{"id":"052d1246-bef3-426e-befc-37e6c757b610","arxiv_id":"2606.20551","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Using solvable fermionic Hamiltonians with depolarizing noise, the work derives energy-error scaling and shows multi-frequency cooling outperforms adiabatic evolution in the topological phase while QAOA competes in the trivial phase.","lead":"This paper benchmarks cooling, adiabatic, and optimization algorithms for ground-state preparation under depolarizing noise using exactly solvable quadratic fermionic models. A smart generalist might read it to understand how noise and system phase affect practical choices in noisy quantum computing.","discovery_kind":"unclear","skeptic_critique":{"model":"grok-4.3","headline":"Representativeness of quadratic fermionic model with depolarizing noise for general noisy systems","rationale":"The reader's weakest_assumption directly identifies the same load-bearing point. The abstract-only review already flags the generalization step as the weakest link; the full-text claim of an \"extendable approach\" does not add independent support for that step. No internal inconsistency or formal error is visible from the given material, so the UNVERDICTED/low-confidence verdict is appropriate and does not require adjustment.","tokens_in":1701,"tokens_out":347,"duration_ms":13380,"concrete_test":"Implement the same adiabatic, multi-frequency cooling, and QAOA protocols on the transverse-field Ising chain (non-quadratic after Jordan-Wigner) with bit-flip noise at equivalent rates; recompute relative energy vs. noise strength in both phases and check whether cooling remains superior in the topological regime and more robust to parameter errors.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (adiabatic favorable in trivial phase; multi-frequency cooling competitive/superior in topological phase due to gap closing; cooling robust to imperfections) is derived and numerically supported only for an exactly solvable family of quadratic fermionic Hamiltonians under depolarizing noise. The abstract positions this as an \"extendable approach to benchmarking,\" but provides no argument or evidence that the phase-dependent ranking or robustness properties survive for non-quadratic Hamiltonians, other noise channels (e.g., dephasing, amplitude damping), or systems without exact solvability. Because the topological phase advantage is explicitly tied to gap closing, any model where gap closing interacts differently with the chosen noise or algorithm ansatz could invert the ranking.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript compares cooling, adiabatic, and optimization algorithms for ground-state preparation under noise. Using an exactly solvable family of quadratic fermionic Hamiltonians with depolarizing noise, the authors derive scaling laws for relative energy versus noise rate, supported by numerics. The model has trivial and topological phases separated by a quantum phase transition. Adiabatic evolution is favorable in the trivial phase; a multi-frequency cooling algorithm is competitive or superior in the topological phase due to gap closing. QAOA is competitive in the trivial phase but typically outperformed in the topological regime. Cooling shows enhanced robustness to parameter imperfections. The work frames the analytical approach as an extendable benchmarking method.","tokens_in":1834,"tokens_out":364,"duration_ms":17725,"significance":"If the results hold, the exact solvability enabling derivation of scaling laws (supported by numerics) is a clear strength, providing concrete, non-fitted predictions for this model class. The phase-dependent performance comparison and the robustness result for cooling are useful insights for noisy state preparation. The extendable benchmarking framing could template similar studies, though its scope remains to be demonstrated.","major_comments":[{"comment":"Abstract: the positioning of the work as establishing an 'extendable approach to benchmarking' is load-bearing for the paper's framing, yet the manuscript provides no concrete argument, example, or evidence that the phase-dependent ranking or robustness properties extend beyond quadratic fermionic Hamiltonians and depolarizing noise.","section":"Abstract"}],"minor_comments":[{"comment":"The abstract references [1] and [2] without full bibliographic details; ensure these are expanded in the reference list.","section":null}],"recommendation":"minor_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the positive assessment and the recommendation for minor revision. We address the single major comment below.","responses":[{"response":"We agree that the manuscript contains no explicit demonstrations, examples, or arguments showing that the observed phase-dependent rankings or the robustness advantage of cooling extend to Hamiltonians outside the quadratic fermionic class or to noise models other than depolarizing. The phrasing in the abstract and conclusion frames the analytical method (exact solvability plus noise-channel analysis) as potentially reusable, but this is an aspirational statement rather than a substantiated claim. To address the concern directly, we will revise the abstract and the final paragraph of the conclusion to remove the implication that the specific performance ordering or robustness result is already shown to be general, and instead state that the present work supplies an exactly solvable benchmark for this model family while the broader applicability of the method remains to be explored in future studies.","revision_made":"yes","referee_comment":"[Abstract] Abstract: the positioning of the work as establishing an 'extendable approach to benchmarking' is load-bearing for the paper's framing, yet the manuscript provides no concrete argument, example, or evidence that the phase-dependent ranking or robustness properties extend beyond quadratic fermionic Hamiltonians and depolarizing noise."}],"tokens_in":1305,"tokens_out":280,"duration_ms":12097,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The useful part here is the explicit scaling of relative energy error with noise rate, derived analytically for this solvable family and backed by numerics. They also map out how adiabatic evolution holds up in the trivial phase while the multi-frequency cooling protocol pulls ahead in the topological phase where the gap closes, and they add a check that cooling is more robust to parameter errors than the others. QAOA sits in between but loses ground in the topological regime.\n\nThat gives a clean benchmark for this class of models. The analytical route is a step beyond just running numerics on individual methods, and the phase comparison is the clearest new quantitative result.\n\nThe soft spot is representativeness. Everything rests on quadratic fermionic Hamiltonians plus depolarizing noise. The topological advantage is explicitly linked to gap closing in this model; nothing in the abstract shows the ranking survives for non-quadratic interactions, other noise channels, or systems without exact solvability. Calling it an \"extendable approach\" is forward-looking but not yet supported by evidence outside this family.\n\nThe work is for people who need benchmarks on noisy fermionic ground-state prep or who want a solvable testbed to try new algorithms against. It is coherent on its own terms and deserves a serious referee, even if the scope stays limited.","headline":"This paper derives concrete scaling laws for energy error under depolarizing noise on an exactly solvable quadratic fermionic model and shows phase-dependent algorithm rankings, but the results stay tightly tied to that narrow setting.","tokens_in":2330,"tokens_out":343,"would_cite":false,"duration_ms":9162,"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":"Adiabatic evolution prepares ground states better in trivial phases of noisy fermionic systems, while multi-frequency cooling is superior in topological phases.","keywords":["quantum algorithms","ground state preparation","noise","adiabatic evolution","cooling algorithms","topological phase","quantum phase transition","depolarizing noise"],"falsifier":"A numerical or experimental demonstration that adiabatic methods outperform cooling in the topological phase of a different noisy Hamiltonian would falsify the ranking.","tokens_in":2596,"feed_emoji":"⚛️","tokens_out":592,"duration_ms":16799,"temperature":0.7,"pith_summary":"The paper benchmarks cooling, adiabatic, and optimization algorithms for preparing ground states on quantum computers when noise is present. It uses a solvable model of quadratic fermions with depolarizing noise that has a phase transition between trivial and topological regimes. Adiabatic methods work well away from the transition but suffer when the gap closes in the topological phase. Cooling algorithms handle the topological case better and are more robust to imperfect parameters. This helps decide which algorithm to use for noisy quantum hardware depending on the system's phase.","feed_headline":"Cooling outperforms adiabatic in topological phases under noise","feed_subtitle":"Benchmark on solvable fermionic models shows algorithm choice depends on phase, with cooling more robust to errors.","key_machinery":"Exactly solvable quadratic fermionic Hamiltonians with depolarizing noise, used to derive scaling of relative energy with noise rate for comparing adiabatic, cooling, and QAOA algorithms across trivial and topological phases.","core_discovery":"Using an exactly solvable family of quadratic fermionic Hamiltonians subject to depolarizing noise, the authors show that the performance of ground-state preparation algorithms depends on the phase: adiabatic evolution is favorable in the trivial phase, while a multi-frequency cooling algorithm becomes competitive or superior in the topological phase, where gap-closing limits adiabatic protocols. The cooling protocol also shows enhanced robustness to parameter imperfections.","pith_inferences":["These benchmarks could guide algorithm selection for other noisy many-body systems beyond fermions.","Future hardware tests might compare these algorithms on actual quantum devices using similar phase diagrams.","Extensions to interacting Hamiltonians could reveal if the phase-dependent ranking persists."],"forward_implications":["Adiabatic protocols should be preferred for ground state preparation in trivial phases of noisy systems.","Multi-frequency cooling algorithms offer better performance near quantum phase transitions in topological phases.","QAOA performs similarly to cooling in trivial phases but lags in topological regimes.","Cooling methods maintain advantage under parameter imperfections in this model."],"fun_headline_variants":["Cooling outperforms adiabatic topologically under noise","Trivial phase favors adiabatic in noisy Hamiltonians","Cooling excels amid topological gap closing and noise","Cooling shows robustness in noisy topological phase"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The exactly solvable family of quadratic fermionic Hamiltonians with depolarizing noise represents general noisy quantum systems well enough to rank preparation algorithms.","fun_headline_variants_meta":{"raw":{"variants":["Cooling outperforms adiabatic topologically under noise","Trivial phase favors adiabatic in noisy Hamiltonians","Cooling excels amid topological gap closing and noise","Cooling shows robustness in noisy topological phase"]},"model":"grok-4.3","cost_usd":0.005801,"raw_usage":{"total_tokens":2748,"prompt_tokens":640,"num_sources_used":0,"completion_tokens":55,"cost_in_usd_ticks":58012000,"prompt_tokens_details":{"text_tokens":640,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2053,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":640,"tokens_out":55,"duration_ms":21291,"temperature":1.0,"reasoning_tokens":2053,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-26T16:54:33.759274+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A numerical or experimental demonstration that adiabatic methods outperform cooling in the topological phase of a different noisy Hamiltonian would falsify the ranking.","supporting_citations":[],"review_version":1}