{"id":"b96607ee-4441-4ca1-b6fc-e840ca2cf40d","arxiv_id":"2607.08235","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":5.5,"correctness_risk":"low","formal_verification":"none","parameter_count":3,"one_line_summary":"ADAPT-SSVQE on a Jordan-Wigner mapped shell-model Hamiltonian recovers five (ten) orthogonal eigenstates for two (three) nucleons in j=9/2 with spectroscopic accuracy in noiseless simulation and restores J^2.","lead":"Researchers show a quantum algorithm that finds many nuclear energy levels at once, not just the ground state, for small shell-model systems. It matters because full nuclear spectra are needed for decay heat and structure, and classical computers hit a wall on Hilbert-space size.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified beyond the reader's already-flagged scope limits of the noiseless few-nucleon demonstration.","rationale":"The reader's strongest claim accurately restates the paper's demonstrated result, and the weakest assumption correctly isolates the gap between the noiseless 10-qubit benchmarks and any claim of readiness for larger valence spaces or real NISQ hardware. No deeper load-bearing flaw (hidden assumption in the JW mapping, failure of orthogonality, or systematic mis-assignment of J) is present in the manuscript. The residual ⟨J²⟩ deviations for three nucleons are already quantified by the authors and do not reverse the spectroscopic-accuracy claim. Consequently the CONDITIONAL verdict stands: the contribution is accept-shaped once code is released and the acknowledged scaling/symmetry-breaking issues are addressed; no stronger or weaker verdict is warranted by a second-pass reading.","tokens_in":11683,"tokens_out":609,"duration_ms":6047,"concrete_test":"Recompute the three-nucleon spectrum of Table 2 and Fig. 3 with a tightened convergence threshold (G_iter or ΔE < 10^{-4}) and verify that every ⟨J²⟩ moves to within 0.01 of the exact half-integer value J(J+1); if the energies remain spectroscopically accurate while the residual symmetry breaking disappears, the only remaining soft spot is purely hardware scaling, not algorithmic correctness.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is carefully scoped to noiseless state-vector simulation of two- and three-nucleon systems in a single j=9/2 orbital (10 qubits). Within that scope the evidence is direct: energies match exact diagonalization to spectroscopic accuracy (residual error driven to zero for the two-nucleon case; relative errors plunge for the three-nucleon case after 39 iterations), the five/ten states remain mutually orthogonal by construction of the unitary ADAPT ansatz, and measured ⟨J²⟩ values recover the expected integer/half-integer spectrum (exact for two nucleons; small residual deviations for three nucleons that the authors themselves attribute to the G_iter/ΔE < 10^{-2} threshold). The M_J-conserving double-excitation pool plus weighted SSVQE loss is a standard, correctly applied combination of known tools; no internal inconsistency appears in the JW mapping, operator selection, or post-convergence diagnostics. The residual three-nucleon J² deviations and the rapid growth of CNOT depth (to 2768) are real practical limitations for hardware or larger spaces, but they are already acknowledged by the authors and correctly identified by the reader as the weakest assumption; they do not undermine the claim as stated.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper introduces ADAPT-SSVQE for simultaneous extraction of multiple nuclear shell-model eigenstates in one optimization run. The effective Hamiltonian (one- and two-body terms) is mapped to qubits by the Jordan-Wigner transformation. An adaptive ansatz is built from an M_J-conserving double-excitation operator pool; a weighted SSVQE loss is minimized so that a single unitary evolves a set of orthogonal Hartree-Fock references into the lowest states of a chosen M_J subspace. Benchmarks are performed in noiseless state-vector simulation for two and three identical nucleons in the 0g9/2 orbital (10 qubits, JUN45 interaction). Five (ten) mutually orthogonal states are recovered with spectroscopic accuracy relative to exact diagonalization; measured ⟨Ĵ²⟩ values restore the expected integer/half-integer spectrum (exactly for two nucleons, approximately for three).","tokens_in":11988,"tokens_out":998,"duration_ms":23244,"significance":"If the numerical claims hold, the work supplies a compact, symmetry-aware route to full low-lying shell-model spectra on quantum devices—an important capability because nuclear applications (decay heat, spectroscopy) require excited states, not only ground states. Strengths that should be credited are the direct comparison with exact diagonalization, the recovery of Clebsch-Gordan/CFP structure in the final state vectors, the unitary preservation of orthogonality without post-processing, and the explicit construction and measurement of Ĵ². The demonstration remains limited to noiseless few-nucleon single-j systems; circuit depths already reach hundreds to thousands of CNOTs, so hardware relevance and multi-j scalability are prospective. Within its stated scope the evidence is solid and the method is a useful, carefully scoped advance.","major_comments":[{"comment":"Abstract vs. §2: the abstract advertises a “symmetry-preserving single and double-excitation operator pool,” yet the algorithm description and all numerical work employ only M_J-conserving double excitations T_cd^ab. The discrepancy must be resolved. If singles were deliberately omitted, the authors should state why a double-only pool remains expressive enough to reach spectroscopic accuracy and approximate Ĵ² restoration for the three-nucleon system.","section":"Abstract and §2"},{"comment":"§3 and Table 2 (three-nucleon case): residual ⟨Ĵ²⟩ deviations of order 1–2 units (e.g. 22.59 vs. exact 24.75 for the lowest J=9/2 candidate) are ascribed to the loose stopping criterion G_iter or ΔE < 10^{-2}. Because the central claim includes “intrinsically restores total angular momentum (Ĵ²) symmetry,” the manuscript should either tighten the threshold and re-report both energies and ⟨Ĵ²⟩, or qualify the restoration claim as approximate under the chosen convergence settings.","section":"§3, Table 2"}],"minor_comments":[{"comment":"Repeated typographical error “ADAPT-SSQVE” / “SSQVE” appears in §2; correct to SSVQE throughout.","section":"§2"},{"comment":"Fig. 2 and Fig. 3 captions and panels are clear, but the CNOT-count scaling (48 CNOTs per selected multi-Pauli operator) is stated only in the text; a brief note in the figure legends would help readers.","section":"Figs. 2–3"},{"comment":"The precise list of ten initial Hartree-Fock references for the three-nucleon M_J=1/2 subspace is given, yet no statement is made about how completeness of that set was verified; a short remark would improve reproducibility.","section":"§3"},{"comment":"Reference [16] is listed as “Acta Physica Polonica B19, 1-A2 (2026)”; confirm the year and volume once the conference proceedings are finalized.","section":"References"}],"recommendation":"minor_revision","confidential_remarks":"The technical content is sound within the noiseless few-nucleon scope and the authors already flag the hardware and multi-j limitations. The work is incremental relative to existing ADAPT-VQE and SSVQE literature, but the nuclear-shell-model application and the simultaneous multi-state Ĵ² diagnostics are useful. Suitable for a specialized nuclear-theory or quantum-simulation journal after the two major points are cleaned up; no ethical or citation concerns."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"This paper cleanly shows that ADAPT-SSVQE with an M_J-conserving double-excitation pool can extract the entire low-lying spectrum for two and three identical nucleons in 0g9/2 (five and ten states) in one optimization run, matching exact JUN45 diagonalization to spectroscopic accuracy and restoring the expected J values. That is the concrete new result: simultaneous multi-state extraction plus post-convergence J^{2} and wave-function diagnostics that line up with CG/CFP structure.\n\nWhat it does well is the execution. Jordan-Wigner mapping is standard and correctly preserves anti-commutation. The adaptive growth of the ansatz, weighted SSVQE loss, and L-BFGS-B re-optimization are applied without internal contradiction. Energies go to residual zero for the two-nucleon case; relative errors plunge for three nucleons after the expected early oscillations. Orthogonality is automatic from the unitary. The two-nucleon state vectors are pure geometric pairing; the three-nucleon ones show the expected seniority mixing. Citations cover the prior ADAPT-VQE shell-model work, the 58Ni ansatz paper, and the authors’ own pairing conference note. Circularity is low because everything is checked against independent classical exact diagonalization of the same Hamiltonian.\n\nSoft spots are real but proportionate to the claim as written. The Hilbert spaces are tiny (classically trivial). Only noiseless state-vector simulation is shown; CNOT depth already hits 480–2768, and the authors themselves flag residual J^{2} deviations for the three-nucleon case as threshold artifacts. Free parameters (weights, gradient/energy cutoffs, HF reference set) exist but are conventional. No code or hardware run is released. Novelty is moderate—combination of known tools—but the full write-up with nuclear diagnostics is useful.\n\nThis is for people already working on quantum algorithms for nuclear structure or wanting a reproducible few-body benchmark. Math and data look solid within the stated scope. I would send it to peer review; the contribution is accept-shaped once residual symmetry breaking and scaling are discussed more explicitly. Engage if that is your subfield; otherwise skim the figures and move on.","headline":"Solid noiseless demo of single-run ADAPT-SSVQE recovering full few-nucleon spectra and J^{2} for j=9/2, but the systems are classically trivial and hardware path is still open.","tokens_in":12616,"tokens_out":563,"would_cite":false,"duration_ms":14877,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["21.60.Cs","03.67.Ac"],"model":"grok-4.5","headline":"A single quantum optimization recovers the full low-lying shell-model spectrum for few nucleons and restores total angular momentum.","keywords":["nuclear shell model","quantum simulation","ADAPT-VQE","SSVQE","Jordan-Wigner transformation","angular momentum restoration","many-body Hilbert space"],"falsifier":"Apply the identical ADAPT-SSVQE procedure, same operator pool and convergence thresholds, to a four-nucleon or multi-j system whose exact spectrum is still classically known; check whether every targeted energy still matches the exact value to spectroscopic accuracy and whether measured J^2 values remain integer or half-integer once the circuit contains thousands of CNOT gates under a realistic noise model.","tokens_in":12550,"feed_emoji":"⚛️","tokens_out":1053,"duration_ms":21539,"temperature":0.7,"pith_summary":"The nuclear shell model gives a complete quantum description of nuclei, but its Hilbert space grows so large that classical computers cannot store or diagonalize the Hamiltonian for realistic valence spaces. This paper introduces a single-run quantum algorithm that finds the ground state and many excited states of the shell-model Hamiltonian at once. The Hamiltonian is mapped to qubits with the Jordan-Wigner transformation so that fermionic statistics are preserved; an adaptive ansatz built from magnetic-projection-conserving excitations then evolves a set of orthogonal reference states under one shared circuit. In noiseless simulation the method reproduces exact energies for two and three identical nucleons in a j=9/2 orbital to spectroscopic accuracy and yields states that are eigenstates of total angular momentum. A reader cares because complete low-lying spectra, not just ground states, are required for nuclear structure and applications such as decay-heat estimates, and the approach is designed to scale with qubit number rather than classical storage.","feed_headline":"One quantum run recovers the full few-nucleon shell spectrum","feed_subtitle":"Adaptive subspace search matches exact energies and restores angular momentum for two and three nucleons.","key_machinery":"ADAPT-SSVQE: a weighted subspace-search variational eigensolver whose ansatz is grown iteratively by selecting, from a pool of M_J-conserving single- and double-excitation operators, the operator of largest weighted energy gradient, then re-optimizing all parameters so that one unitary maps a set of orthogonal Hartree-Fock references onto the full targeted spectrum.","core_discovery":"Using ADAPT-SSVQE with an M_J-conserving double-excitation operator pool on a Jordan-Wigner mapped shell-model Hamiltonian, a single optimization simultaneously produces five (respectively ten) mutually orthogonal eigenstates for two (respectively three) identical nucleons in the 0g9/2 orbital inside a 10-qubit space, matching exact diagonalization to spectroscopic accuracy and intrinsically restoring total angular momentum J^2 within the chosen M_J subspace.","pith_inferences":["If further pool truncation or hardware-efficient ansätze can cut CNOT depth, the method could become usable on near-term devices for nuclei beyond exact classical diagonalization.","The small residual J^2 deviations already visible in the three-nucleon results imply that tighter thresholds or an explicit J^2 term may be required before spin assignments are trusted for odd-mass systems.","Adding proton-neutron operators and isospin conservation would test whether single-run symmetry restoration survives in realistic even-even and odd-odd nuclei.","The two-nucleon wave-function components matching pure Clebsch-Gordan coefficients show that the algorithm reconstructs geometric angular-momentum coupling even when a realistic residual interaction is present."],"forward_implications":["Multiple shell-model eigenstates inside a fixed M_J subspace can be obtained from one variational optimization without separate runs or post-processing.","Total-angular-momentum quantum numbers emerge from the converged wave functions even though the operator pool never enforces J^2.","Circuit depth grows only with the number of selected operators needed to exhaust the energy gradient, giving a compact representation of nucleonic correlations.","The same single-run strategy is in principle applicable to any many-body problem that requires a full low-lying spectrum rather than a ground state alone.","The limiting resource becomes qubit count and two-qubit gate depth instead of classical Hilbert-space storage."],"fun_headline_variants":["One quantum run extracts full few-nucleon shell spectrum","ADAPT-SSVQE recovers multiple orthogonal shell states at once","Single-run quantum solver matches exact nuclear shell energies","Adaptive subspace search yields complete MJ shell eigenstates","Quantum circuit restores J2 for two- and three-nucleon shells"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The central claim rests on the premise that noiseless simulation of ten-qubit systems of only two or three nucleons, stopped when the gradient or energy change falls below a fixed numerical threshold, is enough evidence that the same procedure will keep spectroscopic accuracy and angular-momentum restoration for larger valence spaces or on real noisy hardware.","fun_headline_variants_meta":{"raw":{"variants":["One quantum run extracts full few-nucleon shell spectrum","ADAPT-SSVQE recovers multiple orthogonal shell states at once","Single-run quantum solver matches exact nuclear shell energies","Adaptive subspace search yields complete MJ shell eigenstates","Quantum circuit restores J2 for two- and three-nucleon shells"]},"model":"grok-4.5","effort":"low","cost_usd":0.005142,"raw_usage":{"total_tokens":1489,"prompt_tokens":852,"num_sources_used":0,"completion_tokens":66,"cost_in_usd_ticks":51420000,"prompt_tokens_details":{"text_tokens":852,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":571,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":852,"tokens_out":66,"duration_ms":5399,"temperature":1.0,"reasoning_tokens":571,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-10T10:52:24.401334+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Apply the identical ADAPT-SSVQE procedure, same operator pool and convergence thresholds, to a four-nucleon or multi-j system whose exact spectrum is still classically known; check whether every targeted energy still matches the exact value to spectroscopic accuracy and whether measured J^2 values remain integer or half-integer once the circuit contains thousands of CNOT gates under a realistic noise model.","supporting_citations":[],"review_version":1}