{"id":"117026ae-37e7-4cf7-b576-41d21d4d1201","arxiv_id":"2607.29443","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The time-reversed moonwalking surface code with three-state readout and a branch-and-bound decoder reaches p_L ∝ p^d erasure-like scaling without mid-circuit erasure checks under skip-gate leakage.","lead":"An error-correcting circuit called the moonwalking surface code achieves erasure-level error suppression using only end-of-round three-state readout, without mid-circuit erasure checks, when leaked qubits make two-qubit gates skip. This could remove a major experimental overhead for erasure-based quantum computers.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central p_L ∝ p^ℓ claim is established only for ideal three-state readout and zero seepage (Sec. II B, Sec. VI); both corrupt the disjoint erasure-check information that the B&B decoder relies on.","rationale":"The reader's verdict is CONDITIONAL, and its weakest assumption is exactly the ideal three-state readout and no-seepage assumption. My independent stress-test reaches the same conclusion: the paper's central claim is well-supported within its explicitly stated idealized model. The t_E = ℓ result for the moonwalking code under skip-gate leakage is carefully derived from exhaustive enumeration and sampling, the B&B decoder's role is clearly explained, and the paper discloses the slow-decoder and ideal-readout limitations. The most load-bearing concern is not a flaw in the argument but a missing robustness check: real erasure information is imperfect, and seepage breaks the disjointness property that is essential to the decoder and to the t_E bound. I recommend no change to the reader's CONDITIONAL verdict because the current verdict already reflects this conditionality. A concrete simulation with finite readout error and seepage would determine whether the concern materially degrades the predicted scaling or whether the effect is benign at realistic parameter values.","tokens_in":27630,"tokens_out":11693,"duration_ms":481394,"concrete_test":"Extend the Stim simulation of the moonwalking surface code with EC schedule 8 and skip-gate leakage to include a three-state readout misclassification probability q (e.g., 10^-3 and 10^-4) and a per-round seepage probability s (e.g., 10^-3 and 10^-4). Recompute the t_E value for a 3×3 code using the same exhaustive weight-1/weight-2 enumeration as Sec. V A, and re-fit the LER scaling exponent α for ℓ = 3, 5, 7 with the B&B decoder. If t_E drops below ℓ or α falls significantly below 1, the central zero-overhead scaling claim is not robust to these realistic effects.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's zero-overhead erasure-like scaling result is conditional on ideal three-state readout and the absence of seepage. In Sec. II B, mid-circuit erasure checks and three-state readouts are explicitly modeled as 100% fidelity, and the Conclusions (Sec. VI) defer both seepage and incorrect erasure information to future work. This idealization is load-bearing because the B&B decoder's advantage comes from enforcing the disjointness constraint: a triggered erasure check corresponds to exactly one leakage location. With realistic readout misclassification, a false positive or false negative erasure check breaks this one-to-one mapping; with seepage, a leaked qubit can return to the computational subspace and leak again, so leakage locations are no longer disjoint. Both effects therefore invalidate the t_E = d_L = ℓ entry for the moonwalking code in Table IV, and the p_L ∝ p^ℓ scaling in Sec. V B would no longer follow. The paper is explicit that these effects are not modeled, so the headline claim is best understood as an idealized design-space result, not a statement about current hardware. This is a limitation rather than an internal inconsistency, but it is the most load-bearing caveat to the central claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper maps the design space of erasure-qubit error correction for surface codes by considering three leaked-qubit effects (depolarizing, tailored, skip-gate), three syndrome-extraction circuits (static, walking, moonwalking), and four erasure-check schedules. Its central contribution is the moonwalking surface code—the time reversal of the walking surface code—which, when combined with end-of-line three-state readout (EC schedule 8), skip-gate leakage, and a new branch-and-bound decoder, is claimed to achieve t_E = d_L = ℓ and hence erasure-like logical-error-rate scaling p_L ∝ p^ℓ without mid-circuit erasure checks. The evidence is an exhaustive weight-1/2 fault enumeration on a 3×3, 4-round circuit and Stim circuit-level simulations up to ℓ = 11, from which LER scaling exponents and thresholds are fitted.","tokens_in":28033,"tokens_out":8532,"duration_ms":129723,"significance":"If the idealizations hold, this is a significant design-space result. It identifies concrete circuit and decoder conditions under which the doubled erasure-correction capacity of the surface code can be realized without mid-circuit erasure-check overhead, and it explains why the walking surface code fails in the skip-gate regime while the time-reversed moonwalking circuit succeeds. The paper is methodologically transparent: circuits are generated and sampled with Stim, the decoder and sampling code are released on GitHub, and the predicted scaling exponents are checked against independent simulations. It also provides a useful comparative survey across leakage models, check schedules, and circuit geometries. However, the headline result is conditional on ideal three-state readout and the absence of seepage, and both the decoder's finite-bias optimality and the ℓ-scaling verification are only partial. These points need to be addressed or clearly bounded before the claims can be taken as stated.","major_comments":[{"comment":"The headline zero-overhead erasure-like scaling claim relies on ideal three-state readout and zero seepage, as stated in Sec. II B and deferred to future work in Sec. VI. With false positives/negatives in the three-state readout, or with seepage, the one-to-one and disjoint mapping between a triggered erasure check and a unique leakage location breaks—precisely the structure that the branch-and-bound decoder enforces. The t_E = d_L = ℓ entry for the moonwalking code in Table IV and the p_L ∝ p^ℓ scaling in Sec. V B are therefore not established outside this idealization. This is a disclosed limitation rather than an internal inconsistency, but the abstract and conclusions should state the condition explicitly, and it would strengthen the paper to quantify the impact, for example by extending the imperfect-erasure-check framework of Ref. [23] to three-state readout.","section":"Sec. II B, Sec. VI"},{"comment":"The transfer from the 3×3 exhaustive enumeration to ℓ×ℓ codes is asserted through the 'tiled nature' of the surface code. The enumeration rules out weight-1/2 uncorrectable faults only for a distance-3 patch; it does not prove that two leakage events in different tiles of a larger patch cannot produce the same syndrome/erasure-check pattern as an uncorrectable logical error. A rigorous lower-bound argument for arbitrary ℓ, or at least explicit adversarial constructions for ℓ = 5, 7, 9, 11, is needed to support the t_E = d_L = ℓ claim for all ℓ.","section":"Sec. V A, Tables III and IV"},{"comment":"The central moonwalking/EC8/skip-gate combination requires branch-and-bound decoding to reach t_E = ℓ according to Table IV, but Sec. V B states that branch-and-bound decoding was performed only for ℓ ≤ 7. If the α ≈ 1 points at ℓ = 9, 11 come from marginal decoding, they do not test the claimed t_E = ℓ regime. The manuscript should report the ℓ range of every branch-and-bound data point in Fig. 5 and either extend the branch-and-bound simulations to larger ℓ or state explicitly that the large-ℓ scaling is an extrapolation.","section":"Sec. V B, Fig. 5"},{"comment":"The branch-and-bound decoder is claimed to solve the quasi-MLE problem exactly only for infinite erasure bias; for finite erasure bias it is heuristic. Since finite-bias data (e.g., η = 50 in Fig. 5) are used to support the scaling claim, the paper should either provide a stronger optimality argument for finite bias or explicitly characterize the possible failure modes. As written, the finite-bias result is evidence, not a proof, and the text should not imply that the decoder is quasi-MLE-optimal in that regime.","section":"Appendix B 4 b"}],"minor_comments":[{"comment":"The abstract should mention that the result assumes ideal three-state readout and no seepage; these conditions are stated only later in the paper.","section":"Abstract and Sec. II B"},{"comment":"The categorical x-axis with horizontal offsets and many markers is difficult to read; small multiples or separate panels by decay model would improve clarity.","section":"Fig. 5"},{"comment":"Typo: 'leakage a some point' should read 'leakage at some point.'","section":"Footnote [38]"},{"comment":"The EC schedule labels 1/2/4/8 are counterintuitive because they refer to the maximum number of two-qubit gates between checks. The text explains this, but repeating the definition in the Table II caption would prevent reader confusion.","section":"Table II and Sec. III B"},{"comment":"Figures 12 and 13 include Stim-style gate identifiers that are not human-readable. Replacing or annotating these with a schematic circuit diagram would improve reproducibility and accessibility.","section":"Appendix C"}],"recommendation":"major_revision","confidential_remarks":"The paper is within scope for a quantum-information journal and makes a useful design-space contribution. The main barrier to acceptance is that the headline zero-overhead claim is more conditional than the abstract suggests; the ideal three-state-readout and no-seepage assumptions are load-bearing for the central t_E = d_L = ℓ result. A revision that qualifies the claims, clarifies the ℓ range of branch-and-bound data, and ideally quantifies robustness to readout misclassification and seepage would make the contribution suitable for publication. There is no circularity concern: the t_E enumeration is an input to the scaling prediction, and the LER fit parameters are outputs."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The thing to know: the paper's central result—erasure-like LER scaling p_L ∝ p^ℓ without mid-circuit erasure checks, using the moonwalking surface code with three-state readout and skip-gate leakage—holds under explicitly stated ideal conditions. It is a design-space result, not a claim about current hardware. The authors say so themselves in Sec. VI. The stress-test concern about ideal readout and zero seepage is real, but it is a disclosed limitation rather than an internal inconsistency.\n\nWhat's actually new: the observation that time-reversing the walking surface code gives superior leakage fault distance under skip-gate leakage, and the branch-and-bound decoder that enforces the disjointness of leakage locations. Similar circuits appear in Refs. [24,25], but the characterization—t_E = d_L = ℓ for the moonwalking circuit with EC schedule 8—is new. The paper does the systematic work well: three circuits, four erasure-check schedules, three leaked-qubit-effect models, a clean table of fault distances, and LER scalings that match the predicted exponents. The exhaustive weight-1/2 enumeration on the 3×3 circuit with sampling to 10^-6 residual probability is careful, and the code is on GitHub.\n\nSoft spots, in proportion. The biggest is the one the stress-test flags: the decoder's power comes from the one-to-one mapping between a triggered erasure check and a single leakage location. Realistic readout misclassification or seepage breaks that mapping, and the t_E = d_L = ℓ entry in Table IV no longer follows. The paper defers both effects and is upfront about it. That is fine for a design-space study, but the abstract's flavor of zero-overhead erasure performance is easy to over-read. Second, the branch-and-bound decoder is slow, and for finite erasure bias the algorithm is heuristic, not guaranteed quasi-MLE; the paper's own Appendix B 4 says it may fail in pathological cases. Third, the tiling argument from 3×3 to ℓ×ℓ is plausible but not fully formal; the LER simulations up to ℓ=11 help.\n\nWho should read it: anyone choosing between mid-circuit erasure checks and end-of-line three-state readout for a skip-gate platform like dual-rail superconducting or other leakage-skips-gates qubits. It maps the design space cleanly.\n\nRecommendation: send it to peer review. The claim is well-supported under its stated conditions, the limitations are disclosed, and the result is useful. I would ask the authors to add a short discussion of how readout infidelity and seepage scale into the LER, but that can be a revision rather than a blocker.","headline":"Moonwalking circuit result is real but idealization-dependent; worth a serious referee.","tokens_in":28424,"tokens_out":2637,"would_cite":true,"duration_ms":38818,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A time-reversed surface-code circuit can preserve erasure-level error suppression without mid-circuit erasure checks.","keywords":["surface code","erasure qubits","leakage","three-state readout","skip-gate leakage","logical error rate scaling","branch-and-bound decoder","moonwalking surface code"],"falsifier":"Enumerate all pairs of leakage events in a 3×3 moonwalking surface code with three-state readout and skip-gate leakage that produce the same erasure-check and detector outcomes but different logical outcomes. The paper's t_E = ℓ claim predicts no such pair; a single such pair, of the kind the paper itself finds for the walking code, would falsify the central claim.","tokens_in":27602,"feed_emoji":"🌙","tokens_out":7061,"duration_ms":95904,"temperature":0.7,"pith_summary":"Quantum error-correcting codes can correct twice as many erasure errors as ordinary Pauli errors, but exploiting that usually requires mid-circuit erasure checks, which interrupt the circuit and add hardware overhead. This paper tries to show that the same logical performance can be obtained with only an end-of-line three-state readout, a measurement that distinguishes the erased state from 0 and 1, provided leaked qubits make two-qubit gates be skipped. The vehicle is the 'moonwalking surface code,' the time-reversal of the walking surface code, together with a decoder that enforces the fact that a qubit can leak only once. If the argument holds, an ℓ×ℓ code suppresses logical errors as p^ℓ even with no mid-circuit checks, matching the asymptotic advantage of explicit erasure detection for hardware whose leakage naturally skips gates.","feed_headline":"Moonwalking code gets erasure-class scaling without mid-circuit checks","feed_subtitle":"Three-state readout plus skip-gate leakage gives an ℓ×ℓ patch the same p^ℓ error suppression as explicit erasure checks.","key_machinery":"The central object is the moonwalking surface code, the time-reversal of the walking surface code, built by inserting SWAP operations between reset and the first two-qubit gate and commuting them into the circuit so no real swaps or extra depth are needed. It is paired with three-state readout, skip-gate leakage behavior, and a branch-and-bound quasi-MLE decoder. The circuit reassigns data and ancilla roles every round so every qubit is measured and reset every other cycle, letting three-state readout catch all leakage without additional checks. The decoder's load-bearing job is to enforce leakage disjointness: when an erasure check fires, the true leakage location is one of several possibil","core_discovery":"The paper introduces the moonwalking surface code and claims it achieves erasure-like logical error rate scaling, p_L ∝ p^ℓ, without mid-circuit erasure checks. The recipe: use three-state readout wherever the circuit measures; let leaked qubits cause any two-qubit gate they participate in to be skipped; and decode with a branch-and-bound algorithm that enforces that each detected erasure corresponds to exactly one leakage event. Under those conditions the paper finds that the minimum number of leakage events that can produce an uncorrectable logical error is t_E = ℓ, the full code distance, whereas the original walking surface code degrades to t_E = ⌈ℓ/2⌉ under the same schedule because two","pith_inferences":["A direct experimental prediction follows for dual-rail superconducting or trapped-ion systems: a memory experiment with three-state readout, no mid-circuit checks, and leakage that skips gates should show a logical error exponent near 1 in code size, provided readout errors stay below the physical error rate.","The strong dependence on time reversal suggests similar asymmetry could be found in other time-dynamic or foliated circuits; the controlling quantity is the size and nesting of the leakage Pauli envelope between reset and readout.","If finite readout misclassification or seepage is added, the t_E = ℓ bound likely degrades continuously; mapping that crossover is the natural follow-up that would tell experimentalists when mid-circuit checks are actually worth their cost.","The slow branch-and-bound decoder is the main practical bottleneck; a faster decoder that solves the same anti-correlated error problem would make the zero-overhead advantage usable at larger code distances."],"forward_implications":["For an ℓ×ℓ moonwalking surface code with three-state readout only and skip-gate leakage, logical error rate scales as p_L ∝ p^ℓ, equivalent to what explicit erasure detection would give.","The walking surface code, despite using the same gates and readout schedule, only reaches an exponent near 1/2 under skip-gate leakage; the time direction of the circuit changes how many leakage events are correctable.","The static surface code can match the moonwalking scaling with three-state readout only at the cost of a leakage-SWAP gate per data qubit; the moonwalking circuit removes that overhead.","If the decoder does not respect the one-leak-per-qubit constraint, the claimed t_E = ℓ can fail: the paper shows a marginal decoder can misdecode two leakage events in the moonwalking code.","For hardware where leakage instead depolarizes or induces tailored Pauli errors, infrequent checks are not enough — schedules without mid-circuit checks drop to ⌈ℓ/2⌉ distance, so skip-gate behavior is the enabling ingredient."],"fun_headline_variants":["Moonwalking surface code hits full-distance erasure scaling","Zero-overhead erasure scaling via skip-gate leaked qubit handling","Branch-and-bound decoder makes surface code erasure-class without checks","Three-state readout plus leak-skip gives erasure-capacity scaling","Moonwalking code reaches erasure bound with no mid-circuit checks"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The argument assumes the three-state readout is perfect and a leaked qubit never seeps back into the computational subspace; if readout misclassifies leakage or seepage occurs, the erasure information is corrupted and the t_E = ℓ bound need not hold.","fun_headline_variants_meta":{"raw":{"variants":["Moonwalking surface code hits full-distance erasure scaling","Zero-overhead erasure scaling via skip-gate leaked qubit handling","Branch-and-bound decoder makes surface code erasure-class without checks","Three-state readout plus leak-skip gives erasure-capacity scaling","Moonwalking code reaches erasure bound with no mid-circuit checks"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000273,"raw_usage":{"total_tokens":1477,"prompt_tokens":754,"completion_tokens":723,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":498,"completion_tokens_details":{"reasoning_tokens":643}},"tokens_in":498,"tokens_out":723,"duration_ms":9829,"temperature":1.0,"reasoning_tokens":643,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-04T03:07:37.681244+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Enumerate all pairs of leakage events in a 3×3 moonwalking surface code with three-state readout and skip-gate leakage that produce the same erasure-check and detector outcomes but different logical outcomes. The paper's t_E = ℓ claim predicts no such pair; a single such pair, of the kind the paper itself finds for the walking code, would falsify the central claim.","supporting_citations":[],"review_version":2}