenberg models, the two algorithms perform at essentially the same level.","pith_inferences":["Editorial inference: the reported off-critical advantage should be read warily, because the constant $c=3$ in the denominator $3+e^{-\\delta E}$ was selected on the very same off-critical Ising benchmark that later appears as the success case; the gain may be in-sample.","Editorial inference: the principle of a variance-scaled, always-positive threshold could be dropped into other GP-based acquisition functions, and the six-constant generalization could be optimized per Hamiltonian family to test whether the improvement is structural or just tuned.","Editorial inference: if the result holds out of sample, the practical effect is that VQE users get a more accurate ground-state estimate for the same number of quantum circuit evaluations, which matters where circuit calls are the expensive resource."],"forward_implications":["With PEDT, the Confident Region never fully empties: the threshold remains positive through energy fluctuations, so the exploratory benefit of the region is preserved in late-stage optimization.","On the off-critical 10-qubit Ising benchmark, the reported average final energy is lower than EMICoRe's, so the threshold choice itself, not the optimizer, is what buys the extra accuracy.","PEDT matches EMICoRe on the critical Ising and Heisenberg landscapes, implying the modification does not sacrifice performance when local minima are plentiful.","Because the general PEDT form has six free constants, the same framework can be tuned per system class, which the paper identifies as the next step.","EMICoRe comparisons that keep the old threshold are, from this paper's view, comparisons against a deliberately fragile choice."],"supporting_citations":[{"why":"Defines the EMICoRe acquisition framework that PEDT modifies and supplies the baseline for the benchmarks.","marker":"[1]"},{"why":"Provides the Gaussian-process posterior variance bound that justifies scaling the threshold by $\\sigma_0$.","marker":"[17]"},{"why":"Supplies the implementation detail that the threshold is clamped at zero, the failure mode PEDT removes.","marker":"[21]"},{"why":"Supplies the exact Ising simulation used to compute analytic ground-state energies for comparison.","marker":"[20]"},{"why":"Supplies the Heisenberg Hamiltonian as the more complex benchmark with many local minima.","marker":"[22]"}],"fun_headline_variants":["PEDT avoids zero-collapse, beats EMICoRe on Ising VQE","New VQE threshold keeps exploring, improves Ising energy","Adaptive threshold for VQE: better than EMICoRe on Ising","VQE threshold that never dies: wins Ising benchmark"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The choice of $c=3$ in the threshold was selected on the same off-critical Ising benchmark that later appears as the reported improvement, so the claimed advantage may be in-sample tuning rather than a general property of PEDT.","fun_headline_variants_meta":{"raw":{"variants":["PEDT avoids zero-collapse, beats EMICoRe on Ising VQE","New VQE threshold keeps exploring, improves Ising energy","Adaptive threshold for VQE: better than EMICoRe on Ising","VQE threshold that never dies: wins Ising benchmark"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000342,"raw_usage":{"total_tokens":1930,"prompt_tokens":1039,"completion_tokens":891,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":655,"completion_tokens_details":{"reasoning_tokens":812}},"tokens_in":655,"tokens_out":891,"duration_ms":8024,"temperature":1.0,"reasoning_tokens":812,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:40:41.142732+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run PEDT and EMICoRe on a held-out set of 10-qubit Ising Hamiltonians at several transverse-field values, none of which were used to set $c=3$, and check whether PEDT still ends at a lower average energy. If the advantage disappears outside the benchmark that chose $c$, the central claim is in-sample tuning; if it persists, the threshold is doing genuine work.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the Gaussian-process posterior variance bound that justifies scaling the threshold by $\\sigma_0$."},{"cited_title":"Nicoli et al","cited_arxiv_id":null,"evidence_quote":"Supplies the implementation detail that the threshold is clamped at zero, the failure mode PEDT removes."}],"review_version":2}