{"id":"49a9d985-efcf-4f48-89a7-a8ba53ec3680","arxiv_id":"2504.17923","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"EAQGA, a quantum-genetic hybrid that encodes parent-solution bit correlations as CNOT-entangled pairs, reports higher average fitness than classical GA and AQGA on portfolio optimization across simulators and a 100-qubit IBM test.","lead":"This paper introduces a genetic algorithm that writes the best solutions found so far into small quantum circuits, using entangled qubit pairs to keep beneficial asset correlations across generations. On a 100-stock portfolio problem the method beat a classical genetic algorithm by about 34% on average fitness, but the result rests on one data subset and no published code.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Algorithm 1 does not implement the entanglement-aware crossover described in Section III-B, undermining the central claim and its reproducibility.","rationale":"The reader's verdict of REJECT is supported: the paper's central methodological artifact, Algorithm 1, contradicts the entanglement-aware crossover described in Section III-B, making the proposed method unreproducible and the headline results unattributable. I focus on this algorithmic inconsistency rather than the hardware statistics because the method is the paper's primary contribution; if the algorithm is mis-specified, the contribution collapses regardless of how convincingly the 33.6%/37.2% margins are presented. The hardware comparison weakness (single 100-asset subset, ten repetitions, no error bars) is a separate problem that further weakens the empirical claim, but it is secondary to the core algorithmic flaw. My disagreement with the reader's weakest_assumption is partial: they highlighted the hardware statistics as the weakest premise, while I see the algorithm mismatch as more fundamental. However, the reader's rationale does mention the same algorithmic issue, so the overall conclusion aligns. A concrete static trace of Fig. 2 immediately exposes the flaw, and a re-implementation comparison would settle whether the published pseudocode is merely a typo or whether the actual results come from a different, undocumented method. Thus the verdict remains REJECT with no change needed.","tokens_in":13454,"tokens_out":5657,"duration_ms":53174,"concrete_test":"Perform a static trace of Algorithm 1 on the Fig. 2 example (xb1=[0,0,1,1,0], xb2=[0,1,0,1,1]) with pa=0.95 and selected pairs {(1,2),(1,4)}. According to the pseudocode, pair (1,2) yields RY(2*arccos(sqrt(0.95)), q1) followed by CX(q1,q2) — the |ψp> circuit — even though the text defines (1,2) as a negative-correlation pair that should use the |ψn> circuit of Fig. 3(b). If this mismatch reproduces, the published algorithm demonstrably does not implement the described crossover. As a complementary check, implement both the text's intended algorithm (circuit type chosen from P/N sets) and the pseudocode version, run both on the ten size-30 subsets with the same hyperparameters, and compare final fitness distributions; agreement would indicate the pseudocode is a minor typo, while disagreement would confirm that the reported results depend on an undocumented implementation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's core contribution is a crossover that detects positive/negative correlation patterns between parent bitstrings (sets P and N in Section III-B) and encodes them via the circuits of Fig. 3(a)/(b). However, Algorithm 1 never consults xb2 or the P/N sets: for each selected entangled pair (n1,n2), it branches solely on xb1[n1]. If xb1[n1]==0 it applies the |ψp> circuit (RY then CX); if xb1[n1]==1 it applies the |ψn> circuit (RY, X(n2), CX). The sign of the correlation is determined by the joint pattern of both parents, not by xb1[n1] alone. For the Fig. 2 example, pair (1,2) is negatively correlated (xb1[1]!=xb1[2] and xb2[1]!=xb2[2]), but Algorithm 1 builds the |ψp> circuit because xb1[1]=0. The subsequent loop (line 31) is also malformed: it reuses n1 from the pair loop, and its angle for a target bit value of 1 is wrong (θ = 1 - 2*arccos(sqrt(Pa)) instead of θ = 2*arccos(sqrt(1-Pa))). Thus the published algorithm cannot implement the described entanglement-aware crossover, and the reported simulator/hardware improvements cannot be attributed to the proposed mechanism. This is load-bearing because the method itself is the paper's contribution; without a correct algorithmic description, even strong empirical results would be unverifiable. The discrepancy affects both the methodological narrative and the experimental claims, since the implementation used to produce Fig. 6 is never specified and the pseudocode does not match the text.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes EAQGA, a quantum-enhanced genetic algorithm for combinatorial optimization, and evaluates it on a portfolio-optimization QUBO formulation. The method maintains an elitism pool of the two best binary solutions, detects positively or negatively correlated bit pairs across the parents, encodes selected pairs as entangled states (\\psi_p or \\psi_n) using RY and CNOT gates, and biases non-entangled qubits toward the best solution's bit values. Experiments are reported on simulators for 10 subsets of size 30 and 10 subsets of size 40 with population sizes 10 and 20 and 100 runs each, and on the ibm_quebec 127-qubit processor for a single 100-stock subset with population 10 and 10 runs. The authors report average fitness improvements of 33.6% over GA and 37.2% over AQGA on the hardware experiment, while explicitly disclaiming a formal quantum advantage.","tokens_in":13730,"tokens_out":4044,"duration_ms":43862,"significance":"If the algorithm had been correctly and completely specified, the paper would offer a useful NISQ-oriented quantum crossover that keeps circuit depth low by limiting entanglements. The simulator study is extensive in its own terms: 20 subsets, two population sizes, and 100 runs per configuration, with tabulated averages and standard deviations, and the authors are appropriately cautious in not claiming formal quantum speedup. However, the contribution is defined by the crossover mechanism, and the manuscript's own pseudocode does not implement the described mechanism. Because the central algorithmic description is internally inconsistent, the empirical results cannot currently be attributed to the claimed method, and the hardware comparison rests on a single subset without uncertainty quantification. The strengths of the empirical study do not compensate for the load-bearing algorithmic mismatch.","major_comments":[{"comment":"Algorithm 1 (lines 20-30) does not implement the entanglement-aware crossover described in Section III-B. The prose defines P/N correlations from the joint pattern of both parent bitstrings, but the pseudocode branches only on xb1[n1]: if xb1[n1] == 0 it builds the |\\psi_p> circuit, otherwise the |\\psi_n> circuit. For the example in Fig. 2, pair (1,2) is negatively correlated across both parents, yet with xb1[1] = 0 Algorithm 1 would apply the positive-correlation circuit. The else branch also contains an incorrect rotation formula: line 37 sets θ = 1 - 2*arccos(sqrt(Pa)) when the desired bit value is 1, whereas Section III-B correctly gives θ = 2*arccos(sqrt(1 - Pa)). These are not typographical details; the printed algorithm cannot generate the circuits that the text and figures describe, so the reported simulator and hardware results cannot be verified as coming from the proposed crossover.","section":"Section III-B and Algorithm 1"},{"comment":"The probabilistic pair-selection and chain-formation steps are not specified in the pseudocode. Algorithm 1's line 18 says only \"Select the entangled qubits using Pool elitism, Ps, and Q\", but the manuscript does not define how ps and the decay factor df(t) are used to sample from the candidate sets P and N, how pairs sharing a qubit are merged into chains, or how the control/target assignment within a chain is determined. Without an unambiguous description of these steps, the method is not reproducible even if the P/N branching bug in the previous comment were corrected.","section":"Algorithm 1 and Section III-B"},{"comment":"The hardware experiment uses one randomly selected subset of 100 stocks and only 10 repetitions, and Fig. 6 reports average fitness without standard deviations, confidence intervals, or any statistical test. The abstract's headline improvements of 33.6% over GA and 37.2% over AQGA are therefore not supported as stable statements about the algorithms; they may reflect the particular subset, the particular 10 runs, or hardware noise. Additional subsets or at least per-iteration variability and a statistical comparison are needed before these margins can be taken as evidence of a consistent advantage.","section":"Section IV-D2 and Fig. 6"}],"minor_comments":[{"comment":"Line 31 contains a typo, \"for for n = 1 to S\", and the variable name is inconsistent: line 16 initializes a circuit with n qubits while line 31 uses S; the relationship between n and S should be clarified.","section":"Algorithm 1"},{"comment":"The amplitude probability hyperparameter is written inconsistently as pa in the text and Pa in Algorithm 1; this should be unified.","section":"Throughout"},{"comment":"The reference to Yahoo Finance misspells \"Finance\" as \"Fianance\", and the URL is incomplete for a formal reference.","section":"Reference [38]"},{"comment":"The Bayesian optimization used for hyperparameter tuning is described only as performed on a randomly selected subset; the search space, evaluation budget, and resulting hyperparameter values for GA, AQGA, and EAQGA are not reported, which makes it hard to assess whether the comparisons are demonstrably fair.","section":"Section IV-A"},{"comment":"Figure 6 would benefit from error bars or shaded confidence bands; without them, the eye cannot distinguish systematic advantage from run-to-run variation.","section":"Section IV-D2"},{"comment":"The manuscript does not state whether code or data are available; given that the paper's contribution is an algorithmic procedure, providing either the implementation or a precise, corrected pseudocode is essential for reproducibility.","section":"General"}],"recommendation":"reject","confidential_remarks":"The paper has a strong empirical skeleton, but the core algorithmic description as printed cannot implement the claimed crossover, and the hardware evidence is statistically thin. These are load-bearing because the method itself is the contribution. A resubmission with a corrected and complete Algorithm 1, a matching implementation, and a more rigorous hardware comparison (multiple subsets, error bars, statistical tests) could be considered, but the current manuscript is not publishable in its present form."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: the crossover idea is genuinely new and the simulator numbers are internally consistent, but Algorithm 1 as printed does not implement the entanglement-aware crossover described in Section III-B, and the hardware section is too thin to carry the 33.6% and 37.2% headline. This is a fixable paper, not a hopeless one.\n\nWhat is actually new: instead of rotation-angle updates or amplitude amplification, the authors read matching or opposing bit pairs from two elite parents, weight pair selection by the normalized covariance matrix, and encode the selected pairs into shallow circuits with one RY plus CNOT, or RY-X-CNOT. That is a reasonable NISQ-era crossover heuristic and I do not see it in the QGA papers they cite. The simulator study is solid: 20 non-overlapping subsets, 100 runs per configuration, standard deviations reported, and a brute-force optimum for calibration. The authors also explicitly disclaim formal quantum advantage, which keeps the claim honest. The literature engagement is fair and the citation pattern is unremarkable; the single self-citation is incidental.\n\nThe load-bearing problem is the pseudocode, and I agree with the stress-test reading. In Section III-B the choice between |ψp> and |ψn> depends on the joint pattern across both parents, encoded in the P and N sets. Algorithm 1 branches only on xb1[n1]: if that bit is 0 it builds the positive-correlation circuit, otherwise the negative-correlation circuit. That cannot implement the described crossover. For the paper's own example, pair (1,2) is negative but Algorithm 1 would build the positive circuit because xb1[1]=0. The second loop is also malformed: it tests the stale variable n1 instead of the loop index n, and the else-branch angle θ = 1 - 2 arccos(√Pa) is not the correct inverse probability for target bit value 1. As printed, the algorithm neither implements the method nor explains the reported curves. No code or seeds are supplied, so the reader cannot tell whether the experiments used a corrected version. This is not a side typo; it is central.\n\nThe hardware section is the other weak spot. One randomly chosen 100-stock subset, ten repetitions, no standard deviations, no seeds, no subset membership, no statistical test. The headline margins may be real, but as presented they are not sufficiently supported. The simulator results are the empirical core; the hardware part should be framed as a small demonstration.\n\nWho this is for: people working on quantum-assisted evolutionary computation and NISQ heuristics. It deserves a serious referee because the idea is new and the simulator data look worth reproducing, but only if the authors fix Algorithm 1 and release code. I would not desk-reject; I would send it out with a strong request for code and a corrected pseudocode.","headline":"A novel and plausible crossover heuristic with clean simulator numbers, but the printed Algorithm 1 does not implement the described method and the hardware claim lacks statistics.","tokens_in":14321,"tokens_out":5987,"would_cite":false,"duration_ms":54914,"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 reports a quantum genetic crossover that, on 100-qubit portfolio instances, improves average fitness by 33.6% over classical GA and 37.2% over quantum-inspired GA.","keywords":["quantum genetic algorithm","entanglement-aware crossover","portfolio optimization","combinatorial optimization","QUBO","genetic algorithm","NISQ","quantum computing"],"falsifier":"Re-run the 100-asset comparison on at least ten independently drawn stock subsets with thirty or more repetitions per subset, and report the mean difference and its standard error; if the average advantage of EAQGA over GA and AQGA is not positive across subsets, the paper's central quantitative claim is refuted.","tokens_in":13203,"feed_emoji":"⚛️","tokens_out":11301,"duration_ms":96828,"temperature":0.7,"pith_summary":"The paper proposes a quantum genetic algorithm whose crossover step builds the next generation's circuits from the two fittest binary solutions, encoding observed correlations between bit pairs as small entangled states. The aim is to preserve beneficial variable relationships across generations while keeping circuit depth low enough for near-term quantum hardware. Tested on portfolio optimization, the method (EAQGA) reports the best average fitness and lowest variance among a classical genetic algorithm, an adaptive quantum-inspired genetic algorithm, and itself on all simulator subsets, and a 33.6% average-fitness improvement over classical GA and 37.2% over quantum-inspired GA on a 100-asset run on real hardware. The paper does not claim a formal quantum speedup; its contribution is a shallow-circuit crossover that improves solution quality per iteration.","feed_headline":"Quantum crossover beats classical GA by 33.6% on 100-qubit runs","feed_subtitle":"A 100-qubit portfolio test on real hardware shows the new crossover also outperforms a quantum-inspired GA by 37.2%.","key_machinery":"The load-bearing mechanism is the entanglement-aware crossover: a rule that converts the two fittest binary parents into circuits for the next population. For every bit pair that appears correlated across the parents (matching values or opposite values), the circuit applies a rotation and a CNOT to create an entangled state $\\alpha|00\\rangle+\\beta|11\\rangle$ or $\\alpha|01\\rangle+\\beta|10\\rangle$, with the angle set so the bit values from the best solution are measured with probability $p_a=0.95$. A selection probability $p_s \\cdot df(t) \\cdot |\\Sigma_{i,j}^n|$ decides which detected pairs actually become entangled, using the normalized covariance matrix to favor pairs consistent with the objective; a decay factor $df(t) = 0.5 + t/(2T_{\\max})$ relaxes this consistency penalty over the run. Shared qubits are chained so the number of CNOTs stays below the qubit count, which is why the circuits remain shallow enough for current hardware.","core_discovery":"The central claim is that a genetic algorithm's crossover can be made entanglement-aware: each generation, the two best solutions identify bit pairs whose values match or oppose across both parents, and a probabilistic selection step, guided by the normalized coupling matrix of the objective, chooses which of those pairs to entangle. Each chosen pair is realized in the next circuit by one rotation gate and one CNOT (plus an X gate for opposing pairs), producing a two-qubit state biased toward the elite values, while unpaired qubits receive rotations that nudge them toward the best solution's bits. The authors report that on ten 30-asset and ten 40-asset portfolio subsets, EAQGA achieves the highest average fitness and lowest standard deviation for both population sizes 10 and 20, and that on a 100-asset instance executed on a real 127-qubit device, EAQGA's average fitness after 20 iterations is 33.6% higher than classical GA's and 37.2% higher than AQGA's. They explicitly disclaim a formal quantum advantage because the entanglement count is limited and the circuits remain efficiently simulable classically.","pith_inferences":["The crossover learns only pairwise correlations, so its advantage over classical crossover should shrink on problems whose optimal solutions are governed by higher-order interactions; this could be tested directly on QUBOs with 3-body penalty terms.","The decay factor in the pair-selection probability is effectively an annealing schedule that trades objective-guided against empirically-guided pair selection; trying other schedules (cosine, step, or adaptive) is a natural experiment the paper leaves open.","The hardware result rests on a single 100-asset subset repeated ten times; averaging the same comparison over several independently drawn 100-asset subsets would show whether the 33.6% and 37.2% margins are a property of the algorithm or of that one covariance matrix."],"forward_implications":["Iteration for iteration, EAQGA reaches higher fitness than GA and AQGA at equal population size, which reduces the number of fitness evaluations needed to reach a given solution quality.","Because the crossover is defined for any binary objective through its coupling matrix, the same circuit construction applies to other combinatorial problems such as knapsack, MaxCut, or quadratic assignment.","The shallow depth and limited two-qubit gate count make the algorithm executable on current noisy devices, where alternative full-entanglement QGAs require fault-tolerant hardware.","The consistently lower standard deviations imply the algorithm's outputs are more reproducible across runs, a property that matters for practical deployment."],"supporting_citations":[{"why":"Defines the self-adaptive AQGA baseline whose rotation-angle update rule EAQGA is compared against.","marker":"[10]"},{"why":"Shows why circuits with limited entanglement are efficiently simulable, supporting the use of a matrix-product-state simulator.","marker":"[20]"},{"why":"Supplies the roulette-wheel parent-selection method used in the classical GA baseline.","marker":"[22]"},{"why":"Provides the QUBO mean-variance portfolio formulation used as the fitness function in all experiments.","marker":"[26]"},{"why":"Supplies the Bayesian optimization procedure used to tune hyperparameters for all three algorithms.","marker":"[35]"},{"why":"Provides the matrix-product-state simulator used for the 30- and 40-asset experiments.","marker":"[39]"},{"why":"Documents the 127-qubit processor on which the 100-asset experiments were run.","marker":"[41]"}],"fun_headline_variants":["Entanglement-aware crossover beats classical GA by 33.6% on 100 qubits","Quantum crossover lifts fitness 33.6% above classical GA on 100 qubits","Entanglement crossover outperforms quantum-inspired GA by 37.2% on 100 qubits","New entanglement-aware GA improves fitness 33.6% over classical on real hardware","Entanglement-aware genetic crossover yields 33.6% gain over classical GA"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The 33.6% and 37.2% hardware margins assume that ten repetitions on a single randomly selected 100-stock subset are enough to estimate each algorithm's average fitness reliably; without standard deviations or statistical tests, those margins could come from that particular subset and device noise.","fun_headline_variants_meta":{"raw":{"variants":["Entanglement-aware crossover beats classical GA by 33.6% on 100 qubits","Quantum crossover lifts fitness 33.6% above classical GA on 100 qubits","Entanglement crossover outperforms quantum-inspired GA by 37.2% on 100 qubits","New entanglement-aware GA improves fitness 33.6% over classical on real hardware","Entanglement-aware genetic crossover yields 33.6% gain over classical GA"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.002114,"raw_usage":{"total_tokens":8238,"prompt_tokens":1003,"completion_tokens":7235,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":619,"completion_tokens_details":{"reasoning_tokens":7124}},"tokens_in":619,"tokens_out":7235,"duration_ms":48356,"temperature":1.0,"reasoning_tokens":7124,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-16T10:29:35.246724+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the 100-asset comparison on at least ten independently drawn stock subsets with thirty or more repetitions per subset, and report the mean difference and its standard error; if the average advantage of EAQGA over GA and AQGA is not positive across subsets, the paper's central quantitative claim is refuted.","supporting_citations":[{"cited_title":"IBM and PINQ² unveil utility-scale quantum computer in Qu ´ebec","cited_arxiv_id":null,"evidence_quote":"Documents the 127-qubit processor on which the 100-asset experiments were run."},{"cited_title":"The improvement of quantum genetic algorithm and its application on function optimization,","cited_arxiv_id":null,"evidence_quote":"Defines the self-adaptive AQGA baseline whose rotation-angle update rule EAQGA is compared against."},{"cited_title":"Genetic algorithm performance with different selection strategies in solving tsp,","cited_arxiv_id":null,"evidence_quote":"Supplies the roulette-wheel parent-selection method used in the classical GA baseline."},{"cited_title":"Best practices for portfolio optimization by quantum computing, ex- perimented on real quantum devices,","cited_arxiv_id":null,"evidence_quote":"Provides the QUBO mean-variance portfolio formulation used as the fitness function in all experiments."},{"cited_title":"Practical bayesian opti- mization of machine learning algorithms,","cited_arxiv_id":null,"evidence_quote":"Supplies the Bayesian optimization procedure used to tune hyperparameters for all three algorithms."},{"cited_title":"Matrix Product State Simulation Method","cited_arxiv_id":null,"evidence_quote":"Provides the matrix-product-state simulator used for the 30- and 40-asset experiments."}],"review_version":1}