{"id":"e320c6bd-0d75-4855-9cac-fb10d0835eda","arxiv_id":"1908.03579","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The surface-GKP code has a fault-tolerance threshold of 11.2 dB GKP squeezing when only GKP states are noisy, 0.81% per-component failure when GKP states are ideal, and 18.6 dB with 0.69% when both are noisy.","lead":"This paper simulates a quantum error correcting code that nests GKP bosonic qubits inside the surface code, and reports the noise and squeezing levels at which it becomes fault-tolerant. Generalists should read it because it sets concrete engineering targets for building a scalable quantum computer from continuous-variable bosonic systems.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Unproven 'conservative' mapping of physical noise (coherent finite-squeezing GKP states, loss-only SUM gates) to Gaussian displacement channels is the load-bearing step; if it is not monotonically noise-increasing, the threshold values may not transfer to the stated physical model.","rationale":"I read the paper in good faith and checked the central derivation: the threshold arithmetic (σ_gkp=0.194 ↔ 11.2 dB, σ=0.09 ↔ 0.81% loss, σ=0.083 ↔ 18.6 dB/0.69%) is consistent with the squeezing definition, and the Gaussian channel derivation in Appendix A and Eq. (19) is internally correct. The Monte Carlo methodology is described in unusual detail, and the use of soft GKP information in MWPM edge weights is plausible. No internal inconsistency emerges within the stated noise model. The single most load-bearing external assumption is the claimed conservative mapping from physical finite-squeezing GKP states and lossy circuits to the Gaussian displacement model. The paper itself acknowledges in Section IV that twirling is impractical and that Kerr nonlinearities may invalidate the gate model, so the thresholds are conditional on an idealized representation of the noise. Because no monotonicity proof is given for either substitution, the thresholds could be optimistic if coherent or non-Gaussian effects increase logical error rates relative to the twirled/displacement model. This does not contradict the paper's internal claims, but it means the abstract's physical relevance rests on an unproven assumption. The reader's conditional verdict accurately captures this, and I recommend no change to that verdict. A targeted simulation of the exact approximate GKP states and loss-only gates would settle whether the concern lands.","tokens_in":31574,"tokens_out":28551,"duration_ms":316382,"concrete_test":"Re-run the Monte Carlo simulation of Section III with the same circuit scheduling and MWPM decoder, but replace the twirled ancilla model N[σ_gkp] (Eq. 16) with the exact approximate GKP state |ψΔ> of Eq. (15) (implemented via the envelope exp[−Δn] truncated to a photon-number cutoff), and replace the loss+heating gate exp[L′±Δt] of Eq. (18) with the physical loss-only Lindbladian L± containing D[a] only. Recompute the thresholds for Case I (σ=0) and Case II (σ_gkp=0). If the thresholds move to lower squeezing and/or higher component failure rates than 11.2 dB / 0.81%, the conservative mapping is confirmed; if they move to higher squeezing/lower failure rates, the central claim is not robust to the modeling assumption.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The thresholds (σ_gkp*=0.194, σ*=0.09, and σ=σ_gkp*=0.083) are computed for a noise model in which finite-squeezing GKP states are replaced by N[σ_gkp] applied to ideal states (Eq. 16, justified by twirling in Appendix A) and lossy SUM gates are replaced by ideal SUM followed by correlated Gaussian displacements (Eq. 19, obtained by adding heating D[a†] to L± in Eq. 18). The paper claims these replacements are 'conservative' (Section II C), but no monotonicity proof is provided. For GKP states, twirling in Eqs. (A2)-(A4) averages over stabilizer shifts, destroying coherences between displacement components; coherent errors can behave differently under repeated correction than stochastic mixtures, and a coherent superposition is not obviously majorized by its twirled version. For gates, adding D[a†] with rate κ doubles the variance and removes attenuation, which is likely pessimistic, but the logical error rate under MWPM decoding is not proven monotonic under this parameter change. If either replacement is not conservative in the relevant regime, the quoted thresholds overstate the tolerable physical noise, and the abstract's claim that FT QEC is possible above 11.2 dB squeezing (or below 0.81% loss) may fail for the actual physical states and gates. The authors themselves note in Section IV that twirling is not practical and that implementing the SUM gate without Kerr is an open problem, underscoring that the thresholds are conditional on the idealized model.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies fault-tolerant quantum error correction with a concatenated surface-GKP code under a circuit-level noise model. Finite-squeezing GKP states are modeled as ideal GKP states subject to the Gaussian random displacement channel N[σ_gkp] (Eq. (16)), and noisy SUM/inverse-SUM gates are modeled, via a Lindblad equation with loss and added heating (Eqs. (17)-(18)), as ideal gates followed by correlated Gaussian displacements with variance σ² = κ/g (Eq. (19)). The full syndrome extraction circuit, alternating GKP stabilizer measurements with four-step surface-code stabilizer measurements, is simulated for increasing code distances and decoded by minimum-weight perfect matching on 3D space-time graphs whose edge weights are renormalized using the conditional error probabilities p[σ](z) derived from GKP stabilizer measurements (Appendix B). The paper reports three thresholds: σ*_gkp = 0.194, corresponding to 11.2 dB squeezing, when GKP states are the only noisy components; σ* = 0.09, corresponding to κ/g = 0.81%, when GKP states are ideal; and σ* = σ*_gkp = 0.083, corresponding to 18.6 dB and κ/g = 0.69%, when both are comparably noisy. Below these thresholds the logical X/Z error rate is suppressed with increasing code distance d. The results are compared with earlier toric-GKP and measurement-based GKP computations, and the authors argue that their scheme is deterministic (no post-selection) and scalable.","tokens_in":80,"tokens_out":16968,"duration_ms":246672,"significance":"If the thresholds are taken at face value, the paper is a significant advance in the practical assessment of bosonic quantum error correction: it provides, for this concatenated setting, a full circuit-level simulation in which noise propagation through every gate is tracked, a decoder that exploits the analog syndrome information from GKP stabilizer measurements, and concrete falsifiable predictions (the three threshold values and the exponential scaling of perr(σ) in Eqs. (20)-(21)) that connect state-preparation squeezing to a fault-tolerance threshold. Strengths of the manuscript are the exceptionally detailed simulation protocol (Appendix B gives explicit stochastic update equations for every noise step and the complete MWPM decoding procedure), the careful scheduling of SUM and inverse-SUM gates to avoid correlated-noise amplification (Fig. 5), and the transparent comparison with prior toric-GKP and measurement-based results. The central claims are conditional on the noise model, and the 'conservative' reduction of physical finite-squeezing and loss noise to Gaussian displacement channels is asserted rather than proven; this is the main risk.","major_comments":[{"comment":"The thresholds reported in Section III are computed for the model of Eq. (16), in which every finite-squeezing GKP state is replaced by an ideal state subject to the incoherent Gaussian displacement channel N[σ_gkp], and Section II C asserts that this replacement is 'conservative' compared to the coherent superposition of displacements in Eq. (15). The twirling derivation in Eqs. (A2)-(A4) shows that the incoherent model is obtained from the coherent state by averaging over GKP stabilizer shifts and dropping the (k1,k2)≠(0,0) terms, but it does not establish that the decoded logical error rate is larger for the incoherent model: the logical error probability after repeated rounds of measurement and feedback is not a convex function of the input state, and coherences between distinct displacement components within a peak, which are destroyed by the twirl, could in principle affect subsequent rounds. Because the abstract's headline claim ('fault-tolerant quantum error correction is possible ... if the squeezing ... is higher than 11.2 dB') is phrased in terms of physical squeezing, the identification of the physical state with N[σ_gkp] is load-bearing. Please either prove the monotonicity, provide numerical evidence by simulating the coherent states of Eq. (15) directly for small d and comparing with the N[σ_gkp] model, or explicitly qualify the abstract and Section III as applying to the twirled noise model.","section":"II C and Appendix A"},{"comment":"The gate error model in Eq. (18) replaces the loss-only Lindbladian L± of Eq. (17) by L'± = L± + κ(D[a1†] + D[a2†]), which doubles the added displacement variance relative to pure photon loss and removes the attenuation; the resulting correlated Gaussian displacement model (Eq. (19)) is directionally pessimistic, but the paper gives no monotonicity argument for the final logical error rate under this substitution. Since the MWPM edge weights in Eqs. (B22)-(B33) are themselves computed from the same noise parameters σ and σ_gkp, changing the noise model also changes the decoder, so a monotone relation between the physical loss rate and the simulated logical error rate cannot simply be assumed. The authors should either provide such an argument, or state explicitly that the thresholds (κ/g)* = 0.81% and 0.69% are for the diffusion-type gate model and may not match a pure-loss implementation.","section":"II C, Eqs. (17)-(19)"}],"minor_comments":[{"comment":"The caption does not state which symbol shape corresponds to which code distance d, nor the set of distances used in each panel; listing the distances (apparently d = 3, 5, 7, and possibly 9) would make the threshold crossings checkable.","section":"III, Fig. 6"},{"comment":"The threshold values (σ*_gkp = 0.194, σ* = 0.09, and σ* = 0.083) are quoted to three significant figures, but Fig. 6 shows no error bars or confidence intervals; Appendix B only reports that 10,000-100,000 samples were used, so please quantify the statistical precision of the extracted thresholds.","section":"III"},{"comment":"The decoding procedure says to 'find the path with the minimum total weight' for all pairs of highlighted vertices but does not state which shortest-path algorithm is used; a one-sentence statement (e.g., Dijkstra on the spatio-temporal graph) would aid reproducibility.","section":"Appendix B, MWPM decoding step 3"},{"comment":"There is a typo in the sentence 'for some intergern' which should read 'for some integer n.'","section":"II A, after Eq. (10)"},{"comment":"The paper defines separate noise parameters σ_p, σ_c, σ_m for preparation, gates, and measurement but simulates only the case σ_p = σ_c = σ_m ≡ σ; a sentence on how unequal parameters would be handled, or why equal-time noise is the relevant regime, would clarify the sense in which the noise model is general.","section":"II C"}],"recommendation":"major_revision","confidential_remarks":"I recommend major revision even though the manuscript is a strong and, in my view, essentially correct study; the requested changes are local and constructive (a monotonicity argument or a numerical check for the two 'conservative' noise-model reductions, or a qualified abstract that states the results are for the idealized channel). If the authors choose only to qualify the claims, the paper remains acceptable, since the threshold values are honestly reported as outputs of the stated simulation model. I see no circularity, no missing-novelty-disclosure problem, and no citation-pattern concern: the comparison with Refs. [28-32] is accurate and appropriately credits prior work."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things you should know about this paper. First, it is the first full circuit-level simulation of the surface-GKP code, and it gives concrete thresholds: 11.2 dB squeezing when GKP states are the only noise, 0.81% circuit-element failure when GKP states are ideal, and 18.6 dB / 0.69% when both are comparable. Second, those thresholds are computed for a twirled, incoherent Gaussian displacement noise model, and the paper itself admits the twirling operation is not practically implementable. That does not kill the result, but it does mean the thresholds are conditional on a model, not on a fully realistic device.\n\nWhat is genuinely new: the detailed circuit-level treatment. Prior work on concatenated GKP codes used code-capacity or phenomenological noise models, manually injecting shift errors. Here, Appendix B spells out every noise update step from GKP state preparation through SUM gates, idling, homodyne measurement, and surface-code stabilizer extraction. The renormalized edge-weight method, which uses the analog GKP measurement information, is clearly explained and shown to improve the threshold substantially over ignoring it. The circuit scheduling with inverse-SUM gates to cancel propagated shift errors is also a nice, concrete contribution. The paper is careful about comparisons with earlier measurement-based schemes that rely on post-selection, and it is honest about the practical obstacles, such as Kerr nonlinearities in the SUM gate implementation.\n\nSoft spots, in proportion. The biggest one is the claim that replacing coherent finite-squeezing states and lossy gates by incoherent Gaussian displacements is \"conservative.\" For the GKP state, the twirling argument in Appendix A averages over stabilizer shifts; that is a standard and plausible way to make the analysis tractable, but it is not a proven monotonicity result. A coherent superposition of displacements can behave differently under repeated correction than the twirled mixture, especially with a MWPM decoder that uses soft information. Similarly, adding heating to the loss channel may be pessimistic, but the paper does not show that the logical error rate is monotonic under that change. The stress-test note captures this well, and I think it is the right concern to raise. But it is a limitation, not a fatal flaw: the thresholds are explicitly thresholds for the stated noise model, and the model is stated very clearly. The paper does not overclaim beyond that, aside from the word \"conservative.\"\n\nOther issues are minor by comparison. No code or data are released, and the figures have no error bars, though they report 10,000–100,000 samples per point. The simulation seems reproducible in principle given the level of detail in Appendix B, but a release would be better.\n\nWho this is for: anyone working on GKP codes, bosonic QEC, or concatenation with topological codes. It is a useful reference point for experimental groups chasing squeezing thresholds and for theorists studying decoder design. It deserves a serious referee: I would send it to peer review and lean toward accepting after asking the authors to (1) release code/data, and (2) make the conservative-mapping caveat more prominent, ideally with a proof or at least a cleaner statement of what would be needed to prove it.","headline":"First full circuit-level simulation of surface-GKP code with concrete thresholds; the thresholds are solid within the stated twirled Gaussian noise model, but the 'conservative' mapping to that model is asserted, not proven.","tokens_in":32390,"tokens_out":1830,"would_cite":true,"duration_ms":22606,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81P70","81P68"],"pacs":["03.67.Pp"],"model":"deepseek-v4-flash","headline":"Fault-tolerant quantum error correction is possible with the surface-GKP code if GKP squeezing exceeds 11.2 dB.","keywords":["surface-GKP code","GKP code","fault-tolerant quantum error correction","surface code","continuous-variable quantum computing","bosonic codes","minimum-weight perfect matching","quantum error correction thresholds"],"falsifier":"Run the distance-3 and distance-5 surface-GKP error-correction circuits under the paper's own noise model at $\\sigma_{\\mathrm{gkp}} = 0.19$ with $\\sigma = 0$, and check whether the logical X-error rate drops as the code distance increases; the paper predicts a clear drop, so observing a flat or rising rate would falsify the Case I threshold claim. An experiment with GKP squeezing near 12 dB and otherwise ideal components that shows no error suppression with code distance would contradict the claim directly.","tokens_in":31323,"feed_emoji":"🛡️","tokens_out":5784,"duration_ms":54758,"temperature":0.7,"pith_summary":"This paper tries to establish a concrete noise budget for building a fault-tolerant quantum computer out of bosonic modes: it concatenates the GKP code, which stores a qubit in the continuous position and momentum variables of an oscillator, with the surface code, and simulates the full error-correction circuit under realistic loss and finite-squeezing noise. The result is a set of thresholds: fault tolerance is possible when GKP squeezing exceeds 11.2 dB if GKP states are the only noisy elements, when each circuit element fails below 0.81% if GKP states are ideal, and when both are comparably noisy at 18.6 dB squeezing with 0.69% component failure. The mechanism that carries the argument is a decoding scheme that uses the analog information from GKP-stabilizer measurements to renormalize edge weights in the 3D matching graph fed to a minimum-weight perfect matching decoder. These thresholds matter because they tell experimental groups how good GKP states and two-mode gates have to be for a scalable continuous-variable architecture.","feed_headline":"Surface-GKP code is fault tolerant above 11.2 dB squeezing","feed_subtitle":"Detailed simulation sets 11.2 dB, 18.6 dB, and 0.81 percent circuit-error thresholds for scalable bosonic error correction.","key_machinery":"The central object is the concatenated code: each data mode, ancilla mode, and syndrome mode of a rotated surface code is itself a GKP-encoded qubit, with GKP stabilizers measured by SUM and inverse-SUM gates followed by homodyne detection. The load-bearing simplification is the noise model: finite-squeezing GKP states and lossy gates are represented as incoherent Gaussian random displacement channels with variances $\\sigma_{\\mathrm{gkp}}^2$ and $\\sigma^2$, with covariance matrices derived from a Lindblad evolution that adds heating to convert photon loss into displacement noise. The decoding machinery is a 3D space-time graph whose horizontal and vertical edge weights are renormalized using the analog position and momentum outcomes of the GKP-stabilizer measurements, so that a minimum-weight perfect matching decoder can exploit soft information about how close a measured shift was to the decision boundary where a Pauli error becomes likely.","core_discovery":"The central claim is that the concatenated surface-GKP code is fault tolerant below the reported thresholds: GKP squeezing above 11.2 dB when only the GKP states are noisy, component failure probability below 0.81% when GKP states are noiseless, and 18.6 dB squeezing with 0.69% component failure when both are comparably noisy. The paper further claims that, below threshold, the logical X or Z error rate decreases as the code distance increases, and that the decoder's use of continuous GKP-stabilizer information is essential, since ignoring it lowers the thresholds and raises logical error rates by one to several orders of magnitude. The paper also derives simple effective noise variances, such as $\\sqrt{5\\sigma_{\\mathrm{gkp}}^2 + (59/3)\\sigma^2}$ for the probability of a Pauli error after a GKP-stabilizer measurement, showing that these probabilities decay exponentially as the noise parameters approach zero.","pith_inferences":["The twirling step that justifies replacing coherent finite-squeezing noise with an incoherent displacement channel is acknowledged to be impractical because it raises the average photon number; a natural follow-up is to repeat the threshold simulation with coherent, non-twirled GKP states and check how much the 11.2 dB and 18.6 dB values move.","If SUM-gate implementations introduce Kerr nonlinearities, the assumed Gaussian displacement noise model breaks down, so the thresholds should be re-evaluated for any specific gate hardware that is not well approximated by the loss-plus-heating Lindblad model.","The renormalized-edge-weight technique is not obviously limited to GKP codes and could plausibly transfer to other analog bosonic codes, such as cat or binomial codes, when concatenated with a topological code, provided their stabilizer measurements supply similar soft error information.","The comparison with measurement-based GKP schemes suggests a systems-level trade-off: deterministic operation costs higher squeezing thresholds than post-selection-based approaches, which is relevant when choosing between gate-based and measurement-based architectures."],"forward_implications":["Below the thresholds, larger surface-GKP codes suppress logical error rates with increasing code distance, so the architecture is scalable without post-selection.","The decoder works without 3D space-time correlated edges, simplifying the matching-graph construction relative to optimized bare-qubit surface-code decoders.","Circuit-element failure thresholds around 0.7 to 0.8 percent are comparable to the roughly one-percent threshold of the rotated surface code with depolarizing noise, suggesting that bosonic encoding does not inherently require an order-of-magnitude worse noise tolerance.","Because the GKP inner code converts small shift errors into exponentially suppressed Pauli-error probabilities, a small-distance surface code may reach a target logical error rate with fewer total modes than a bare surface code in the low-noise regime."],"supporting_citations":[{"why":"Defines the GKP qubit, its stabilizers, and the shift-error correction idea that forms the inner code of the concatenated scheme.","marker":"[8]"},{"why":"Supplies the minimum-weight perfect matching algorithm used as the decoder on the 3D space-time graphs.","marker":"[34, 35]"},{"why":"Provides the optimized circuit-level surface-code threshold and renormalized edge-weight methodology that this paper adapts and simplifies for the GKP setting.","marker":"[36]"},{"why":"Earlier high-threshold fault-tolerant computation with analog GKP error correction, used as a comparison for the squeezing threshold.","marker":"[29]"},{"why":"Prior toric-GKP code thresholds under a phenomenological noise model, which this paper argues do not account for noise propagation and serve only as a rough upper bound.","marker":"[30]"},{"why":"Establishes a measurement-based GKP squeezing threshold of 20.5 dB, used as the no-post-selection comparison point.","marker":"[31]"},{"why":"Shows a lower 8.3 dB threshold with post-selection in a measurement-based scheme, used to highlight the trade-off with deterministic operation.","marker":"[32]"},{"why":"Demonstrates experimental GKP states with squeezing between 5.5 and 9.5 dB, providing the hardware context for whether the 11.2 dB threshold is near-term.","marker":"[13]"},{"why":"Reports an experimental two-mode coupling with loss rate about $10^{-2}$ relative to coupling strength, supporting the feasibility of the SUM-gate noise regime assumed here.","marker":"[68]"}],"fun_headline_variants":["Surface-GKP code: fault tolerant at 11.2 dB squeezing","11.2 dB GKP squeezing enables fault-tolerant bosonic QEC","Surface-GKP code passes 11.2 dB fault-tolerance threshold","Bosonic error correction: 11.2 dB squeezing hits fault tolerance","GKP+surface code: 11.2 dB squeezing unlocks fault tolerance"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"Everything rests on modelling realistic finite-squeezing GKP states, photon loss, and gate noise as incoherent Gaussian random displacement channels with known variances; if actual devices produce non-Gaussian or correlated noise, the numerical thresholds may not transfer.","fun_headline_variants_meta":{"raw":{"variants":["Surface-GKP code: fault tolerant at 11.2 dB squeezing","11.2 dB GKP squeezing enables fault-tolerant bosonic QEC","Surface-GKP code passes 11.2 dB fault-tolerance threshold","Bosonic error correction: 11.2 dB squeezing hits fault tolerance","GKP+surface code: 11.2 dB squeezing unlocks fault tolerance"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000937,"raw_usage":{"total_tokens":4067,"prompt_tokens":1065,"completion_tokens":3002,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":681,"completion_tokens_details":{"reasoning_tokens":2905}},"tokens_in":681,"tokens_out":3002,"duration_ms":21061,"temperature":1.0,"reasoning_tokens":2905,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:08:54.953700+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the distance-3 and distance-5 surface-GKP error-correction circuits under the paper's own noise model at $\\sigma_{\\mathrm{gkp}} = 0.19$ with $\\sigma = 0$, and check whether the logical X-error rate drops as the code distance increases; the paper predicts a clear drop, so observing a flat or rising rate would falsify the Case I threshold claim. An experiment with GKP squeezing near 12 dB and otherwise ideal components that shows no error suppression with code distance would contradict the claim directly.","supporting_citations":[{"cited_title":"Efficient quantum computa- tion using coherent states,","cited_arxiv_id":null,"evidence_quote":"Defines the GKP qubit, its stabilizers, and the shift-error correction idea that forms the inner code of the concatenated scheme."},{"cited_title":"Surface code quantum computing with error rates over 1%,","cited_arxiv_id":null,"evidence_quote":"Provides the optimized circuit-level surface-code threshold and renormalized edge-weight methodology that this paper adapts and simplifies for the GKP setting."},{"cited_title":"Ultra- high error threshold for surface codes with biased noise,","cited_arxiv_id":null,"evidence_quote":"Earlier high-threshold fault-tolerant computation with analog GKP error correction, used as a comparison for the squeezing threshold."},{"cited_title":"Quantum error correction with the toric Gottesman-Kitaev-Preskill code,","cited_arxiv_id":null,"evidence_quote":"Prior toric-GKP code thresholds under a phenomenological noise model, which this paper argues do not account for noise propagation and serve only as a rough upper bound."},{"cited_title":"Analog quan- tum error correction with encoding a qubit into an oscil- lator,","cited_arxiv_id":null,"evidence_quote":"Shows a lower 8.3 dB threshold with post-selection in a measurement-based scheme, used to highlight the trade-off with deterministic operation."},{"cited_title":"New class of quantum error-correcting codes for a bosonic mode,","cited_arxiv_id":null,"evidence_quote":"Demonstrates experimental GKP states with squeezing between 5.5 and 9.5 dB, providing the hardware context for whether the 11.2 dB threshold is near-term."},{"cited_title":"Modular Bosonic Subsystem Codes","cited_arxiv_id":"1907.08210","evidence_quote":"Reports an experimental two-mode coupling with loss rate about $10^{-2}$ relative to coupling strength, supporting the feasibility of the SUM-gate noise regime assumed here."}],"review_version":1}