{"id":"e7485cc9-a47b-422b-9395-35622728adac","arxiv_id":"2607.01364","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":4.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Maps decohered toric code under GAD and SGAD channels to classical spin models and derives logical failure probabilities versus temperature and squeezing.","lead":"The paper maps a toric code under generalized amplitude-damping and squeezed generalized amplitude-damping channels to classical statistical-mechanical spin models via double Hilbert-space formalism and Pauli twirling. A smart generalist might read it to see how realistic damping noise affects logical error rates in topological quantum error correction.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.3","headline":"Pauli twirling for SGAD may discard squeezing-induced correlations that affect toric-code logical rates","rationale":"The reader's weakest_assumption is precisely the load-bearing point: whether the two formalisms introduce uncontrolled changes to logical rates for the non-Markovian squeezed channels. The abstract-only review already flags this; the concrete test above would decide whether the concern is realized once the full text is examined.","tokens_in":1620,"tokens_out":340,"duration_ms":18460,"concrete_test":"On a distance-3 toric code, compute the exact logical failure probability under the SGAD channel (full Kraus operators, no twirling) for three squeezing values; compare to the failure probability obtained from the twirled asymmetric depolarizing channel at the same parameters. A discrepancy exceeding Monte-Carlo error bars falsifies the claim that twirling leaves logical rates unchanged.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that the double-Hilbert-space mapping and the Pauli-twirling step both preserve the logical failure probabilities as functions of temperature and squeezing. Pauli twirling replaces the SGAD channel by an asymmetric depolarizing channel; for a squeezed bath this step averages over phase-sensitive operators whose coherences can survive the stabilizer measurements and couple differently to the logical subspace than the twirled Pauli errors. The double-Hilbert-space construction for the non-Markovian case likewise assumes a specific bath correlation structure whose effect on the code space is not bounded in the abstract. If either mapping alters the effective error rates by an amount comparable to the reported dependence on squeezing, the claimed functional dependence on channel parameters is uncontrolled.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper maps the toric code under generalized amplitude-damping (GAD) and squeezed generalized amplitude-damping (SGAD) channels to classical statistical-mechanical models via the double Hilbert-space formalism. It also applies Pauli twirling to obtain asymmetric depolarizing channels, relates the damping-channel parameters to spin-coupling constants, and computes logical failure probabilities as functions of temperature and squeezing.","tokens_in":1778,"tokens_out":420,"duration_ms":11423,"significance":"If the mappings hold without uncontrolled approximations, the work would connect realistic damping noise (including squeezing and non-Markovian effects) on a topological code to classical spin models, enabling computation of logical error rates via established statistical-mechanics techniques. The explicit parameter mapping and functional dependence on squeezing would be a concrete contribution.","major_comments":[{"comment":"The Pauli-twirling step that replaces the SGAD channel by an asymmetric depolarizing channel (described in the abstract) averages over phase-sensitive operators. For a squeezed bath these coherences can survive stabilizer measurements and couple to the logical subspace differently than the twirled Pauli errors; no bound is given showing that the resulting logical failure probability remains accurate to the order of the reported squeezing dependence. This is load-bearing for the central claim that logical failure probabilities are obtained as a function of squeezing.","section":"Abstract (mapping via Pauli twirling)"},{"comment":"The double-Hilbert-space construction for the non-Markovian GAD/SGAD case likewise assumes a specific bath-correlation structure. The manuscript does not provide an error bound demonstrating that this structure preserves the logical-subspace dynamics to the precision needed for the claimed temperature and squeezing dependence.","section":"Abstract (double Hilbert-space formalism)"}],"minor_comments":[{"comment":"Notation for the spin-coupling constants obtained from the channel parameters should be introduced with an explicit equation relating each damping parameter to each coupling.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their careful reading of the manuscript and for raising these points concerning the approximations underlying our mappings. We address each major comment below.","responses":[{"response":"The Pauli twirling is used as a distinct second approach to obtain an effective asymmetric depolarizing channel whose parameters are related to temperature and squeezing; the logical failure probabilities are then computed for this effective channel via the spin-model mapping. The abstract presents this as a separate procedure from the double-Hilbert-space construction. While we acknowledge that the twirling neglects coherences that could in principle survive, the reported squeezing dependence is that of the twirled model. We will revise the manuscript to state this scope explicitly and to add a qualitative discussion of why the leading squeezing dependence is expected to be representative for the toric-code logical subspace.","revision_made":"partial","referee_comment":"[Abstract (mapping via Pauli twirling)] The Pauli-twirling step that replaces the SGAD channel by an asymmetric depolarizing channel (described in the abstract) averages over phase-sensitive operators. For a squeezed bath these coherences can survive stabilizer measurements and couple to the logical subspace differently than the twirled Pauli errors; no bound is given showing that the resulting logical failure probability remains accurate to the order of the reported squeezing dependence. This is load-bearing for the central claim that logical failure probabilities are obtained as a function of squeezing."},{"response":"The double-Hilbert-space formalism supplies an exact mapping of the decoherence process onto a classical spin model once the bath-correlation structure of the GAD/SGAD channels is fixed. Temperature and squeezing enter directly as parameters of the resulting spin couplings, and the logical failure probabilities follow from this mapping without further approximation. The manuscript states the bath-correlation assumptions; within those assumptions the claimed dependences are exact. We will revise the text to reiterate that the results hold exactly for the assumed structure.","revision_made":"partial","referee_comment":"[Abstract (double Hilbert-space formalism)] The double-Hilbert-space construction for the non-Markovian GAD/SGAD case likewise assumes a specific bath-correlation structure. The manuscript does not provide an error bound demonstrating that this structure preserves the logical-subspace dynamics to the precision needed for the claimed temperature and squeezing dependence."}],"tokens_in":1266,"tokens_out":491,"duration_ms":43472,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main move here is taking the toric code under generalized amplitude damping and its squeezed variant, including thermal and non-Markovian pieces, and mapping both to classical spin models. One route uses the double Hilbert-space formalism to connect channel parameters directly to spin couplings. The other applies Pauli twirling to produce asymmetric depolarizing channels and then writes logical failure probabilities as functions of temperature and squeezing. That gives a concrete way to import statistical-mechanics tools for threshold estimates under these specific noises.\n\nThe inclusion of squeezing and non-Markovian effects is the clearest addition over standard GAD treatments. If the mappings are clean, it lets existing Ising or Potts solvers estimate how squeezing changes the logical error rate without running full quantum simulations.\n\nThe soft spot is the twirling step for the squeezed channel. Twirling replaces the SGAD operator with a Pauli channel, but squeezing creates phase-sensitive correlations that stabilizer measurements might not fully erase. If those survive into the logical subspace, the effective error rates after twirling could differ from the true rates by an amount comparable to the squeezing dependence the paper reports. The double-Hilbert-space construction for the non-Markovian case also assumes a particular bath correlation function whose impact on the code space is not bounded in the abstract. Without the explicit derivations or a check against exact numerics on small lattices, it is hard to know whether the claimed functional dependence holds.\n\nThe work is aimed at people who already use stat-mech mappings for quantum error correction and want to extend them to squeezed baths. A reader looking for a new general framework will not find one. The paper deserves referee time because the mappings, if they check out, are practically useful; the main task for review is to verify that the twirling and bath assumptions do not introduce uncontrolled errors in the logical rates.","headline":"The paper applies known double-Hilbert-space and Pauli-twirling techniques to GAD and SGAD on the toric code, relating parameters to spin couplings and logical failure rates, but the squeezing case rests on an unverified approximation.","tokens_in":2259,"tokens_out":456,"would_cite":false,"duration_ms":17416,"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":"Decohered toric codes under generalized amplitude-damping channels map to statistical-mechanical models where channel parameters set the spin couplings and logical failure rates depend on temperature and squeezing.","keywords":["toric code","generalized amplitude damping","squeezed generalized amplitude damping","Pauli twirling","statistical mechanical models","logical failure probability","quantum damping noise"],"falsifier":"A direct simulation of logical error rates on a small toric code under the SGAD channel at fixed temperature but varying squeezing strength that deviates from the temperature-and-squeezing dependence predicted by the mapped spin model.","tokens_in":2538,"feed_emoji":"🌀","tokens_out":666,"duration_ms":23957,"temperature":0.7,"pith_summary":"The paper maps the action of generalized amplitude-damping and squeezed generalized amplitude-damping channels on the toric code to equivalent statistical-mechanical models. It does this first through the double Hilbert-space formalism and second by applying Pauli twirling to obtain asymmetric depolarizing channels. Logical failure probabilities are then expressed directly in terms of the channel's temperature and squeezing parameters, with those parameters tied to the coupling constants of the resulting spin model. A sympathetic reader would care because the mapping lets standard tools from classical statistical mechanics be used to analyze error rates under realistic damping noise that includes thermal and non-Markovian effects.","feed_headline":"Toric code under damping noise maps to classical spin model","feed_subtitle":"GAD and SGAD channels relate to spin couplings, with failure rates depending on temperature and squeezing.","key_machinery":"Double Hilbert-space formalism that converts the quantum damping channels into classical spin models, together with Pauli twirling that produces the asymmetric depolarizing error rates.","core_discovery":"The action of the GAD and SGAD channels on the toric code is mapped to statistical-mechanical models using the double Hilbert-space formalism, and via Pauli twirling to stochastic Pauli-type errors yielding asymmetric depolarizing channels, with channel parameters related to spin-coupling constants and logical failure probabilities obtained as a function of temperature and squeezing.","pith_inferences":["The mapping could be used to estimate error thresholds for toric codes in environments dominated by squeezed thermal noise.","Direct comparison of the analytic failure-rate curves against small-code numerics would test the accuracy of the twirling step.","Similar mappings might apply to other topological codes or to different non-Markovian damping models."],"forward_implications":["Logical failure probabilities are obtained as explicit functions of temperature and squeezing.","The parameters of the GAD and SGAD channels become the spin-coupling constants of the equivalent statistical model.","The toric code under these channels can be analyzed with classical statistical-mechanics techniques for both the full mapping and the twirled error model.","Both the GAD and SGAD channels admit such mappings, allowing comparison of their effects on logical stability."],"fun_headline_variants":["Damped toric code maps to classical spin model","Toric code damping channels map to spin model","Decohered toric code to classical spin model via damping","GAD SGAD map toric code to spin couplings"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The double Hilbert-space formalism and Pauli twirling capture the full effect of the non-Markovian and squeezed damping channels without introducing uncontrolled approximations that change the logical failure rates.","fun_headline_variants_meta":{"raw":{"variants":["Damped toric code maps to classical spin model","Toric code damping channels map to spin model","Decohered toric code to classical spin model via damping","GAD SGAD map toric code to spin couplings"]},"model":"grok-4.3","cost_usd":0.004777,"raw_usage":{"total_tokens":2299,"prompt_tokens":561,"num_sources_used":0,"completion_tokens":64,"cost_in_usd_ticks":47774500,"prompt_tokens_details":{"text_tokens":561,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":1674,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":561,"tokens_out":64,"duration_ms":10944,"temperature":1.0,"reasoning_tokens":1674,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-03T20:08:48.162136+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A direct simulation of logical error rates on a small toric code under the SGAD channel at fixed temperature but varying squeezing strength that deviates from the temperature-and-squeezing dependence predicted by the mapped spin model.","supporting_citations":[],"review_version":1}