{"id":"afa45ee5-9799-42ce-956c-6191a9412926","arxiv_id":"2411.08177","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"Belief propagation with guided decimation, enhanced with damping and adjusted initial log-likelihood ratios, performs competitively on erasure channels for several quantum LDPC codes, approaching the vertical-horizontal decoder's performance.","lead":"This paper applies a belief-propagation decoder with guided decimation to quantum erasure channels and shows that adding damping and adjusting initial confidence values makes it competitive with existing erasure decoders for several quantum LDPC code families. The work is relevant because erasure conversion is being demonstrated in neutral atoms, trapped ions, and superconducting qubits, so efficient erasure decoders are directly useful for fault-tolerant quantum computing.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'general-purpose solution' claim rests on per-code, per-rate grid-searched hyperparameters; without a fixed-parameter or holdout demonstration, the reported curves may reflect tuning rather than algorithmic strength.","rationale":"BPGD's unadjusted version is not uniformly better than pruned peeling (Section V), so the reported improvements in Figures 1-3 come from the damping and LLR-scaling modifications in Section IV. Those modifications depend on copt and gamma, which are found by grid search for each code and each erasure rate (Tables 1–3). The paper's own description 'To select the optimal value of copt, we performed experiments over different ranges of values for different erasure rates' makes clear that the plotted failure rates are the result of tuning on the same data used for evaluation. This is the weakest point because the 'general-purpose solution' claim in the abstract and conclusion is supported only by three tuned curves; if the parameters are fragile or code-specific, the curves do not establish general applicability. A holdout-based evaluation, or a demonstration that a single reasonable parameter choice works across the tested codes and rates, would resolve this. The comparison to VH is a secondary issue because the VH code from [27] is a fixed public baseline and the paper does not claim to beat VH, only to approach it. The absence of released code is also secondary because the algorithm is described algorithmically and the baseline code is public. Overall, the conditional verdict is appropriate; the added value here is a concrete test that would either validate or falsify the generalization claim.","tokens_in":13154,"tokens_out":4620,"duration_ms":46697,"concrete_test":"Select (copt, gamma) on a training subset of erasure rates for a given code (e.g., p = 0.10, 0.14, 0.18, 0.22, 0.26 for [[1600,64]]) by grid search, freeze them, and evaluate BPGD on the held-out rates (e.g., p = 0.08, 0.12, 0.16, 0.20, 0.24, 0.28, 0.30, 0.32). If the held-out failure rates exceed the reported tuned curves by more than the simulation uncertainty, the reported performance is overfit to the test points. Repeat for [[2025,81]] and B1 to test cross-code generalization.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section IV states that optimized copt and gamma values are found by grid search for each code and each erasure rate (Tables 1–3), and Section V plots failure rates using those same tuned values. The paper never evaluates a single fixed (copt, gamma) across rates or codes, nor a selection rule that avoids using the test data. This matters because the unadjusted BPGD does not uniformly outperform pruned peeling: for the [[2025,81]] code it is worse, and for the B1 code it 'does not uniformly outperform pruned peeling.' Thus the headline advantage of 'adjusted' BPGD comes entirely from the tuned parameters, and the central claim of a 'general-purpose solution' generalizes from three codes only if those parameters generalize. Without holdout tests, the reported curves are consistent with overfitting to the plotted points.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript applies belief propagation with guided decimation (BPGD) to the quantum erasure channel, modifying the decoder by adjusting the prior LLRs of non-erased qubits and by damping variable-to-check messages. It reports Monte Carlo simulation results for two hypergraph product codes and one lifted-product code, comparing BPGD against peeling, pruned peeling, vertical-horizontal (VH), and maximum-likelihood decoders. The main claims are that BPGD outperforms peeling and pruned peeling, that adding damping and adjusted LLRs brings BPGD close to VH performance for HGP codes while retaining lower complexity, and that BPGD is an effective general-purpose erasure decoder across the quantum LDPC landscape.","tokens_in":13405,"tokens_out":4392,"duration_ms":46426,"significance":"The paper's strength is its direct empirical comparison of a simple, natural adaptation of BPGD against several established erasure decoders on nontrivial quantum LDPC codes, including an honest account of the cases where unadjusted BPGD does not outperform pruned peeling. If the reported performance were obtained with a principled parameter-setting rule, the finding that tuned BPGD approaches VH performance would be a useful contribution. However, the quantitative claims are not yet established: the optimal values of copt and γ are selected by grid search on the same failure-rate data used for the plots, no holdout or fixed-parameter evaluation is reported, no error bars are shown, and the complexity advantage is asserted without complexity analysis. As presented, the results demonstrate that tuned BPGD can perform well on three specific codes, but they do not support the 'general-purpose solution' conclusion.","major_comments":[{"comment":"The optimal values of copt and γ are obtained by grid search over the same simulation data that is later plotted as the failure-rate curves, with different parameter values reported for each code and each erasure-rate interval. This makes the plotted curves post-selection optima, and the paper provides no test on held-out codes or rates, nor any parameter-selection rule that avoids using the test data. Since the claimed advantage of adjusted BPGD over pruned peeling depends entirely on these tuned values, the central 'general-purpose solution' conclusion is not supported as stated. A concrete remedy would be to select (copt, γ) on one code or one rate and evaluate on others, or to show that the optimal parameters vary smoothly enough that a simple fixed or cross-validated rule recovers the same curves.","section":"§IV, Tables 1–3 and §V, Figs. 1–3"},{"comment":"The paper itself concedes that unadjusted BPGD performs worse than pruned peeling for the [[2025,81]] HGP code and 'does not uniformly outperform pruned peeling' for the B1 code. Thus the reported advantage of BPGD over pruned peeling is entirely due to the per-code, per-rate tuning described in Section IV. This is a load-bearing distinction: the abstract and conclusion claim that BPGD is an effective general-purpose solution, but the empirical content only shows that carefully tuned BPGD can outperform the baselines on the three tested instances. I would ask the authors to present a comparison under a single fixed parameter-setting protocol, or to clearly limit the claim to 'tuned BPGD' with a stated selection method.","section":"§V, Figs. 2–3 and §VI, Conclusion"},{"comment":"The manuscript repeatedly claims a 'significant computational advantage' and 'substantially lower' complexity compared to the VH decoder, but no complexity analysis or runtime measurement is provided. Algorithm 1 runs up to n rounds of BP, each with T iterations and message updates that are at least linear in the number of edges; a naive implementation could scale as O(T n^2) or worse, depending on code degree. To make the computational-advantage claim credible, the authors should state the per-round and total complexity of BPGD in terms of n and code parameters, and compare it explicitly with the O(n^2) complexity quoted for VH.","section":"Introduction and §VI, Conclusion"},{"comment":"The heuristic justification in Section III-D states that after peeling stops, BPGD 'simply guesses bits in the stopping set randomly and continues decoding,' adding that 'some of the guesses will be correct and the others can hopefully be absorbed by the stabilizer.' This is presented with no guarantees and no analysis of when such guess-and-continue succeeds or fails. Given that the paper's main claim is that BPGD is a general-purpose decoder, a failure-mode analysis or at least a detailed empirical characterization of when the guided-decimation guesses fail would be needed to substantiate that claim.","section":"§III-D, Algorithm 1"}],"minor_comments":[{"comment":"In Algorithm 1, the decimation chooses vi = arg max γ(vi), but γ is never defined in the algorithm as a reliability measure; in Section IV-B the symbol γ denotes the damping factor. The pseudocode should instead write arg max |m_v| or introduce a separate symbol for the LLR magnitude.","section":"§III-D, Algorithm 1, line 12"},{"comment":"The phrase 'In the content of BPGD decoding' appears to be a typo; it should read 'In the context of BPGD decoding.'","section":"§IV-A, line after Eq. (15)"},{"comment":"The sentence 'Due to its good performance for channels with erasures and channels with erros' contains a typo: 'erros' should be 'errors.'","section":"§VI, Conclusion"},{"comment":"The erased bits are assigned µ_vi = llr_min and non-erased bits µ_vi = llr_max, but the text says erased bits should have LLR 0 while llr_min is described as 'a very small value, llr_min≈0.' If llr_min is not exactly zero, the statement in Section III-D is slightly imprecise; please clarify the exact values and the rationale for using a nonzero value.","section":"§III-D, Algorithm 1, lines 3–5"},{"comment":"The figure captions state that the number of simulations per data point was chosen to ensure short error bars, but no error bars are shown in any figure. Please either show confidence intervals or explicitly state the estimated failure rates and their statistical uncertainty.","section":"§V, Figs. 1–3"},{"comment":"The tables label the values as 'optimized,' but the text does not specify the grid resolution or the exact criterion used to select them (e.g., minimum mean failure rate over some range). Stating the grid and the selection criterion would improve reproducibility.","section":"Tables 1–3"},{"comment":"Reference [47] is listed as 'M. T. S.' which is an incomplete author name; the full author list should be provided.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is a compact empirical study that fits the journal's scope, but the headline claims are stronger than the evidence. The per-rate grid-search tuning on the same data is the central problem: it makes the plotted curves post-selection optima, and the paper provides no cross-validation or fixed-parameter demonstration. The missing complexity analysis for the claimed computational advantage is also a substantive gap. With additional experiments using a principled parameter-selection rule and a complexity statement, the contribution could be made solid; without those, I would not recommend acceptance in its current form. I also note that the authors state that the VH decoder from [27] was used with its default settings, so the performance gap between BPGD and VH might be implementation-specific rather than fundamental."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe short version: this is a useful but incremental decoder paper. The authors apply BPGD to the quantum erasure channel, add two well-known stabilizers—damping and a scaled prior on non-erased bits—and show that the combination gets close to the VH decoder on two HGP codes and beats pruned peeling on a lifted product code. The B1 code result is the most interesting: BPGD with adjustments tracks ML far better than pruned peeling does. The writing is clear and honest; they openly state that unadjusted BPGD does not uniformly beat pruned peeling and that the parameters were chosen by grid search.\n\nThe soft spot is exactly that grid search. Tables 1–3 give per-code, per-rate values of copt and gamma, selected to minimize failure rates on the same data that later appears in the figures. For the [[2025,81]] code, plain BPGD is worse than pruned peeling; all of the reported advantage comes from the tuned parameters. So the curves are plausible upper bounds on what the decoder can do, not a demonstration of a robust general-purpose algorithm. The authors would need either a fixed parameter setting across rates, a holdout evaluation, or a principled selection rule to make that stronger claim. The complexity advantage over VH is also asserted but never quantified; BPGD runs BP multiple times, so a simple 'reduced complexity' needs a real analysis. And there is no released code or error bars, which makes independent verification harder.\n\nNone of this is fatal. The qualitative conclusion—that damping and scaled LLRs meaningfully improve BPGD convergence on erasures—is well supported. The paper deserves a serious referee; a good report would ask for a fixed-parameter or holdout experiment, code release, and at least a heuristic for setting the hyperparameters without per-rate simulation. I'd cite it as the erasure variant of BPGD, with a mental footnote about the tuning.","headline":"Useful incremental results on BPGD for erasures, but the 'general-purpose' claim outruns evidence that is tuned per code and rate on the same data.","tokens_in":13817,"tokens_out":3584,"would_cite":true,"duration_ms":38234,"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":"BPGD, with two small tuning adjustments, is a general-purpose decoder for quantum erasure channels.","keywords":["quantum LDPC codes","erasure decoding","belief propagation","guided decimation","damping","log-likelihood ratio initialization","hypergraph product codes","lifted product codes"],"falsifier":"Fix the tuning parameters found for the [[1600,64]] hypergraph-product code at erasure rate 0.1, run BPGD on a different quantum LDPC code of a different rate without retuning, and compare with the vertical-horizontal decoder; a failure rate that jumps well above the tuned-curve gap would show the parameters do not transfer.","tokens_in":12986,"feed_emoji":"⚛️","tokens_out":6351,"duration_ms":58748,"temperature":0.7,"pith_summary":"The paper sets out to show that belief propagation with guided decimation (BPGD), a decoder previously applied to bit-flip and depolarizing noise, also works well on quantum erasure channels. The natural adaptation is to assign erased qubits a near-zero log-likelihood ratio and known qubits a large positive ratio, so that belief propagation starts from the erasure locations. The paper then shows that scaling down that large ratio by a factor $c_{\\mathrm{opt}}$ and damping the message updates by a factor $\\gamma$ improves convergence, so that BPGD beats peeling and pruned peeling on two hypergraph-product codes and a lifted-product code, and approaches the vertical-horizontal decoder with lower computational cost. The conclusion is that BPGD is an effective general-purpose erasure decoder across the quantum LDPC landscape.","feed_headline":"BPGD decoder approaches best erasure decoders at lower cost","feed_subtitle":"Tuned priors and damping bring BPGD close to specialized decoders for quantum LDPC codes at lower complexity.","key_machinery":"The load-bearing mechanism is guided decimation: each round runs belief propagation for a fixed number of iterations; if the hard decision does not match the syndrome, the variable node with the largest belief magnitude is fixed to its most likely value, and belief propagation is rerun. On erasure channels this is initialized by setting the log-likelihood ratio of each erased bit to $\\mathrm{llr}_{\\min}\\approx 0$ and each non-erased bit to $\\mathrm{llr}_{\\max}=25$. Two tuning parameters carry the performance gain: $c_{\\mathrm{opt}}\\in[0,1]$ scales down the confident priors, and $\\gamma\\in[0,1]$ damps each variable-to-check update as a weighted average of old and new messages.","core_discovery":"The paper's central claim is that BPGD's guided decimation breaks the stopping-set deadlock that limits peeling decoders on quantum LDPC erasures: when belief propagation stalls, fixing the most reliable undecimated bit and rerunning belief propagation produces guesses that are often harmless, because an X-stabilizer fully covered by erasures can absorb the difference. The paper shows this mechanism works on erasures once the channel priors are set correctly, and that two small modifications—scaling the confident priors with $c_{\\mathrm{opt}}$ and damping variable-to-check messages with $\\gamma$—turn a decoder that is merely competitive into one that approaches the vertical-horizontal decoder on hypergraph-product codes and maximum likelihood on a lifted-product code. The supporting evidence is simulation-based, on codes of length 882, 1600, and 2025.","pith_inferences":["The paper tunes $c_{\\mathrm{opt}}$ and $\\gamma$ by grid search on the same curves it plots; a transferable protocol for setting these parameters automatically (for example, from the code's degree distribution or the observed syndrome weight) would be needed to make the 'general-purpose solution' claim robust.","The threshold-like behavior reported for the lifted-product code suggests erasure decoding of quantum LDPC codes may admit a density-evolution or finite-length-scaling analysis analogous to classical LDPC erasure thresholds; the paper does not attempt this.","The random-guessing interpretation of BPGD on stopping sets could be quantified: if each guessed bit is correct with probability near $1/2$ and stabilizers absorb a constant fraction of mistakes, one might predict the observed failure-rate floor from the stopping-set statistics alone.","A natural test bed is a mixed erasure-plus-Pauli channel, where BPGD's prior LLR could be set from the erasure probability and the residual Pauli error rate; the paper mentions this as motivation but does not simulate it."],"forward_implications":["On the tested hypergraph-product codes, BPGD with erasure-adapted priors outperforms both peeling and pruned peeling, and with damping or adjusted LLRs it approaches the failure rate of the vertical-horizontal decoder.","On the lifted-product B1 code, adjusted BPGD is much closer to maximum-likelihood decoding than pruned peeling, and displays a sharp threshold-like transition rather than the slow decay typical of pruned peeling.","Because BPGD already handles bit-flip and depolarizing noise, the same decoder is a candidate for channels that combine erasures and ordinary errors, a regime the paper notes is likely when erasure conversion is used.","BPGD offers a lower-complexity alternative to the vertical-horizontal decoder for hypergraph-product codes, trading a small performance gap for substantially lower computational cost."],"supporting_citations":[{"why":"Supplies the peeling, pruned-peeling, and vertical-horizontal baselines plus the two hypergraph-product codes whose simulation curves are reproduced.","marker":"[27]"},{"why":"Introduces belief propagation with guided decimation for quantum LDPC codes under bit-flip and depolarizing noise, the decoder this paper adapts to erasures.","marker":"[28]"},{"why":"Supplies the B1 lifted-product code used for the near-maximum-likelihood demonstration.","marker":"[45]"},{"why":"Defines the quantum erasure channel noise model used throughout the paper.","marker":"[12]"},{"why":"First introduces belief-propagation decoding for quantum LDPC codes, the starting point of the BPGD pipeline.","marker":"[6]"},{"why":"Provides the lifted-product construction that generalizes hypergraph products and underlies the B1 code.","marker":"[36]"},{"why":"Supplies the factor-graph and sum-product update rules on which the BP rounds in BPGD rest.","marker":"[37]"}],"fun_headline_variants":["BPGD erasure decoding rivals specialized decoders","Adding damping boosts BPGD for erasure decoding","Erasure decoding with BPGD: competitive and tunable","BPGD erasure decoder: competitive, with tweaks to beat best"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the two tuning knobs, chosen by grid search on the same simulations used to plot the results, will keep working on other codes and erasure rates; if those choices are fragile, the claim that BPGD is a general-purpose erasure decoder is not established.","fun_headline_variants_meta":{"raw":{"variants":["BPGD erasure decoding rivals specialized decoders","Adding damping boosts BPGD for erasure decoding","Erasure decoding with BPGD: competitive and tunable","BPGD erasure decoder: competitive, with tweaks to beat best"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000655,"raw_usage":{"total_tokens":2983,"prompt_tokens":912,"completion_tokens":2071,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":528,"completion_tokens_details":{"reasoning_tokens":2002}},"tokens_in":528,"tokens_out":2071,"duration_ms":14750,"temperature":1.0,"reasoning_tokens":2002,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T21:52:50.974686+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Fix the tuning parameters found for the [[1600,64]] hypergraph-product code at erasure rate 0.1, run BPGD on a different quantum LDPC code of a different rate without retuning, and compare with the vertical-horizontal decoder; a failure rate that jumps well above the tuned-curve gap would show the parameters do not transfer.","supporting_citations":[{"cited_title":"Degenerate Quantum LDPC Codes With Good Finite Length Performance,","cited_arxiv_id":null,"evidence_quote":"Supplies the B1 lifted-product code used for the near-maximum-likelihood demonstration."},{"cited_title":"Sparse-g raph codes for quantum error correction,","cited_arxiv_id":null,"evidence_quote":"First introduces belief-propagation decoding for quantum LDPC codes, the starting point of the BPGD pipeline."},{"cited_title":"Quantum LDPC codes with a lmost linear minimum distance,","cited_arxiv_id":null,"evidence_quote":"Provides the lifted-product construction that generalizes hypergraph products and underlies the B1 code."},{"cited_title":"Factor gr aphs and the sum- product algorithm,","cited_arxiv_id":null,"evidence_quote":"Supplies the factor-graph and sum-product update rules on which the BP rounds in BPGD rest."}],"review_version":1}