{"id":"fdf4f197-2df1-48f5-a9d0-d73cc662547b","arxiv_id":"2411.16632","paper_version":1,"verdict":"REJECT","confidence":"HIGH","novelty_score":2.0,"correctness_risk":"high","formal_verification":"none","parameter_count":5,"one_line_summary":"A VQE-based variant of Schnorr's factoring algorithm factors 1961 in simulation, but only when the lattice diagonal and sr-pair from the original QAOA paper are reused, and the VQE step itself changed nothing.","lead":"This preprint replaces the QAOA subroutine in Yan et al.'s hybrid Schnorr factoring scheme with VQE and reports factoring 1961. The single success case actually used the same lattice diagonal and the same smooth relation pair as the original paper, and the VQE step returned the no-change solution.","discovery_kind":"replication","skeptic_critique":{"model":"deepseek-v4-flash","headline":"In the sole successful run, VQE returns [000] (Table 1), so b_h = bop exactly; the sr-pair (2025,1) and factorization 53×37 are produced by classical Babai alone, leaving the central claim that VQE improves Babai's solution unsupported.","rationale":"The reader's stated weakest assumption was the post-hoc fixing of the lattice diagonal order to [1,1,2], which is a legitimate concern about experimental fairness. I find a more fundamental, directly observable problem: in the only successful experiment, VQE selects the zero displacement and therefore does not improve Babai's solution at all. The sr-pair and factors are entirely classical outputs. This defeats the central claim even under the most favorable configuration, so the post-hoc-order issue, while real, is secondary. The final verdict remains REJECT as the reader concluded; my analysis confirms rather than moves that verdict. Agreement is partial because the reader's rationale mentions the zero bitstring but does not make it the primary load-bearing flaw.","tokens_in":8127,"tokens_out":9645,"duration_ms":86229,"concrete_test":"Run the N=1961 pipeline with the VQE step deleted: after fpylll/Babai, take bop from Eq. 22, read off its coefficient vector (0,4,2) in the original basis, form the sr-pair u=3^4·5^2=2025, v=1, solve Eq. 16, and factor. If this reproduces 53 and 37—as the arithmetic shows it must—the VQE subroutine is superfluous and the paper's central claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 3.2 states that the goal of VQE is to improve the approximate CVP solution from Babai's algorithm, and Section 4.1 claims N=1961 was factored 'using VQE'. The paper's own data contradict this. For N=1961, Babai returns bop=(0,4,4,242) (Eq. 22). The Hamiltonian of §3.1 is F(x)=||t−bop−Σ x_i b_i||². Using the reduced basis of Eq. 21, F(0,0,0)=36, which is exactly ||t−bop||². Table 1 reports the VQE optimum as [000] with value 36 and probability 1.0, so the selected displacement is x=(0,0,0) and b_h=bop. The published sr-pair (2025,1) is already encoded in bop: in the original basis bop=0·b1+4·b2+2·b3, giving u=3^4·5^2=2025 and v=1. Hence the factorization 53×37 is obtained from the classical Babai solution alone; the VQE subroutine contributes nothing. This is compounded by Table 2 (7 of 8 runs fail) and Remark 4 (the one success fixes the diagonal order [1,1,2] to match [14]). These facts are internal to the paper: the stated improvement is directly contradicted by its own numerics, independent of any external benchmark.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes replacing the QAOA subroutine in the hybrid Schnorr factoring pipeline of Yan et al. [14] with the Variational Quantum Eigensolver (VQE). The workflow converts integer factorization into a closest-vector problem, applies LLL reduction and Babai's algorithm, and then uses VQE to minimize an Ising Hamiltonian that searches for a displacement improving the Babai solution. The authors report a successful factorization of N = 1961 into 53 and 37, and they also report failed runs for a 5-qubit case and for hyperparameter l = 2. The paper claims that the VQE-assisted algorithm can factor integers and discusses implications for RSA security.","tokens_in":8453,"tokens_out":4195,"duration_ms":36930,"significance":"If the central claim were valid, the paper would provide evidence that a variational quantum eigensolver can replace QAOA in Schnorr's factoring pipeline and improve Babai's CVP solution. The manuscript is commendably transparent about its failures and about the fixed diagonal order, and it makes a useful cautionary replication attempt. However, the reported experimental data contradict the central claim: the lone successful run shows no quantum improvement, and the configuration that succeeds is selected to match [14]. Thus the significance of the claimed result is not currently established.","major_comments":[{"comment":"The central claim that VQE improves Babai's solution is contradicted by the paper's own data. In the successful N = 1961 run, Table 1 lists [000] as the VQE optimum with value 36 and probability 1.0, i.e., x = (0, 0, 0) and b_h = bop. The value 36 equals ||t − bop||^2, and the sr-pair used, (2025, 1), is already encoded in Babai's output bop = (0, 4, 4, 242): using the original basis of Eq. (20), bop = 0·b1 + 4·b2 + 2·b3, giving u = 3^4·5^2 = 2025 and v = 1. Hence the factorization 53 × 37 is produced by classical Babai alone, and the VQE subroutine contributes nothing to this success.","section":"§3.2, §4.1, Table 1"},{"comment":"The successful configuration is selected post hoc. Remark 4 states that the diagonal order [1, 1, 2] was fixed to match [14] even though it is supposed to be a random permutation. Table 2 shows that using the authors' own Algorithm 1 for LLL-reduction, which they demonstrate yields a valid δ-LLL-reduced basis, the same N = 1961 case produces no sr-pair and fails to factor. Thus the single success depends on a known-good lattice ordering and on a specific LLL implementation, not on the proposed VQE method.","section":"Remark 4, Table 2"},{"comment":"Seven of the eight reported runs fail, including all l = 2 runs and both N = 48567227 attempts; the authors attribute this to running each configuration only once with a fixed seed. With a single success that is also the only configuration in which VQE is inactive, the data do not support the conclusion that VQE-assisted Schnorr factoring works, and the claimed 'potential to factorize the targeted integer in specific scenarios' remains an unsupported conjecture.","section":"Table 2"}],"minor_comments":[{"comment":"There is a typo: 'The subsequent method we proceeded was he LLL-reduction algorithm' should read '...was the LLL-reduction algorithm'.","section":"§2.2, after Eq. (8)"},{"comment":"The statement that 'VQE does not need it actually' is misleading because bop is still used to construct the Hamiltonian H; the sentence should clarify that VQE does not use bop as an initial ansatz, not that bop is unnecessary.","section":"§3.2"},{"comment":"The table would be clearer if the caption explicitly noted that the selection [000] corresponds to x = (0, 0, 0) and therefore b_h = bop, since this is the key observation for evaluating the quantum contribution.","section":"§4.1, Table 1 caption"}],"recommendation":"reject","confidential_remarks":"The authors are honest about limitations, but the manuscript's central claim is contradicted by its own data. The work could be recast as a negative or benchmarking study of LLL-implementation sensitivity in Schnorr's algorithm, but in its current form it should not be published as a successful VQE-assisted factoring demonstration."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Thanks for the report. Summary: this is a replication study of Yan et al.'s Schnorr+QAOA factoring paper, swapping QAOA for VQE and reproducing the 3-qubit N=1961 example. The paper is honest and useful in parts, but the central claim does not survive contact with its own data.\n\nWhat's new and good: the authors carefully reimplemented the LLL reduction and found that the pseudocode in [14] does not reproduce their published reduced basis; they trace the discrepancy to fpylll/L2. That is a concrete, checkable finding and a genuine service. They also report all their failures (7 of 8) explicitly, including the failure of the 5-qubit N=48567227 case, and they flag in Remark 4 that the only success fixes the lattice diagonal order [1,1,2] to match [14]. That transparency is to their credit.\n\nThe problem: in the single successful run, VQE returns [000] with probability 1.0. That means the selected displacement is the zero vector, so b_h = bop: the variational step does nothing. The sr-pair (2025,1) and hence the factorization 53×37 are already encoded in the classical Babai solution. Section 3.2's stated goal—improving Babai's approximate solution to find good sr-pairs—is therefore not demonstrated; the quantum subroutine is a spectator. The paper's title and Section 4.1 claim factoring \"using VQE\", but the evidence shows VQE does not contribute. This is not a minor gap; it is the load-bearing claim. The only successful run is a classical factoring pipeline with a fixed, known-good configuration copied from [14].\n\nProportion: the LLL discrepancy is a real contribution, but it is peripheral to the claimed result. The paper would be a decent arXiv note about reproducibility of [14], with the VQE part explicitly labeled as a null result. As a research paper claiming VQE-assisted factoring, it should be rejected.\n\nWho is it for: people working on lattice-based quantum factoring and reproducibility of claimed quantum speedups. It could be a useful reading-group example of how easily a null result gets dressed up as a demonstration.\n\nRecommendation: desk reject as a research claim; if the venue has a comments/replication track, that would be the right home after the authors rewrite the claims to match what the data show.","headline":"A transparent replication note whose central claim—that VQE improves Babai's solution—is contradicted by its own only successful run.","tokens_in":9055,"tokens_out":2334,"would_cite":false,"duration_ms":21526,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["11Y05","81P68","68Q12"],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper claims that VQE can replace QAOA as the quantum subroutine in a hybrid lattice-based factoring pipeline, and demonstrates the factorization of 1961.","keywords":["VQE","Schnorr's algorithm","integer factorization","closest vector problem","smooth relation pairs","hybrid quantum-classical algorithm","lattice basis reduction","RSA"],"falsifier":"Re-run the same VQE pipeline for $N=1961$ with randomized lattice diagonal orders and several seeds, and repeat it for other small semiprimes; if factors appear only for the $[1,1,2]$ configuration taken from the QAOA paper, or no more often than a classical-only Babai baseline, the claim that VQE assists Schnorr factoring is not supported.","tokens_in":7908,"feed_emoji":"🔐","tokens_out":13676,"duration_ms":114500,"temperature":0.7,"pith_summary":"At stake is whether a classical factoring pipeline built on lattice geometry — Schnorr's algorithm, which turns factoring into a search for smooth relation pairs — can be assisted by a variational quantum eigensolver (VQE) instead of the QAOA optimizer used in the 2022 approach it replicates. The paper reports one successful factorization: for $N=1961$, VQE improves Babai's approximate solution to the closest vector problem enough to yield the sr-pair $(2025,1)$, which in turn produces the factors $53$ and $37$. Seven of the eight experimental configurations reported in the paper fail to find sr-pairs, a fact the authors attribute to single-run seeding, VQE returning a single candidate, and Schnorr's assumption-based nature. If the claim generalizes, quantum-assisted factorization gains a second, low-qubit route that could matter for RSA-style cryptography.","feed_headline":"VQE, not QAOA, factors 1961 in hybrid lattice pipeline","feed_subtitle":"A variational quantum eigensolver can stand in for QAOA to find smooth relations and crack a small RSA-style product.","key_machinery":"The load-bearing object is the cost Hamiltonian built around Babai's lattice point. After LLL lattice-basis reduction, the approximate solution $b_{op}$ from Babai's nearest-plane algorithm is used to define $F(x_1,\\dots,x_n)=\\|t-b_{op}-\\sum_i x_i b_i\\|^2$, with binary $x_i\\in\\{0,1\\}$; substituting $x_i=(\\sigma_i^z+I)/2$ turns $F$ into the Ising Hamiltonian $\\hat H$ whose ground state VQE seeks. The minimum selects a lattice vector that encodes a smooth pair $(u,v)$ through the signs of its coordinates; when $u-vN$ is also smooth, the pair is an sr-pair, and solving the resulting modulo-2 linear system yields the factors. Unlike QAOA, VQE does not need Babai's solution as an ansatz, but that solution is still needed to construct the Hamiltonian. Replacing QAOA with VQE shortens the quantum circuit, which the paper argues makes the computation less noise-sensitive on current hardware.","core_discovery":"The authors' central claim, stated in Section 4.1, is that they 'have factored the given number using VQE in a similar way as they did with QAOA in [14]', and that VQE can improve the approximate solution given by Babai's algorithm to obtain sr-pairs. In the demonstrated case, $N=1961$, the $3$-qubit calculation ends with the VQE ground state $[000]$, which leads to the sr-pair $(2025,1)$ — in fact the fourth sr-pair of the QAOA paper — and solving the linear system gives the factors $53$ and $37$. The paper also reports that seven of its eight attempted configurations failed to find sr-pairs; it attributes this to single-seed runs, VQE producing only one candidate, and the strength of Schnorr's assumption. The successful run fixes the lattice diagonal order to $[1,1,2]$, the same order used in the replicated QAOA work.","pith_inferences":["The paper leaves open whether VQE itself, rather than the fixed $[1,1,2]$ lattice diagonal order borrowed from the QAOA work, is what produces the sr-pair; a direct test would randomize the diagonal permutation across many runs.","A natural extension is to seed VQE with several Babai candidates or to use excited-state VQE to obtain multiple lattice vectors per run, which could raise the sr-pair yield that the single-candidate output currently limits.","The classical stages — lattice reduction, Babai's algorithm, and smoothness checking — dominate the pipeline, so isolating their failure rate from the quantum subroutine's would show where the bottleneck actually lies.","The success probability of the method is essentially unmeasured because each configuration was run once; a multi-seed benchmarking study would convert the reported yes-or-no results into a rate."],"forward_implications":["VQE can stand in for QAOA in a Schnorr-style factoring pipeline, providing at least one concrete integer factorization as a proof of concept.","Because VQE circuits are shorter, the hybrid approach may be less susceptible to noise on near-term quantum hardware than the QAOA version it replaces.","A single VQE run returns one lattice candidate, so repeated runs or adjusted hyperparameters would be needed to make the method reliable; the successful $3$-qubit case is the existence proof.","For larger targets the method does not scale trivially, since increasing the qubit count from $3$ to $6$ or $10$ in the reported experiments did not produce factors.","If the approach can be made reliable, the practical consequence is a potential low-qubit quantum threat to RSA-style cryptography, because even one successful factorization of a target integer compromises the key."],"supporting_citations":[{"why":"It supplies the QAOA-based hybrid factoring pipeline being replicated, including the $N=1961$ example, the $[1,1,2]$ diagonal order, and the fourth sr-pair $(2025,1)$.","marker":"[14]"},{"why":"It defines Schnorr's original construction that turns factoring into finding smooth relation pairs through lattice approximation.","marker":"[10]"},{"why":"It provides Babai's nearest-plane algorithm, whose approximate solution $b_{op}$ is the starting point that VQE tries to improve.","marker":"[1]"},{"why":"It supplies the sr-pair extraction implementation used by the authors and flags scalability issues in the QAOA method that motivate the VQE variant.","marker":"[6]"},{"why":"It gives the original LLL lattice-reduction algorithm, which is needed to prepare a basis on which Babai's algorithm can run.","marker":"[7]"},{"why":"It describes the floating-point lattice-reduction technique that reproduces the reduced basis and Babai output reported in the replicated paper.","marker":"[8]"}],"fun_headline_variants":["VQE replaces QAOA to factor 1961","Hybrid VQE cracks 1961, not QAOA","VQE steps in for QAOA to factor 1961","VQE assists Schnorr to factor 1961"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The factorization rests on treating the fixed diagonal order $[1,1,2]$ as an acceptable experimental choice, because with the authors' own lattice-reduction code and that same order, no sr-pair is found and the factorization of $N=1961$ fails.","fun_headline_variants_meta":{"raw":{"variants":["VQE replaces QAOA to factor 1961","Hybrid VQE cracks 1961, not QAOA","VQE steps in for QAOA to factor 1961","VQE assists Schnorr to factor 1961"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000793,"raw_usage":{"total_tokens":3458,"prompt_tokens":878,"completion_tokens":2580,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":494,"completion_tokens_details":{"reasoning_tokens":2513}},"tokens_in":494,"tokens_out":2580,"duration_ms":17806,"temperature":1.0,"reasoning_tokens":2513,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T12:53:28.451679+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the same VQE pipeline for $N=1961$ with randomized lattice diagonal orders and several seeds, and repeat it for other small semiprimes; if factors appear only for the $[1,1,2]$ configuration taken from the QAOA paper, or no more often than a classical-only Babai baseline, the claim that VQE assists Schnorr factoring is not supported.","supporting_citations":[{"cited_title":"In: Davies, D.W","cited_arxiv_id":null,"evidence_quote":"It defines Schnorr's original construction that turns factoring into finding smooth relation pairs through lattice approximation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It provides Babai's nearest-plane algorithm, whose approximate solution $b_{op}$ is the starting point that VQE tries to improve."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It gives the original LLL lattice-reduction algorithm, which is needed to prepare a basis on which Babai's algorithm can run."},{"cited_title":"Q., Stehlé, D.: An LLL algorithm with quadratic complexity, SIAM Journal on Computing, 39(3), 874-903 (2009)","cited_arxiv_id":null,"evidence_quote":"It describes the floating-point lattice-reduction technique that reproduces the reduced basis and Babai output reported in the replicated paper."}],"review_version":1}