{"id":"04637b23-f823-47ef-8cf8-d304d85ecf73","arxiv_id":"2608.06415","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"Hardware-assisted sample-based quantum diagonalization reproduces CCSD-quality ground-state energies for HeH+, ArH+, and H2O, with deviations from exact active-space CASCI of 0.00, 2.51, and 6.34 mHa respectively.","lead":"Researchers used IBM quantum hardware to sample molecular wavefunctions and then solved a small quantum chemistry problem classically to estimate ground-state energies of HeH+, ArH+, and water. It matters as a test of whether today's noisy quantum chips can assist classical algorithms for molecular energies, and demonstrates a 46-qubit water calculation.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 6.34 mHa H2O SQD–CASCI gap may be a systematic subspace-limitation of the one-repetition CCSD-initialized LUCJ sampler, not a hardware-noise artifact, and the paper's single-run min-batch estimator cannot distinguish these.","rationale":"The reader's weakest assumption identified the sampled subspace's overlap with the true active-space ground state, and that is exactly the load-bearing point. My concern sharpens it: the H2O equilibrium gap, not just stretched geometries, already strains the feasibility claim, and the current error analysis cannot separate a systematic ansatz limitation from hardware noise because the min-batch estimator and the single empirical pool preclude that separation. The proposed concrete test—comparing the SQD-recovered subspace against an independent classical selected-CI determinant list—would directly settle whether the 6.34 mHa residual is a missing-determinant problem (systematic) or a sampling/noise problem (correctable). This does not change the verdict: the paper is an honest feasibility study, and the appropriate action remains CONDITIONAL acceptance pending repeated runs, error bars, and the subspace-completeness check. I therefore keep the reader's CONDITIONAL verdict unchanged while adding a concrete route to validate the central claim.","tokens_in":13913,"tokens_out":3457,"duration_ms":39970,"concrete_test":"Run an independent classical selected-CI (e.g., CIPSI or heat-bath CI) in the same frozen-core cc-pVDZ active space for H2O at R_OH = 0.95782 Å, converged to near the CASCI energy, and record the top determinants by weight. Then inspect the SQD-recovered subspace from the reported run: are those dominant determinants present, and with comparable weights? If key determinants are missing, the 6.34 mHa gap is a systematic state-preparation/subspace limitation; if they are present but with distorted weights, finite-shot or hardware-noise effects dominate and repeated QPU runs or increased shots would be the appropriate remedy.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central feasibility claim rests on the SQD–CASCI deviations reported in Table 2, especially the 6.34 mHa H2O result. The LUCJ ansatz uses one repetition (L=1) with parameters fixed from CCSD t1/t2 amplitudes and no hardware optimization (Sec. 2.2). The sampled determinant subspace is therefore anchored to a single-reference CCSD-like wavefunction, and the close SQD–CCSD agreement in Fig. 1 is partly by construction. The independent active-space reference is CASCI, and the residual 6.34 mHa at equilibrium could arise because the truncated LUCJ circuit cannot generate important determinants (e.g., those requiring more than the restricted nearest-neighbor/on-site diagonal-Coulomb terms), rather than from finite-shot noise or device errors. The paper's convergence analysis (Fig. 2) does not settle this: it reuses the same 20,000-shot pool across recovery iterations and reports the minimum over five subsampled batches, so the plateaus only show stability of the recovery procedure on one finite pool, not subspace completeness. If the dominant missing determinants are absent because of the ansatz, then additional hardware shots or error mitigation will not reduce the deviation, and the 'feasibility' conclusion for larger active spaces would need to be qualified as ansatz-limited rather than hardware-limited.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports hardware-assisted Sample-Based Quantum Diagonalization (SQD) calculations for the ground states of HeH+, ArH+, and H2O, using shallow LUCJ circuits initialized from RHF-CCSD t1/t2 amplitudes on IBM quantum hardware. The authors compute potential-energy curves with 6-31G and cc-pVDZ basis sets, compare equilibrium-region energies against same-active-space CASCI and CCSD references, and report SQD-CASCI deviations of 0.00, 2.51, and 6.34 mHa for HeH+, ArH+, and H2O, respectively. The central claim is that the SQD workflow is feasible for these benchmarks, including a 46-qubit H2O active space, while explicitly acknowledging that the SQD-CCSD comparison is an internal-consistency check and that repeated independent executions are needed before drawing scalability conclusions.","tokens_in":14284,"tokens_out":5060,"duration_ms":56085,"significance":"If the reported deviations are representative, the paper provides useful evidence that SQD can produce chemically meaningful equilibrium energies for small molecules and a polyatomic active space on near-term hardware. The manuscript is transparent in several important ways: the CASCI references diagonalize the same frozen-core active-space Hamiltonian used by SQD, the circuit resource counts and sampling parameters are reported in detail, and the text explicitly cautions that the SQD-CCSD agreement is partly internal consistency because the LUCJ parameters come from CCSD amplitudes. These strengths make the feasibility claim defensible as a demonstration. However, the independent validation is concentrated at three equilibrium geometries, and the origin of the largest SQD-CASCI gap, the 6.34 mHa H2O deviation, is not resolved; whether it is a hardware-noise effect or a systematic limitation of the one-repetition CCSD-initialized LUCJ sampler is load-bearing for the paper's broader applicability claim.","major_comments":[{"comment":"The 6.34 mHa H2O SQD-CASCI gap may be dominated by a systematic subspace limitation of the sampling circuit rather than by hardware noise. The LUCJ ansatz uses L=1, a restricted nearest-neighbor/on-site diagonal-Coulomb pattern, and parameters fixed from CCSD amplitudes with no hardware-side optimization, so the sampled determinant manifold is anchored to a single-reference CCSD-like state. Because the convergence analysis in Fig. 2 reuses the same 20,000-shot empirical pool across recovery iterations, the plateaus show stability of the recovery procedure on that finite pool, not completeness of the sampled subspace. To support the feasibility claim, the authors should perform a noiseless classical simulation of the same LUCJ circuit for H2O (or an alternative state-preparation scheme) and show whether the 6.34 mHa gap persists; if it does, the deviation is an ansatz-expressibility error and additional hardware shots or error mitigation will not remove it.","section":"Sec. 2.2 / Sec. 2.6 / Table 2"},{"comment":"The paper's single-run measurement pool and min-over-batches estimator do not separate hardware noise from other error sources. The final SQD energy is defined as the minimum over B=5 subsamples of one empirical pool, and the reported 0.0423 mHa subsampling spread is explicitly not an independent QPU uncertainty. The conclusion that the H2O deviation 'cannot be attributed to intra-pool batch fluctuations alone' is reasonable, but the feasibility claim would be considerably stronger with at least a few independent hardware executions at one or two geometries. Without such repetitions, the statement that the deviation reflects 'state preparation, finite-shot hardware sampling, configuration recovery, and subspace construction' remains a list of possibilities rather than a diagnosis.","section":"Sec. 2.3 / Sec. 2.6 / Table 1(b)"},{"comment":"The potential-energy-curve comparisons to CCSD are only an internal-consistency benchmark, because the LUCJ parameters are initialized from CCSD amplitudes and the paper itself calls the CCSD comparison an internal-consistency check. The independent same-active-space CASCI references are reported only at the three equilibrium geometries in Table 2, not along the scanned curves. As a result, the claim that the SQD curves 'closely follow' CCSD and reproduce the equilibrium-region trends is not independently validated for the stretched regions, where the RHF-CCSD reference itself becomes unreliable. The authors should provide CASCI reference points at selected stretched geometries (at least for the smaller HeH+ and ArH+ systems, where FCI in the active space is cheap) to verify that the SQD subspace remains accurate where the CCSD benchmark is not a valid reference.","section":"Sec. 3 / Fig. 1"}],"minor_comments":[{"comment":"The manuscript contains duplicated text blocks in Section 3, including the passage beginning 'ROH = 0.95782Å.Theupperpanelsshow...' and repeated wording in the Fig. 2 caption; these should be removed.","section":"Sec. 3 / Fig. 2"},{"comment":"The sentence 'Under this configuration, four α and four β electrons were explicitly treated' is ambiguous because it applies only to ArH+ and H2O, not to HeH+; specify the electron counts separately for each molecule.","section":"Sec. 2.6"},{"comment":"There are run-together words resulting from the text extraction (for example, 'Forthepresentcalculations,butstringsweregenerated'), which should be corrected in the final typeset version.","section":"Abstract / full text"},{"comment":"The entry mentioning 'ffsim.qiskit.PRE_INIT' introduces the ffsim package without defining it; either name the package and version or provide a reference.","section":"Table 1(b)"},{"comment":"Using the minimum over B subsamples as the final estimator is not a standard unbiased estimator; the paper should clarify the rationale or report both the minimum and the mean over batches.","section":"Sec. 2.3 / Eq. (11)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within scope for physics.chem-ph and the authors are appropriately cautious in their claims. The main missing piece is a diagnostic experiment that distinguishes ansatz-limited from hardware-limited error in the H2O result; I would encourage the editor to request such an experiment or a clear classical-simulation proxy before publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: this is a useful, honestly reported feasibility data point, not a methodological breakthrough. The new content is hardware-executed SQD potential curves for HeH+, ArH+, and a 46-qubit H2O active space, with transparent same-active-space CASCI deviations of 0.00, 2.51, and 6.34 mHa. It deserves a serious referee, but the reported deviations should be read as single-run demonstrations, not robust error estimates.\n\nWhat is actually new: the specific hardware results and the 46-qubit benchmark. SQD itself, the LUCJ ansatz, and CCSD-initialized circuits are all prior work, and the paper does not pretend otherwise. What it does well is transparency. The authors explicitly label the SQD–CCSD agreement as an internal-consistency benchmark because the LUCJ parameters come from CCSD amplitudes. They give a more independent check against same-active-space CASCI and report the gaps without spin. They also provide circuit depths, shot counts, and make clear that no variational optimization was performed on the device. That candor is genuinely useful.\n\nThe soft spots are real but not hidden. The 6.34 mHa H2O residual is above chemical accuracy, and the paper does not identify its source. The convergence plots reuse the same 20,000-shot pool, so the plateaus only show that the recovery procedure stabilizes on one finite dataset; they do not demonstrate subspace completeness. Given the LUCJ ansatz uses one repetition and only nearest-neighbor/on-site diagonal-Coulomb terms, it is entirely plausible that the remaining gap is a systematic subspace limitation of the sampler rather than a finite-shot or noise artifact. On that point the stress-test note is right: more hardware shots will not reduce the deviation if the missing determinants are never generated. The min-batch estimator, taking the minimum over five subsamples, also makes the results look better than the central tendency would, and there are no repeated independent QPU runs to provide error bars.\n\nThe central feasibility claim holds up: SQD on current IBM hardware can track CCSD-quality curves for these benchmarks and handle a 46-qubit active space. That is worth knowing. What would strengthen the paper for publication at a higher level: a few repeated runs, an uncertainty estimate on the min-batch estimator, and a same-basis CCSD/6-31G reference to separate basis-set error from method error. Code and data should be released.\n\nThis paper is for people tracking practical quantum chemistry on NISQ hardware, especially those interested in SQD's strengths and limits. It is not a methods paper; it is an application with honest caveats. I would send it to peer review and ask the authors to address the repetition and error-bar issues in revision.","headline":"A candid, useful SQD feasibility study on three small molecules; treat the reported deviations as single-run demonstrations, because the H2O 6.34 mHa gap likely reflects the truncated ansatz, not hardware noise.","tokens_in":14828,"tokens_out":3530,"would_cite":false,"duration_ms":31746,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper reports that sample-based quantum diagonalization on a superconducting quantum processor reproduces the CCSD potential-energy curves of HeH+, ArH+, and H2O near equilibrium, with deviations of 0.00, 2.51, and 6.34 mHa from…","keywords":["sample-based quantum diagonalization","ground-state energy","LUCJ ansatz","quantum chemistry","NISQ devices","potential-energy curves","molecular ions","water molecule"],"falsifier":"Take the H2O/cc-pVDZ system at a stretched O-H bond length, say $R_{\\mathrm{OH}}=1.5$ Å, and compare the SQD energy against a full diagonalization of the same active-space Hamiltonian; if the deviation there is much larger than the 6.34 mHa found at equilibrium, the sampled subspace is missing determinants in the multireference region.","tokens_in":13686,"feed_emoji":"⚛️","tokens_out":9590,"duration_ms":87650,"temperature":0.7,"pith_summary":"This paper tries to establish that sample-based quantum diagonalization (SQD), a hybrid workflow that builds a low-energy determinant subspace from bitstrings sampled on quantum hardware and then diagonalizes the Hamiltonian classically inside that subspace, can compute chemically meaningful ground-state energies for small molecules. Using the cc-pVDZ basis, the SQD curves for HeH+, ArH+, and H2O closely follow the same-basis CCSD references near equilibrium, and at the adopted equilibrium geometries the SQD energies differ from the exact same-active-space CASCI energies by 0.00, 2.51, and 6.34 mHa, respectively. The H2O case uses a 46-qubit active space and is presented as evidence that the workflow extends beyond diatomic ions to a polyatomic benchmark. The residual error grows with active-space size, so the paper presents the result as a proof of principle for feasibility rather than as a demonstration of established scaling.","feed_headline":"SQD matches CCSD curves for HeH+, ArH+, and H2O","feed_subtitle":"Shallow-circuit sampling lands within 0.00–6.34 mHa of exact active-space references.","key_machinery":"The carrying object is the sampled determinant subspace $X = \\{x_1,\\dots,x_D\\}$ of bitstrings measured from the LUCJ circuit, together with the projected Hamiltonian $P_X \\hat{H} P_X$, whose lowest eigenvalue is the SQD energy. The LUCJ ansatz, a shallow composition of orbital rotations and spin-balanced diagonal Coulomb interactions, is initialized from CCSD amplitudes by double factorization with a single repetition, so the circuit is a sampler rather than a variational ansatz. A self-consistent configuration-recovery procedure repairs bitstrings with wrong spin-resolved particle numbers, subsamples into five batches, and iterates until both the minimum batch energy and the spin-orbital occupations stabilize; selected-CI diagonalization of the sparse projected Hamiltonian then yields the ground-state estimate.","core_discovery":"The central claim is that a shallow, one-repetition local unitary cluster Jastrow (LUCJ) circuit, initialized from CCSD t1 and t2 amplitudes, can act as a structured sampler whose measured bitstrings define a determinant subspace in which classical diagonalization recovers the ground-state energy of the active-space Hamiltonian. For the cc-pVDZ basis, the SQD potential-energy curves reproduce the equilibrium-region trends of the CCSD curves for all three systems. The deviations from the same-active-space CASCI references are 0.00 mHa for HeH+, 2.51 mHa for ArH+, and 6.34 mHa for H2O at equilibrium, and the corresponding deviations from CCSD are 0.00, 0.04, and 2.67 mHa. The H2O result demonstrates execution of the full workflow on a 46-qubit polyatomic active space.","pith_inferences":["A testable consequence is that enlarging the subspace, for example with two LUCJ repetitions or a re-optimized circuit, should reduce the H2O deviation below 6.34 mHa while keeping the shot count fixed; if it does not, the remaining error is not subspace truncation.","The stretched O-H region is the natural stress test: if a same-active-space CASCI comparison at $R_{\\mathrm{OH}}=1.5$ Å shows a sharply growing deviation, then the single-repetition CCSD-initialized sampler misses the determinants that dominate as the bond breaks.","Because all recovery iterations reuse the same finite shot pool, the reported convergence may underestimate run-to-run hardware variability; repeated independent executions would give a truer picture of the method's stability.","If SQD is extended to larger active spaces, the sparse structure of the projected Hamiltonian means the classical diagonalization step will stay manageable as long as the sampled subspace remains compact; the bottleneck would then be whether the shallow sampler keeps finding the important determinants."],"forward_implications":["If the claim holds, SQD offers a near-term route to molecular ground-state energies that avoids repeated on-hardware expectation-value estimation, using only shallow circuit sampling plus classical selected-CI diagonalization.","The workflow is executable on a 46-qubit polyatomic active space on current superconducting processors, so the practical reach of hardware-assisted quantum chemistry extends beyond two-center ions.","Because the LUCJ parameters come from CCSD, the SQD-CCSD agreement is an internal-consistency check, and independent benchmarks such as same-active-space CASCI or experiment are needed to validate absolute accuracy.","The growing deviation from CASCI, from 0.00 to 2.51 to 6.34 mHa, identifies subspace completeness rather than sampling noise as the next limiting factor, since the reported intra-pool batch spread is much smaller.","The method can be viewed as a quantum-assisted selected configuration interaction: the quantum device proposes determinants, and classical diagonalization decides the weights."],"supporting_citations":[{"why":"Introduces the SQD approach of reconstructing a low-energy determinant subspace from sampled bitstrings.","marker":"[13]"},{"why":"Provides the self-consistent configuration-recovery procedure and hardware SQD workflow used for the measured data.","marker":"[14]"},{"why":"Supplies the theoretical foundation for SQD subspace diagonalization and the recovery and selected-CI iterations.","marker":"[21]"},{"why":"Defines the local unitary cluster Jastrow ansatz whose shallow structure enables hardware sampling.","marker":"[23]"},{"why":"Provides the spin-balanced LUCJ parametrization and double-factorization mapping used to initialize from CCSD amplitudes.","marker":"[24]"},{"why":"Maps the fermionic Hamiltonian to qubit Pauli strings, the representation in which measurements produce occupation-number bitstrings.","marker":"[22]"},{"why":"Supplies the equilibrium geometry of H2O used for the polyatomic benchmark.","marker":"[25]"},{"why":"Supplies the cc-pVDZ correlation-consistent basis set used throughout the SQD calculations.","marker":"[27]"}],"fun_headline_variants":["Shallow circuits deliver CCSD-grade energies for HeH+, ArH+, H2O","SQD with LUCJ: potential curves match CCSD for three molecules","Quantum diagonalization from shallow samples hits CASCI targets","HeH+, ArH+, H2O: SQD reproduces CCSD curves on hardware"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the one-shot sampling circuit built from classical coupled-cluster results has enough overlap with the true ground state at every geometry—if it misses the important electron configurations, the final energy will be biased.","fun_headline_variants_meta":{"raw":{"variants":["Shallow circuits deliver CCSD-grade energies for HeH+, ArH+, H2O","SQD with LUCJ: potential curves match CCSD for three molecules","Quantum diagonalization from shallow samples hits CASCI targets","HeH+, ArH+, H2O: SQD reproduces CCSD curves on hardware"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000253,"raw_usage":{"total_tokens":1656,"prompt_tokens":1131,"completion_tokens":525,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":747,"completion_tokens_details":{"reasoning_tokens":440}},"tokens_in":747,"tokens_out":525,"duration_ms":6087,"temperature":1.0,"reasoning_tokens":440,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T04:25:30.242562+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the H2O/cc-pVDZ system at a stretched O-H bond length, say $R_{\\mathrm{OH}}=1.5$ Å, and compare the SQD energy against a full diagonalization of the same active-space Hamiltonian; if the deviation there is much larger than the 6.34 mHa found at equilibrium, the sampled subspace is missing determinants in the multireference region.","supporting_citations":[{"cited_title":"Shaian, D","cited_arxiv_id":null,"evidence_quote":"Introduces the SQD approach of reconstructing a low-energy determinant subspace from sampled bitstrings."},{"cited_title":"Robledo-Moreno, M","cited_arxiv_id":null,"evidence_quote":"Provides the self-consistent configuration-recovery procedure and hardware SQD workflow used for the measured data."},{"cited_title":"Motta, K","cited_arxiv_id":null,"evidence_quote":"Defines the local unitary cluster Jastrow ansatz whose shallow structure enables hardware sampling."},{"cited_title":"Fradkin, Phys","cited_arxiv_id":null,"evidence_quote":"Maps the fermionic Hamiltonian to qubit Pauli strings, the representation in which measurements produce occupation-number bitstrings."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the equilibrium geometry of H2O used for the polyatomic benchmark."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the cc-pVDZ correlation-consistent basis set used throughout the SQD calculations."}],"review_version":1}