{"id":"9c7c2b23-e0f1-4a03-8a93-9e7c756cd410","arxiv_id":"2606.18240","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Degeneracy in quantum LDPC codes equals classical code shortening at the decoder, enabling impulse decoding that beats BP+OSD plus a residual-error follow-up step.","lead":"The paper links degeneracy in quantum stabilizer codes to classical code shortening and introduces impulse decoding for quantum LDPC codes. This new parallel decoder outperforms belief propagation with ordered statistics decoding under code-capacity and circuit-level noise with lower complexity.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Equivalence of degeneracy to decoder-side shortening may not preserve all correctable error patterns without new failure modes in the derived impulse decoder.","rationale":"The reader's weakest assumption directly identifies the same gap: turning the claimed equivalence into a working decoder whose advantage survives the tested noise models. Because the abstract supplies no explicit mapping or proof sketch, the load-bearing risk is precisely whether that mapping is exact rather than heuristic. No other internal inconsistency is visible from the given material.","tokens_in":1720,"tokens_out":344,"duration_ms":23265,"concrete_test":"Take the smallest quantum LDPC code appearing in the paper's numerical results; enumerate all weight-≤d/2 errors, apply the impulse-decoding rule as defined in the manuscript, and check whether every degenerate error is mapped to a valid shortened syndrome whose correction matches the original code's logical action. If any error is misclassified, the equivalence is incomplete.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim requires that degeneracy (multiple equivalent errors) maps exactly onto classical shortening performed at the decoder, such that impulse decoding recovers the same logical outcomes as an optimal decoder on the original code. This mapping must be shown to be faithful: every degenerate coset leader must correspond to a shortened-code syndrome without introducing undetectable logical errors or altering the effective distance. If the construction in the full text relies on an implicit assumption that the parity-check matrix admits a uniform shortening rule across all stabilizers (e.g., without case-by-case handling of weight-2 or higher stabilizers), the performance advantage over BP+OSD could vanish or reverse under circuit-level noise where residual errors interact with the shortening.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper claims that degeneracy in quantum stabilizer codes (multiple equivalent error estimates with no classical counterpart) is equivalent to the classical operation of shortening a linear block code, but performed at the decoder rather than the encoder. Leveraging this, it introduces 'impulse decoding'—a parallel scheme for quantum LDPC codes that significantly outperforms belief propagation with ordered statistics decoding (BP+OSD) and other methods under both code-capacity and circuit-level noise, at lower complexity. A second algorithm for decoding residual errors is proposed; when combined with impulse decoding it yields further gains under circuit-level noise.","tokens_in":1861,"tokens_out":520,"duration_ms":31877,"significance":"If the equivalence is shown to be faithful (i.e., the decoder-side shortening preserves all correctable cosets without new undetectable logical errors) and the reported performance advantage holds for the tested quantum LDPC constructions, the work would supply a missing coding-theoretic interpretation of degeneracy and a practical, lower-complexity decoder for codes relevant to scalable fault tolerance. The explicit link to classical shortening and the parallel nature of the decoder are potentially useful strengths.","major_comments":[{"comment":"The central claim requires that the mapping from degenerate cosets to shortened syndromes is faithful: every degenerate coset leader must correspond to a shortened-code syndrome without introducing undetectable logical errors or altering the effective distance. This mapping is load-bearing for the assertion that impulse decoding recovers the same logical outcomes as an optimal decoder on the original code and for the claimed performance gains over BP+OSD under circuit-level noise. The manuscript must supply an explicit construction or proof that the parity-check matrix admits a uniform shortening rule across stabilizers (without case-by-case handling of weight-2 or higher stabilizers) that does not create new failure modes when residual errors interact with the shortening.","section":"Section presenting the equivalence and impulse decoding construction"}],"minor_comments":[{"comment":"The abstract states that impulse decoding 'significantly outperforms' BP+OSD 'with significantly lesser complexity' but supplies no quantitative metrics, code parameters, or noise-model details; adding these would allow readers to assess the scope of the gains.","section":"Abstract"},{"comment":"Performance claims under circuit-level noise should be accompanied by explicit statements of the noise model parameters, number of Monte Carlo trials, and any post-selection or fitting procedures used to generate the reported curves.","section":"Performance evaluation section"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their careful reading and constructive comments. We address the major comment below and will revise the manuscript to incorporate an explicit construction and proof as requested.","responses":[{"response":"We agree that a rigorous demonstration of the faithfulness of the mapping is essential. The manuscript establishes the equivalence by interpreting degeneracy as shortening performed at the decoder rather than the encoder. In the revised version, we will add an explicit uniform shortening rule derived from the parity-check matrix structure that applies consistently to all stabilizers without case-by-case handling based on weight. We will also include a proof that this rule maps every degenerate coset leader to a valid shortened syndrome, preserves all correctable cosets, introduces no new undetectable logical errors, and does not alter the effective distance. The proof will further address interactions between residual errors and the shortening operation under circuit-level noise, confirming that impulse decoding achieves the same logical outcomes as an optimal decoder on the original code.","revision_made":"yes","referee_comment":"[Section presenting the equivalence and impulse decoding construction] The central claim requires that the mapping from degenerate cosets to shortened syndromes is faithful: every degenerate coset leader must correspond to a shortened-code syndrome without introducing undetectable logical errors or altering the effective distance. This mapping is load-bearing for the assertion that impulse decoding recovers the same logical outcomes as an optimal decoder on the original code and for the claimed performance gains over BP+OSD under circuit-level noise. The manuscript must supply an explicit construction or proof that the parity-check matrix admits a uniform shortening rule across stabilizers (without case-by-case handling of weight-2 or higher stabilizers) that does not create new failure modes when residual errors interact with the shortening."}],"tokens_in":1360,"tokens_out":365,"duration_ms":27646,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main point is that degeneracy in quantum stabilizer codes gets recast as shortening the underlying classical code, but done at the decoder instead of the encoder. From that they derive impulse decoding, a parallel scheme they say beats belief propagation with ordered statistics decoding on both code-capacity and circuit-level noise while using less complexity; they also add a residual-error step for extra gains under circuit noise.\n\nThe explicit link between degeneracy and shortening is the genuinely new piece. Prior work treated degeneracy mostly as a nuisance or as something to exploit in minimum-weight decoding, but this framing gives it a direct classical operation to work with. If the mapping is faithful, it explains why certain error patterns behave the way they do and supplies a concrete way to handle them in parallel.\n\nThe soft spot is whether the shortening rule stays exact across all stabilizers and noise models. The stress-test concern is real: if the construction assumes a uniform shortening that does not cover every degenerate coset leader, or if it interacts badly with residual errors in circuit-level noise, the reported gains could shrink or reverse. The abstract gives no equations or tables, so the full text needs to show the precise mapping, the failure-mode analysis, and the actual performance numbers on concrete codes.\n\nThis is for people already working on decoding quantum LDPC codes. A reader who needs practical decoders for fault tolerance will get value from the new angle even if they adapt the method. The work is coherent on its own terms and addresses a real gap, so it deserves a serious referee.","headline":"The paper maps quantum degeneracy to decoder-side classical shortening and builds an impulse decoder that claims better performance than BP+OSD for quantum LDPC codes.","tokens_in":2362,"tokens_out":382,"would_cite":false,"duration_ms":28152,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Degeneracy in quantum stabilizer codes corresponds to shortening the classical code at the decoder rather than the encoder.","keywords":["quantum LDPC codes","degeneracy","code shortening","impulse decoding","belief propagation","ordered statistics decoding","stabilizer codes","quantum error correction"],"falsifier":"Implement impulse decoding on a standard quantum LDPC code under circuit-level depolarizing noise and measure whether the logical error rate is lower than that of BP+OSD at the same computational budget; absence of improvement would falsify the practical utility claim.","tokens_in":2629,"feed_emoji":"","tokens_out":614,"duration_ms":20003,"temperature":0.7,"pith_summary":"The paper shows that the degeneracy of quantum codes, where several different errors produce the same syndrome, has a direct classical counterpart in the shortening operation on linear block codes. This shortening is performed on the decoder side instead of during code construction. The insight leads to a new parallel decoding method called impulse decoding for quantum low-density parity-check codes. This method outperforms belief propagation combined with ordered statistics decoding and other techniques under both code-capacity and circuit-level noise models while requiring significantly less computational effort. A combined approach with residual error decoding yields additional gains specifically under circuit-level noise.","feed_headline":"Decoder-side shortening explains quantum degeneracy","feed_subtitle":"The equivalence enables impulse decoding that outperforms BP+OSD for LDPC codes with lower complexity under circuit noise.","key_machinery":"The equivalence mapping degeneracy to decoder-side shortening of the underlying classical code, which directly motivates the impulse decoding algorithm.","core_discovery":"We demonstrate that degeneracy is closely related to the classical operation of shortening of a linear block code, where the shortening takes place at the decoder. This equivalence enables impulse decoding, a parallel scheme for quantum LDPC codes that significantly outperforms belief propagation with ordered statistics decoding under both code-capacity and circuit-level noise with significantly lesser complexity. An additional algorithm based on decoding of residual errors, when combined with impulse decoding, achieves further performance improvement under circuit-level noise.","pith_inferences":["The decoder-side shortening view may extend to other families of quantum codes beyond LDPC.","Explicit code constructions that anticipate decoder shortening could be designed to minimize degeneracy effects.","Impulse decoding's parallel nature suggests scalability advantages for larger quantum systems."],"forward_implications":["Impulse decoding provides a lower-complexity alternative to BP+OSD for quantum LDPC codes.","Performance gains hold for both code-capacity and circuit-level noise models.","Combining impulse decoding with residual error decoding further reduces error rates under circuit-level noise.","The approach bridges quantum degeneracy to a standard classical coding operation."],"fun_headline_variants":["Decoder shortening equates quantum degeneracy","Quantum degeneracy equals decoder shortening","Degeneracy matches decoder shortening in quantum LDPC","Equivalence of degeneracy and decoder shortening"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The mapping from degeneracy to decoder-side shortening produces a practical algorithm whose performance advantage persists for the quantum LDPC codes and noise models considered.","fun_headline_variants_meta":{"raw":{"variants":["Decoder shortening equates quantum degeneracy","Quantum degeneracy equals decoder shortening","Degeneracy matches decoder shortening in quantum LDPC","Equivalence of degeneracy and decoder shortening"]},"model":"grok-4.3","cost_usd":0.006786,"raw_usage":{"total_tokens":3140,"prompt_tokens":636,"num_sources_used":0,"completion_tokens":48,"cost_in_usd_ticks":67862000,"prompt_tokens_details":{"text_tokens":636,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2456,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":636,"tokens_out":48,"duration_ms":18391,"temperature":1.0,"reasoning_tokens":2456,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-27T00:43:41.581931+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Implement impulse decoding on a standard quantum LDPC code under circuit-level depolarizing noise and measure whether the logical error rate is lower than that of BP+OSD at the same computational budget; absence of improvement would falsify the practical utility claim.","supporting_citations":[],"review_version":1}