{"id":"fc2935e7-cabd-494f-b6d1-5e544b6b065e","arxiv_id":"2606.20166","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Modified QAE on D-Wave hardware yields magnetic dipole HFS constants for four light atomic systems that match GRASP results at limited precision.","lead":"The paper applies a modified quantum annealing algorithm on D-Wave hardware to compute magnetic dipole hyperfine structure constants for neutral Li, Li-like Be, neutral Na, and Na-like Mg. It benchmarks these against classical relativistic calculations and reports consistency at three-decimal-place precision for small configuration sets.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"CSF truncation criterion (significant ground-state contributions) may not preserve HFS constant to three decimals","rationale":"The reader's weakest assumption correctly isolates the truncation step as the point where the central consistency claim is least secured; the concrete test above directly quantifies whether that step introduces error beyond the reported three-decimal tolerance.","tokens_in":1779,"tokens_out":273,"duration_ms":25585,"concrete_test":"For neutral Li (or Na) with the extended orbital set, recompute the magnetic dipole HFS constant in GRASP once with the full CSF list and once with the exact 12-CSF subset retained by the QAE truncation; if the two GRASP values differ by more than 0.001 the truncation assumption fails at the claimed precision.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The modified QAE retains at most 12 CSFs chosen by their contribution to the ground-state wavefunction of the Dirac-Coulomb Hamiltonian. The magnetic dipole HFS constant is the expectation value of a distinct one-body operator whose radial weighting differs from the energy functional (especially the nuclear-region behavior). The abstract and method description give no explicit check that the energy-based truncation error remains below 0.001 for the HFS observable when the same truncated basis is used in GRASP.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript reports the first application of a modified Quantum Annealer Eigensolver (QAE) on D-Wave hardware to compute magnetic dipole hyperfine structure (HFS) constants for neutral Li, Li-like Be, neutral Na, and Na-like Mg. It employs a zooming-and-sigma-annealing approach with floating-point encoding on Dirac-Coulomb Hamiltonian matrices constructed from at most 12 configuration state functions (CSFs), applies an energy-based CSF truncation for larger orbital sets, and claims that hardware results are fully consistent with GRASP relativistic CI calculations at the chosen three-decimal-place precision.","tokens_in":1886,"tokens_out":512,"duration_ms":36869,"significance":"If the central claims hold, the work provides an initial hardware demonstration that quantum annealing can be extended from energy eigenvalues to a distinct one-body observable (magnetic dipole HFS) in relativistic atomic structure. The explicit benchmarking against an independent classical code (GRASP) and the use of actual QPU runs are positive features. However, the restriction to very small truncated bases and three-decimal precision limits the immediate impact on atomic physics.","major_comments":[{"comment":"Method section on CSF truncation: the scheme retains at most 12 CSFs chosen by their contribution to the ground-state wavefunction of the Dirac-Coulomb Hamiltonian, yet no direct comparison (full vs. truncated basis) is shown to confirm that the truncation error on the magnetic dipole HFS constant remains below 0.001. Because the HFS operator has different radial weighting (especially near the nucleus) from the energy functional, energy-based selection does not automatically guarantee the reported precision for the HFS observable.","section":"Method (CSF truncation scheme)"},{"comment":"Results and abstract: the floating-point encoding scheme and the precise mapping of eigenvector components to the HFS expectation value are only sketched; without an explicit error analysis or reported uncertainty for each system and matrix dimension, it is difficult to assess whether the claimed three-decimal consistency with GRASP is robust or an artifact of the limited precision (up to 10 qubits).","section":"Results and abstract"}],"minor_comments":[{"comment":"Abstract: the statement that 'accuracy varying across systems and H_DC matrix dimensions' is not accompanied by any tabulated values or quantitative measure of that variation.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive feedback. We address each major comment below.","responses":[{"response":"We agree the truncation criterion is energy-based and that a direct full-vs-truncated comparison for the HFS constant is not shown. Given the deliberately small bases (≤12 CSFs) used for this hardware demonstration, the dominant contributions are retained, but we acknowledge the different radial weighting of the HFS operator. In revision we will add an explicit statement noting this limitation and that quantitative truncation-error checks for the observable are left to future work with larger resources.","revision_made":"partial","referee_comment":"Method section on CSF truncation scheme: the scheme retains at most 12 CSFs chosen by their contribution to the ground-state wavefunction of the Dirac-Coulomb Hamiltonian, yet no direct comparison (full vs. truncated basis) is shown to confirm that the truncation error on the magnetic dipole HFS constant remains below 0.001. Because the HFS operator has different radial weighting (especially near the nucleus) from the energy functional, energy-based selection does not automatically guarantee the reported precision for the HFS observable."},{"response":"The floating-point encoding and the mapping of the extracted eigenvector to the HFS expectation value are described in the Methods. The reported consistency is at the three-decimal precision level matching our QAE implementation. We will expand the Results section with a clearer step-by-step description of the mapping together with per-system uncertainty estimates tied to the qubit precision and annealing parameters.","revision_made":"yes","referee_comment":"Results and abstract: the floating-point encoding scheme and the precise mapping of eigenvector components to the HFS expectation value are only sketched; without an explicit error analysis or reported uncertainty for each system and matrix dimension, it is difficult to assess whether the claimed three-decimal consistency with GRASP is robust or an artifact of the limited precision (up to 10 qubits)."}],"tokens_in":1486,"tokens_out":425,"duration_ms":40291,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The paper's core contribution is the first reported use of D-Wave hardware to extract magnetic dipole hyperfine constants rather than just energies. They modify the quantum annealer eigensolver with zooming, sigma annealing, and floating-point encoding, then apply it to small Dirac-Coulomb matrices for Li, Li-like Be, Na, and Na-like Mg. The hardware outputs match GRASP to the three-decimal precision they target.\n\nThey do the benchmarking cleanly against both GRASP and simulated annealing, and they handle the eigenvector extraction needed for the one-body HFS operator. That step is new relative to earlier QAE energy-only runs.\n\nThe truncation to at most 12 CSFs chosen by ground-state energy contribution is the main soft spot. The HFS operator weights the nuclear region differently, so it is not automatic that the same cutoff keeps the HFS error below 0.001; the abstract gives no separate check on that observable. Matrix sizes stay tiny (11 or fewer CSFs), precision is capped at three decimals with up to 10 qubits, and no error bars or larger-system tests appear. These are real limits on how far the result travels.\n\nThe work is for groups tracking early quantum-hardware applications to atomic structure. A reader already following QAE or D-Wave chemistry experiments will find the extension useful. It is honest on its own terms and deserves referee time because it is the first hardware result for this property, even if the scope stays modest.","headline":"First hardware demo of QAE for magnetic dipole HFS constants on four light atoms, but the work stays narrow due to small matrices and truncation limits.","tokens_in":2354,"tokens_out":377,"would_cite":false,"duration_ms":18137,"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":"Quantum annealing on D-Wave hardware computes magnetic dipole hyperfine structure constants for Li, Be, Na, and Mg atoms to three decimal places, matching GRASP relativistic calculations.","keywords":["quantum annealing","hyperfine structure","D-Wave","magnetic dipole","atomic structure","configuration state functions","GRASP","Dirac-Coulomb Hamiltonian"],"falsifier":"A GRASP run that includes the full untruncated CSF basis for any of the four systems and produces an HFS constant differing by more than 0.001 from the QAE result would falsify the accuracy claim.","tokens_in":2689,"feed_emoji":"⚛","tokens_out":695,"duration_ms":30423,"temperature":0.7,"pith_summary":"The paper applies a modified Quantum Annealer Eigensolver to the problem of magnetic dipole hyperfine structure constants in light atoms and their ions. Relativistic Dirac-Coulomb Hamiltonian matrices are built from at most twelve configuration state functions, and a zooming-and-sigma-annealing scheme with floating-point encoding extracts the ground-state eigenvector on D-Wave hardware. Hardware results are benchmarked directly against GRASP multiconfiguration Dirac-Hartree-Fock values and against simulated annealing, showing agreement at the reported precision. This constitutes the first reported use of quantum annealing for hyperfine constants rather than energies alone.","feed_headline":"D-Wave quantum annealer matches GRASP on hyperfine constants","feed_subtitle":"Hardware results for Li, Be, Na, Mg agree with relativistic calculations at three decimal places using up to twelve CSFs.","key_machinery":"Modified Quantum Annealer Eigensolver (QAE) with zooming-and-sigma-annealing and floating-point encoding, applied to small relativistic Dirac-Coulomb Hamiltonian matrices constructed from truncated sets of configuration state functions.","core_discovery":"The modified QAE algorithm, run on the D-Wave QPU, produces magnetic dipole HFS constants for neutral Li, Li-like Be, neutral Na, and Na-like Mg that remain consistent with full GRASP calculations when the H_DC matrix is limited to eleven or fewer CSFs or to a truncated set of twelve significant CSFs, with all values agreeing to three decimal places.","pith_inferences":["Scaling the same encoding to matrices larger than twelve CSFs would require more qubits or improved precision schemes.","The method could be tested on electric quadrupole or magnetic octupole constants using the same Hamiltonian matrices.","If the truncation error remains small for heavier atoms, the approach might serve as a hybrid quantum-classical tool for selected atomic properties."],"forward_implications":["Hardware QPU output for the four atomic systems agrees with GRASP at three decimal places for the chosen matrix sizes.","The accuracy achieved depends on the specific atom and on the dimension of the H_DC matrix.","The CSF truncation scheme permits use of extended correlation orbital sets while preserving the reported precision.","Quantum annealing supplies an alternative route to hyperfine constants once the ground-state eigenvector is obtained."],"fun_headline_variants":["D-Wave QAE produces hyperfine constants matching GRASP for Li Be Na Mg","Quantum annealing on D-Wave computes magnetic dipole HFS constants","Modified QAE on D-Wave hardware agrees with GRASP on HFS constants","D-Wave quantum results for hyperfine structure in Li-like and Na-like atoms"],"cache_read_input_tokens":64,"weakest_assumption_plain":"Retaining only the twelve configuration state functions that contribute most to the ground-state wavefunction keeps the magnetic dipole HFS constant accurate to three decimal places.","fun_headline_variants_meta":{"raw":{"variants":["D-Wave QAE produces hyperfine constants matching GRASP for Li Be Na Mg","Quantum annealing on D-Wave computes magnetic dipole HFS constants","Modified QAE on D-Wave hardware agrees with GRASP on HFS constants","D-Wave quantum results for hyperfine structure in Li-like and Na-like atoms"]},"model":"grok-4.3","cost_usd":0.008077,"raw_usage":{"total_tokens":3695,"prompt_tokens":713,"num_sources_used":0,"completion_tokens":82,"cost_in_usd_ticks":80774500,"prompt_tokens_details":{"text_tokens":713,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2900,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":713,"tokens_out":82,"duration_ms":32612,"temperature":1.0,"reasoning_tokens":2900,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-30T10:39:04.559519+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A GRASP run that includes the full untruncated CSF basis for any of the four systems and produces an HFS constant differing by more than 0.001 from the QAE result would falsify the accuracy claim.","supporting_citations":[],"review_version":1}