{"id":"7f99e420-8b95-40ba-9dd9-89316a568e36","arxiv_id":"2608.07783","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"A multistage rewinding decoder that forces suspicious qubit values in a beam search improves QLDPC decoding over normalized min-sum and approaches BP-OSD-10 performance.","lead":"This paper introduces a rewinding decoder for quantum LDPC codes that forces suspicious qubit values and restarts message passing inside a beam search. It reports large logical error rate gains over normalized min-sum decoding and performance close to a much heavier ordered-statistics decoder.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No trial counts or error bars are reported; the claimed 286× gain at α=0.03 rests on LER estimates near 1e-6 that could be sampling noise.","rationale":"The reader identified the unreliability metric as the weakest assumption and noted missing error bars in the rationale. I agree that the metric's predictive power is untested and important for the method's novelty. However, the single most load-bearing concern for the central claim is the statistical reliability of the reported LER values themselves. The headline result—a 286× gain—depends on LER estimates in the 1e-6 range, which are extremely sensitive to the number of trials. If the true LER is even one order of magnitude higher, the claimed gain drops from two orders of magnitude to one, materially weakening the abstract's statement that the decoder 'significantly outperforms' nMS. The metric concern would affect the explanation of why the decoder works, but the statistical concern affects whether the reported numbers are real. Both are addressable in revision, so the CONDITIONAL verdict is unchanged; the paper should be required to provide trial counts, error bars, and ideally an ablation study of the metric.","tokens_in":14743,"tokens_out":7463,"duration_ms":63768,"concrete_test":"Re-run the [[288,12,18]] simulation at α=0.03 with the multistage decoder, nMS, and nMS-OSD-10, accumulating at least 100 logical errors per decoder (or 10^8 trials as a cap). Report the LER with Wilson 95% confidence intervals and the exact trial counts. If the upper confidence bound of the multistage LER is not at least 10× below the lower bound of the nMS LER, the claimed 286× improvement is not statistically supported.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the proposed decoder significantly outperforms nMS and is competitive with nMS-OSD-10, as demonstrated by LER simulations in Figs. 1 and 4. The paper never states the number of Monte Carlo trials or provides error bars. For [[288,12,18]] at α=0.03, the reported 286× improvement implies the multistage decoder's LER is roughly 1e-6 if nMS is ~3e-4. Estimating an LER of 1e-6 requires accumulating many failures; with 10^6 trials, a single observed failure gives a 95% Wilson CI from roughly 0.03e-6 to 5.6e-6, making the true gain anywhere from about 50× to unbounded. If the multistage curve is based on zero failures, the reported factor is only an upper bound, not a measured LER. The same issue affects the LP Tanner code results and the comparison against nMS-OSD-10, where the two curves may differ by less than the statistical uncertainty. Without trial counts, confidence intervals, or a stopping rule, the numerical claim is not falsifiable and the conclusion is not demonstrated by the presented data. The heuristic metric M_j is also unvalidated by ablation, but the statistical reliability of the headline numbers is the more immediate threat to the central claim.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a multistage rewind decoder for quantum LDPC codes. A syndrome-based normalized min-sum decoder is run to failure, a heuristic unreliability metric M_j (Eqs. 8–12) ranks variable nodes using unsatisfied-check participation, opposing check-to-variable messages, and hard-decision oscillations; the decoder then forces the initial LLRs of the top-K ranked nodes to ±A and restarts message passing inside a beam search with pruning score P(v) (Eq. 25). The algorithm is given as Algorithm 1. Simulations are reported for four bivariate bicycle codes ([[72,12,6]], [[108,8,10]], [[144,12,12]], [[288,12,18]]) and the lifted-product Tanner code [[1054,124,20]], claiming substantial gains over normalized min-sum and competitiveness with nMS-OSD-10, including a reported 286× improvement for [[288,12,18]] at α=0.03.","tokens_in":15061,"tokens_out":4529,"duration_ms":43146,"significance":"If the empirical claims are statistically substantiated, the proposed decoder would be a practically interesting alternative to BP-OSD-type post-processing for finite-rate QLDPC codes, since it replaces matrix-inversion-based post-processing with guided beam search. Strengths of the manuscript include a precise algorithmic specification (Algorithm 1), stage-wise correction diagnostics (Figs. 2 and 5), and a parameter trade-off study for Tmax and K (Figs. 3 and 6). The main gap is statistical: the headline LER claims are presented without trial counts, confidence intervals, or a stopping rule, and the heuristic suspicion metric is not validated by ablation or sensitivity analysis. These issues directly affect the central claim, so the manuscript needs revision before the results can be accepted.","major_comments":[{"comment":"No Monte Carlo trial counts, confidence intervals, or simulation stopping rule are reported anywhere. The headline claim of a 286× improvement over nMS at α=0.03 for [[288,12,18]] implies a multistage LER near 1e-6; with no failure counts, the reported factor could be based on a single observed failure or even zero failures, in which case it is only an upper bound. The same issue affects the two-order-of-magnitude claim for the LP Tanner code and the comparison against nMS-OSD-10. Please report, for each plotted point, the number of trials, the number of logical failures, and Wilson or Clopper-Pearson confidence intervals, together with the criterion used to terminate simulations.","section":"Section V, Figs. 1 and 4, and the text following Fig. 1"},{"comment":"The suspicion metric M_j is the load-bearing component of the search: the decoder spends its beam width on the nodes ranked highest by M_j, and the pruning score P(v) decides which branches survive. However, the weights cU=0.5, cE=0.3, cO=0.2 are stated without justification, and λ_s, λ_ξ, and the forced magnitude A are not specified at all. Figure 3 studies only Tmax and K; it does not test whether the metric's three terms each contribute, nor whether the reported gains are sensitive to these coefficients. Please add ablation experiments removing each term of M_j and a sensitivity analysis over cU, cE, cO, λ_s, λ_ξ, and A, or otherwise provide a principled selection method.","section":"Section III, Eqs. (8)–(12), and Section IV, Eq. (25)"},{"comment":"The claim that the decoder is 'competitive with BP-OSD-10' and 'in some cases outperforms it' is supported by a single baseline comparison: nMS-OSD-10 for [[288,12,18]] in Fig. 1. No OSD baseline is provided for the other three BB codes or for the LP Tanner code [[1054,124,20]], so the broad comparative claim is not demonstrated for those instances. Please either add nMS-OSD-10 curves for the remaining codes or restrict the conclusion to the [[288,12,18]] case for which the comparison is actually shown.","section":"Section V, Fig. 1, and Section VI"}],"minor_comments":[{"comment":"The text states 'at crossover probability α=0.4, the multistage decoder provides a two order of magnitude improvement', but Fig. 4 and the surrounding discussion indicate the intended value is α=0.04; this typo should be corrected.","section":"Section V, paragraph on the LP Tanner code"},{"comment":"Line 15 passes F(v') to FNMS, but the child node was just defined with F(ν'); the argument should be F(ν'). In addition, line 24 selects from S(t+1) while the successful-node set was defined as G(t+1) in Eq. (26); the notation should be made consistent.","section":"Section IV, Algorithm 1"},{"comment":"Equation (8) is typeset as 'M_j = N_j D_j + ε' in the submitted text, which is inconsistent with the description of D_j as a denominator and with the numerical-stability role of ε; it should read M_j = N_j/(D_j + ε) (or N_j/D_j with ε absorbed in D_j).","section":"Section III, Eq. (8)"},{"comment":"The search complexity is not quantified: with W=64, Tmax=11, and K=1, the worst-case number of FNMS runs per syndrome is up to 2·K·W·Tmax = 1408; the paper should report the average number of decoder calls or runtime per frame to support the practical-feasibility discussion in Section V.","section":"Section IV, Eq. (18) and Algorithm 1"},{"comment":"Several references to internal equations are informal ('as discussed in Eq. 8', 'pruning score in Equation P(v)'); these should be replaced with precise equation references, and the notation D_out(v) in Eq. (14)–(15) should be reconciled with the D(ν) notation used in Algorithm 1.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within scope for a quantum error correction / coding theory journal, and the algorithmic idea is plausible. My main concern is statistical reporting: the central quantitative claims are not falsifiable without trial counts and error bars. The heuristic metric also needs at least an ablation study. Both are fixable within the manuscript's scope, so I recommend major revision rather than rejection. There is also a notable reliance on the authors' own prior work, but this does not itself affect the technical assessment."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a legitimate engineering contribution that deserves a serious referee, but the central numerical claims are weaker than the text suggests because the paper reports no trial counts, no error bars, and no stopping rule. The stress-test note lands: at LER ~1e-6, a 286x gain over nMS could easily be sampling noise, and the same applies to the LP Tanner results.\n\nWhat is actually new: the specific combination of a four-feature suspicion metric (unsatisfied-check participation, opposing check messages, hard-decision oscillations, APP reliability) with LLR forcing and beam search in a rewind-and-restart framework for QLDPC codes. That exact mix is not in the cited prior work. The algorithm is precisely specified with pseudocode and equations, the stage-correction statistics are a nice diagnostic, and the parameter-sensitivity experiments (Tmax vs K) are a real attempt to understand the search behavior. The paper is honest that the metric is heuristic.\n\nSoft spots, in order of importance. First, the statistical reliability problem: no trial counts, no error bars, and the 286x claim rests on an estimated LER near 1e-6 that is not falsifiable from the data shown. This is the load-bearing issue. Second, the decoder has many hand-tuned hyperparameters (cU, cE, cO, lambda_s, lambda_xi, A, epsilon, beta, W, K, Tmax) and no ablation isolating the contribution of each metric component. Third, missing baselines: no comparison to BPGD or to the beam-search decoders of [29] and [30], which are the closest prior art. Fourth, minor presentation issues: the text says \"crossover probability α = 0.4\" where 0.04 is meant, and there are small typos (\"Ni\" for \"Nj\", \"wts\" for \"ws\"). None of these are fatal.\n\nOn the citation pattern: the self-citations are relevant and appropriate, and the related-work coverage is adequate. The paper does not oversell the theory; it sells an empirical decoder, and the empirical case is currently incomplete rather than wrong.\n\nBottom line: this paper is for researchers working on practical QLDPC decoders who want another tool in the toolbox. It deserves peer review, but the referee should require code/data and a proper statistical analysis before acceptance.","headline":"A plausible and well-specified engineering decoder for finite-length QLDPC codes, but the headline LER gains are not statistically demonstrated without trial counts or error bars.","tokens_in":727,"tokens_out":1657,"would_cite":true,"duration_ms":22982,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81P70","94B35"],"pacs":[],"model":"deepseek-v4-flash","headline":"A beam-search rewind that forces the LLRs of the most suspicious qubits lets min-sum decoding of QLDPC codes escape trapping sets and match order-10 ordered-statistics decoding on the tested codes.","keywords":["quantum LDPC codes","trapping sets","degenerate errors","min-sum decoding","beam search","ordered statistics decoding","stabilizer codes","multistage decoding"],"falsifier":"Use the same hyperparameters on the [[288,12,18]] code at $\\alpha=0.03$ but replace the unreliability ranking with a random ordering of qubits; if the logical error rate remains near the reported 286x improvement over nMS, then the metric is not the mechanism that makes the decoder work.","tokens_in":1589,"feed_emoji":"🔁","tokens_out":1614,"duration_ms":62859,"temperature":0.7,"pith_summary":"The paper tries to establish that iterative min-sum decoding of QLDPC codes can be rescued from its two main failure classes—classical trapping sets and degenerate errors on symmetric stabilizers—by rewinding: force the initial LLRs of a small set of suspicious qubits and rerun the decoder. A heuristic unreliability metric ranks qubits using the decoder's own dynamics, and a beam search explores forced configurations with a pruning score that balances residual syndrome weight and average posterior reliability. On bivariate-bicycle codes and a lifted-product Tanner code, the paper reports logical error rates far below normalized min-sum and competitive with belief propagation plus order-10 ordered-statistics decoding. A sympathetic reader would care because the method offers a decoder-only route to near-best post-processing performance without OSD's matrix inversion.","feed_headline":"Rewinding decoder cuts QLDPC logical errors 286-fold","feed_subtitle":"Guided beam search forces suspicious qubits' beliefs and matches BP-OSD-10 at lower cost.","key_machinery":"The load-bearing object is the unreliability metric $M_j = N_j/(D_j+\\epsilon)$, whose numerator $N_j$ is a weighted sum of three decoder-dynamics features—how many residual unsatisfied checks touch qubit $j$, how strongly the unsatisfied checks push against the final posterior sign, and how often qubit $j$'s hard decision oscillated—and whose denominator discounts qubits with large final APP magnitude. Around this ranking, the method builds a beam search: each stage forces the top-$K$ unforced qubits in each active path to $\\pm A$, reruns normalized min-sum, and keeps at most $W$ paths using a pruning score $P(v) = -\\lambda_s w_s(v) + \\lambda_\\xi \\xi(v)$ that rewards low residual syndrome weight and high average posterior magnitude. The metric is what turns an otherwise exponential search over forced values into a guided rewinding procedure.","core_discovery":"The central claim is that the internal dynamics of a failed message-passing decode contain enough information to locate the qubits whose erroneous values keep the decoder trapped, and that forcing their initial log-likelihood values to opposite signs and restarting resolves both classical and quantum trapping sets. The authors formalize this as a beam search over forced configurations, where each node's children are the top-K qubits under the unreliability metric and each child forces one qubit to $+A$ or $-A$. The search stops at the first stage with a zero residual syndrome and chooses the lightest consistent error estimate. They report, for example, a 286x logical-error-rate improvement over normalized min-sum on the [[288,12,18]] BB code at crossover probability 0.03 and a 3.2x improvement over nMS-OSD-10, with comparable or better performance on other tested BB codes and a two-order-of-magnitude gain on the LP Tanner code.","pith_inferences":["The paper fixes $c_U,c_E,c_O$ and the forced magnitude $A$ by hand; a natural extension the authors do not pursue is tuning these per code family, and the reported saturation behavior suggests such tuning could change the gains.","The stage-correction data imply a latency-adaptive decoder could stop after the first few stages or widen the beam only when early stages fail; that adaptive policy is not constructed in the paper.","Because the experiments use only the binary symmetric channel, it remains open whether the rewind mechanism also helps under circuit-level or biased noise, where syndrome errors and error correlations alter the failure dynamics."],"forward_implications":["For the tested BB codes, the multistage decoder reaches or beats the logical error rate of nMS-OSD-10; on [[288,12,18]] at $\\alpha=0.03$ it improves over nMS by 286x and over nMS-OSD-10 by 3.2x.","On the LP Tanner code [[1054,124,20]], it improves the logical error rate by two orders of magnitude at $\\alpha=0.04$ over conventional nMS.","Most failures are corrected in early stages: for BB-288 about 99.35% of successful corrections happen within the first three stages, so beam width can be traded against search depth.","The method targets both classical trapping sets inherited from constituent codes and quantum trapping sets caused by degeneracy, not just one failure class.","Reducing the maximum number of stages from 11 to 3 with a larger top-$K$ parameter substantially mitigates the performance loss, indicating that low-latency configurations are possible."],"supporting_citations":[{"why":"Defines the (a,b) trapping-set taxonomy and quantum trapping sets that motivate the decoder's failure model.","marker":"[13]"},{"why":"Supplies the bivariate-bicycle code family used for the main performance comparisons.","marker":"[7]"},{"why":"Identifies degenerate errors on symmetric stabilizers as the dominant nMS failures for BB codes, the target of the rewinding procedure.","marker":"[15]"},{"why":"Provides the basis for generating the nMS-OSD-10 benchmark that the multistage decoder is compared against.","marker":"[24]"},{"why":"Supplies the beam-search framework that controls the combinatorial growth of forced configurations.","marker":"[38]"},{"why":"Provides the lifted-product Tanner code instance [[1054,124,20]] used in the experiments.","marker":"[44]"},{"why":"Establishes the classical trapping-set ontology that the paper extends to the quantum setting.","marker":"[9]"},{"why":"Introduces ordered-statistics decoding, the post-processing approach whose performance the multistage decoder aims to match at lower cost.","marker":"[20]"}],"fun_headline_variants":["Rewinding decoder slices QLDPC errors 286x","Beam-search rewinds beat nMS on QLDPC codes","Force qubits, rewind decoder: 286x error cut","Multistage rewinding matches BP-OSD at lower cost","Decoder rewinds target trapping sets for 286x gain"],"cache_read_input_tokens":17664,"weakest_assumption_plain":"The entire gain rests on the heuristic score that decides which qubits to rewind; if that ranking is not much better than chance, the beam search wastes its budget and the reported error-rate gains disappear.","fun_headline_variants_meta":{"raw":{"variants":["Rewinding decoder slices QLDPC errors 286x","Beam-search rewinds beat nMS on QLDPC codes","Force qubits, rewind decoder: 286x error cut","Multistage rewinding matches BP-OSD at lower cost","Decoder rewinds target trapping sets for 286x gain"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000234,"raw_usage":{"total_tokens":1504,"prompt_tokens":961,"completion_tokens":543,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":577,"completion_tokens_details":{"reasoning_tokens":454}},"tokens_in":577,"tokens_out":543,"duration_ms":5052,"temperature":1.0,"reasoning_tokens":454,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T04:12:34.131682+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Use the same hyperparameters on the [[288,12,18]] code at $\\alpha=0.03$ but replace the unreliability ranking with a random ordering of qubits; if the logical error rate remains near the reported 286x improvement over nMS, then the metric is not the mechanism that makes the decoder work.","supporting_citations":[{"cited_title":"Trapping Sets of Quantum L DPC Codes,","cited_arxiv_id":null,"evidence_quote":"Defines the (a,b) trapping-set taxonomy and quantum trapping sets that motivate the decoder's failure model."},{"cited_title":"High-threshold and low-overhead fault-toler ant quantum memory,","cited_arxiv_id":null,"evidence_quote":"Supplies the bivariate-bicycle code family used for the main performance comparisons."},{"cited_title":"Enhanced Min-Sum Decoding of Quantum Codes with Iteration Dynamics Memory,","cited_arxiv_id":null,"evidence_quote":"Identifies degenerate errors on symmetric stabilizers as the dominant nMS failures for BB codes, the target of the rewinding procedure."},{"cited_title":"Beam-Stack Search: Integrati ng Backtrack- ing with Beam Search,","cited_arxiv_id":null,"evidence_quote":"Supplies the beam-search framework that controls the combinatorial growth of forced configurations."},{"cited_title":"On the Minim um Distances of Finite-Length Lifted Product Quantum LDPC Cod es,","cited_arxiv_id":null,"evidence_quote":"Provides the lifted-product Tanner code instance [[1054,124,20]] used in the experiments."},{"cited_title":"Trapping set ontology,","cited_arxiv_id":null,"evidence_quote":"Establishes the classical trapping-set ontology that the paper extends to the quantum setting."},{"cited_title":"Degenerate Quantum LDPC Codes With Good Finite Length Performance,","cited_arxiv_id":null,"evidence_quote":"Introduces ordered-statistics decoding, the post-processing approach whose performance the multistage decoder aims to match at lower cost."}],"review_version":1}