{"id":"302710e8-20d6-4cd2-9f14-00bf6a9f5ced","arxiv_id":"2411.09861","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"The first implementation of density matrix embedding theory with sample-based quantum diagonalization is demonstrated on quantum hardware for an 18-hydrogen ring and cyclohexane, yielding energies close to classical reference methods.","lead":"This paper combines two existing quantum chemistry methods, DMET and sample-based quantum diagonalization, and runs the combined workflow on an IBM quantum processor to compute molecular energies. It demonstrates that active regions of 27 and 32 qubits can be treated on near-term hardware, a step toward simulating larger molecules such as peptides and proteins.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim rests on the adequacy of CCSD-parametrized LUCJ sampling for the embedded subspace; the paper's own unfragmented H18 results show this assumption can fail, and DMET-SQD convergence to DMET-FCI in the strongly correlated regime is not demonstrated.","rationale":"The paper's strongest claim is that DMET-SQD gives ground-state energies in agreement with reference classical methods while reducing qubit counts. The SQD solver constructs its subspace from bitstrings sampled from the LUCJ state, Eq. (2), with parameters taken from CCSD. For the claim to hold, that subspace must contain a good approximation to the embedded ground state. The evidence in Fig. 2 shows this condition is not automatically met: for unfragmented H18, SQD's error relative to HCI grows to roughly 2.5 kcal/mol per atom at R ≥ 1.1 Å, and the text attributes this to inefficient sampling and CCSD-based parametrization. DMET-SQD is presented as improving this because the subsystem is smaller, but no convergence study of DMET-SQD against DMET-FCI is shown for the largest bond lengths and largest |χ_b|. Moreover, the H6 fragment at stretched geometries is itself a strongly correlated half-filled system, so the improvement is not obvious and could be specific to the DMET bath construction. The proposed overlap and convergence test would directly probe whether the sampled subspace captures the embedded ground state; if it fails, the headline conclusion is overgeneralized. This does not negate the value of the demonstration, but it makes the central claim conditional on a property that the paper does not verify. The reader's weakest assumption identified the same point; this check is the natural way to settle it.","tokens_in":16434,"tokens_out":14049,"duration_ms":146074,"concrete_test":"Run the DMET-SQD workflow on the H18 R = 1.3 Å embedded (12e,12o) problem with |χ_b| increased from 5×10^3 to 1×10^4, and compute both the energy relative to DMET-FCI and the squared overlap between the LUCJ state (Eq. 2) and the DMET-FCI ground state. If the energy error does not decrease toward below 1 kcal/mol or the overlap is below roughly 0.1, the sampled subspace misses essential determinants in the strongly correlated regime, and the central claim is not established for such fragments.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim — that DMET-SQD computes accurate ground-state energies of extended molecules on near-term hardware — requires that the subspace spanned by SQD-sampled determinants contain a good approximation to the embedded ground state. That requirement is exactly what fails in the unfragmented H18 benchmark: at R ≥ 1.1 Å, SQD deviates from HCI by roughly 2.5 kcal/mol per atom (Section III, Fig. 2), and the paper attributes this to inefficient configuration sampling and the CCSD-based LUCJ parametrization. DMET-SQD is then asserted to improve matters because the subsystems are smaller, but the paper does not report a systematic convergence study of DMET-SQD to DMET-FCI at the largest bond lengths (R = 1.2–1.3 Å) for the largest |χ_b|. This matters because the embedded H6 fragment at those geometries is a half-filled six-site system — precisely the strongly correlated regime where a CCSD-parametrized sampling state has no guarantee of overlap with the true ground state. The improvement could be an artifact of DMET's mean-field bath making these particular embedded problems single-reference, which would not generalize. The paper's own limitation note (Section III) concedes SQD's sensitivity to the LUCJ circuit and its CCSD parametrization, so the conclusion 'in agreement with reference classical methods' is conditional on an undemonstrated subspace-quality assumption in exactly the regime where the method's predecessor fails.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper combines density matrix embedding theory (DMET) with sample-based quantum diagonalization (SQD) as a subsystem solver, and applies the resulting DMET-SQD workflow to a ring of 18 hydrogen atoms and to four conformers of cyclohexane. The authors report ground-state energies for H18 along a symmetric stretch and relative conformer energies for cyclohexane, obtained on the ibm_cleveland quantum computer with 27 and 32 qubits, and compare them with DMET-FCI, HCI, CCSD, and CCSD(T) references. The main claims are that DMET-SQD reproduces the reference energies within roughly 1 kcal/mol for sufficient sampling, and that the embedding reduces the qubit count from 41/89 to 27/32, marking a step toward quantum-centric simulations of larger molecules.","tokens_in":16791,"tokens_out":10284,"duration_ms":86598,"significance":"If the reported accuracy is robust, this is a valuable proof-of-concept for using SQD as a practical subsystem solver inside DMET on noisy hardware. The paper leverages open-source tools (Qiskit, ffsim, Tangelo, PySCF) and provides a reproducible workflow. It also identifies a clear convergence trend of SQD results with the number of sampled configurations |χ_b|. However, because the accuracy claim depends on the quality of the CCSD-parameterized LUCJ sampling state and on a hand-chosen configuration count, and because no statistical uncertainties are reported, the significance is currently tempered.","major_comments":[{"comment":"The paper reports no error bars or statistical uncertainties for the SQD and DMET-SQD energies. The visible fluctuations in the bottom panel of Fig. 3 and the strong dependence of the cyclohexane conformer ordering on |χ_b| in Fig. 5 indicate that single-shot estimates are not sufficient to support the claim of 'within 1 kcal/mol' agreement. Please provide standard errors across batches or repeated runs for the reported energies.","section":"Section III, Figs. 2 and 3"},{"comment":"The central accuracy claim in the strong-correlation regime is not fully supported. The unfragmented SQD results deviate from HCI by about 2.5 kcal/mol per atom at R≥1.1 Å (Fig. 2), which the text attributes to inefficient sampling and the CCSD-based LUCJ parametrization. For DMET-SQD, the paper asserts sub-kcal/mol non-variationality biases, but does not report the quantitative DMET-SQD-to-DMET-FCI deviation at R=1.2–1.3 Å as a function of |χ_b|. Please include a systematic convergence study at these stretched geometries, with error bars, and discuss why the embedded H6 fragment becomes sufficiently single-reference for the CCSD-derived sampling state.","section":"Section III, Fig. 3"},{"comment":"The cyclohexane results depend critically on the manually chosen |χ_b|; the conformer ordering is wrong for |χ_b|=6·10^3 and correct only for |χ_b|≥8·10^3. Since this parameter is not determined self-consistently, the paper should provide guidance on how to select it in practice (e.g., monitoring the d′/d ratio or energy variance) or demonstrate stability over a range of |χ_b|.","section":"Section III, Fig. 5"},{"comment":"The hardware experiments are not described in enough detail for reproducibility. Please report the number of shots per circuit, the number of circuits per S-CORE iteration, the total measurement budget, the device calibration data, and the post-selection criteria.","section":"Section II, Computational details"}],"minor_comments":[{"comment":"The phrase 'computing the the ground-state potential energy curve' contains a duplicated 'the'.","section":"Section IV, first paragraph"},{"comment":"The column headers such as 'd [10^5]' are ambiguous because the numerical entries (e.g., 2656) can be misread as raw counts; clarify the units explicitly in the caption or use scientific notation.","section":"Table I"},{"comment":"The statement that DMET-CCSD and DMET-SQD have 'sub-kcal/mol non-variationality biases' should be supported by a table or by error bars in the figures, as this is a key quantitative claim.","section":"Section III, text near Fig. 2"},{"comment":"The abstract refers to 'ibm_cleveland device' without specification; please use the full processor name and mention the Eagle family as in the introduction.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":"The paper is a credible proof-of-concept, and the novelty claim of first DMET-SQD simulations is plausible given the cited prior work. The main barriers to acceptance are the absence of uncertainty quantification and the strong dependence of the results on the hand-chosen parameter |χ_b|, especially in the strongly correlated regime. A revision that adds error bars, a convergence study at stretched geometries, and practical guidance on selecting |χ_b| would substantially strengthen the paper."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Read this one. It is the first DMET-SQD combination, and it shows 27- and 32-qubit active-space simulations on real hardware for H18 and cyclohexane. That is a legitimate step forward: SQD is a good match for DMET subsystem Hamiltonians, and the comparison against DMET-FCI cleanly isolates the SQD error from the fragmentation error. The cyclohexane conformer ordering comes out right once |chi_b| is large enough, and the paper is refreshingly honest about the sensitivity to the LUCJ circuit, CCSD parametrization, and noise.\n\nThe soft spots are real but not fatal. There are no error bars on the quantum-computed energies, and the results clearly depend on the hand-chosen |chi_b|: at 6e3 configurations the cyclohexane ordering is wrong. More importantly, the unfragmented H18 benchmark shows SQD deviating by ~2.5 kcal/mol per atom at stretched bonds, and the paper attributes this to inefficient sampling and the CCSD-based LUCJ state. DMET-SQD improves matters because the subsystems are smaller, but the paper does not systematically demonstrate convergence to DMET-FCI at the largest R values in that strongly correlated regime. The stress-test note worries that the improvement might be an artifact of DMET's bath making the embedded problem single-reference. That concern is fair: the paper's own limitation note concedes the sensitivity, so the abstract's 'in agreement with reference classical methods' is conditional on an undemonstrated subspace-quality assumption where the predecessor fails.\n\nThat said, the paper does not oversell the method as a solution to a long-open problem. It is a proof-of-concept with credible benchmarks and clear reporting. The missing error bars and the lack of a convergence study at large R are addressable without changing the method. I would send this to peer review, asking for those additions. It is citable as a methods demonstration, and I would bring it to reading group to discuss the subspace-quality assumption.\n\nRecommendation: serious referee, with requests for error bars, a DMET-SQD convergence study at the largest bond lengths, and ideally released data or a commit hash for exact reproduction.","headline":"A genuine first DMET-SQD combination with honest reporting and real hardware results, but the accuracy claim in the strongly correlated regime rests on a subspace-quality assumption that the paper does not fully nail down.","tokens_in":17351,"tokens_out":1435,"would_cite":true,"duration_ms":16464,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper reports the first use of sample-based quantum diagonalization as the subsystem solver inside density matrix embedding theory, computing molecular energies on 27-32 qubits in agreement with classical references.","keywords":["density matrix embedding theory","sample-based quantum diagonalization","quantum-centric supercomputing","LUCJ ansatz","hydrogen ring benchmark","cyclohexane conformers","noisy intermediate-scale quantum hardware"],"falsifier":"Run DMET-SQD on an embedded subsystem where single-reference CCSD is known to fail, such as the stretched hydrogen ring at R = 1.3 Å or a bond-breaking transition-metal complex, and compare against DMET-FCI; if the energy error grows several-fold beyond the roughly 1 kcal/mol seen here, the claim that SQD is a reliable DMET solver fails.","tokens_in":16275,"feed_emoji":"⚛️","tokens_out":7904,"duration_ms":75703,"temperature":0.7,"pith_summary":"This paper reports the first use of sample-based quantum diagonalization (SQD) as the high-level solver inside density matrix embedding theory (DMET), so that a quantum computer only needs to handle a small active region of a molecule while classical mean-field theory treats the rest. If correct, it matters because it reduces quantum resource requirements by roughly half for the test systems: an 18-hydrogen ring drops from 41 to 27 qubits, and cyclohexane drops from 89 to 32 qubits. The authors run the approach on a superconducting quantum processor and obtain ground-state energies and conformational energy differences that agree with classical CCSD(T), HCI, and exact-diagonalization references. The central evidence is that DMET-SQD tracks the reference methods more closely than unfragmented SQD, with lower non-parallelity error, making larger molecules a realistic near-term target.","feed_headline":"DMET-SQD reproduces molecular energies on 27-32 qubits","feed_subtitle":"Embedding plus sampled diagonalization matches reference energies for an 18-hydrogen ring and cyclohexane.","key_machinery":"The machinery is the DMET embedding Hamiltonian plus the SQD subspace diagonalization. DMET's Schmidt decomposition reduces the full molecule to a subsystem of fragment and bath orbitals, yielding the active-space Hamiltonian in Eq. (1), which is small enough for a quantum method to solve. SQD samples computational basis states from the LUCJ ansatz in Eq. (2), whose parameters come from a classical CCSD calculation, and then classically diagonalizes the projected Hamiltonian; S-CORE iteratively restores particle number and spin-z symmetry and keeps the lowest-energy batch. The reason this works here is that DMET subsystems have a higher ratio of significant to total sampled configurations than unfragmented systems, so the sampled subspace captures the relevant physics with fewer samples.","core_discovery":"The central claim is that SQD is an accurate subsystem solver for DMET on noisy near-term hardware. DMET builds a small fragment-plus-bath active-space Hamiltonian from a mean-field density matrix; SQD samples Slater determinants from a CCSD-parametrized LUCJ circuit, restores particle-number and spin-z symmetry through the iterative S-CORE loop, and classically diagonalizes the Hamiltonian in the sampled subspace. For a ring of 18 hydrogen atoms, this produces a potential energy curve that agrees with HCI better than unfragmented SQD, with sub-kcal/mol non-variationality errors. For cyclohexane, DMET-SQD ranks the chair, half-chair, twist-boat, and boat conformers correctly once roughly 8,000 or more configurations per batch are used, with deviations from DMET-FCI mostly within 1 kcal/mol. The paper also notes the method's sensitivity to the LUCJ circuit, to its CCSD-derived parameters, and to device noise.","pith_inferences":["A natural untested extension is to replace the CCSD-derived LUCJ parameters with a self-consistent or adaptive ansatz; if the CCSD amplitudes are poor, DMET-SQD accuracy is likely to degrade in strongly multireference embedded systems, which is precisely where embedding is needed most.","The observed sampling threshold suggests a practical stopping criterion: monitor the ratio of significant to total configurations and the convergence of the lowest batch energy, rather than fixing S-CORE iterations in advance.","Because DMET shrinks the active space, the same quantum device could plausibly handle embedded fragments of transition-metal or protein active sites beyond the reach of unfragmented SQD; testing this scaling is a direct next step.","The first S-CORE iteration uses occupation numbers inherited from noisy measurements, so comparing DMET-SQD energies on processors with different noise rates would isolate how much of the residual error is device noise versus sampling."],"forward_implications":["For these benchmarks, DMET-SQD lowers the quantum resources from 41 to 27 qubits and from 89 to 32 qubits, roughly halving the hardware requirement.","SQD becomes a viable substitute for exact diagonalization inside DMET, extending the active-space sizes that can be treated accurately.","With adequate sampling, DMET-SQD correctly orders the cyclohexane conformers, so the method can be used for conformational energy differences in organic molecules.","Smaller DMET subsystems mitigate both CCSD's breakdown under strong correlation and SQD's sampling inefficiency, giving better accuracy than unfragmented runs.","The workflow demonstrates a quantum-centric division of labor: classical computation prepares the embedding, post-processes samples, and assembles energies, while the quantum device only generates candidate configurations."],"supporting_citations":[{"why":"Supplies the SQD algorithm and S-CORE procedure that the paper uses as a subsystem solver, including the LUCJ sampling ansatz.","marker":"[29]"},{"why":"Introduces DMET and the Schmidt-decomposition construction of the embedding Hamiltonian.","marker":"[44]"},{"why":"Derives the DMET subsystem Hamiltonian and its active-space form used in Eq. (1).","marker":"[45]"},{"why":"Provides the practical one-shot DMET formulation with global chemical potential that the paper follows.","marker":"[46]"},{"why":"Defines the LUCJ ansatz whose CCSD-parametrized circuit in Eq. (2) generates the sampled configurations.","marker":"[59]"},{"why":"Provides the heat-bath configuration interaction method used as the classical reference for the hydrogen ring energies.","marker":"[76]"},{"why":"Establishes the hydrogen ring as a benchmark for strongly correlated methods, motivating the H18 test.","marker":"[36]"}],"fun_headline_variants":["DMET-SQD on quantum hardware: accurate energies for H18 ring and cyclohexane","Hybrid DMET-SQD: from 89 qubits down to 27-32 active space","DMET-SQD: sub-kcal/mol errors on noisy hardware for 18-H ring","Quantum-centric simulation of extended molecules via DMET-SQD"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method assumes that the configurations sampled from a CCSD-parametrized quantum circuit cover enough of the true embedded ground state, and that hardware noise does not distort that sampling.","fun_headline_variants_meta":{"raw":{"variants":["DMET-SQD on quantum hardware: accurate energies for H18 ring and cyclohexane","Hybrid DMET-SQD: from 89 qubits down to 27-32 active space","DMET-SQD: sub-kcal/mol errors on noisy hardware for 18-H ring","Quantum-centric simulation of extended molecules via DMET-SQD"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00029,"raw_usage":{"total_tokens":1723,"prompt_tokens":998,"completion_tokens":725,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":614,"completion_tokens_details":{"reasoning_tokens":635}},"tokens_in":614,"tokens_out":725,"duration_ms":8419,"temperature":1.0,"reasoning_tokens":635,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T20:12:26.930150+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run DMET-SQD on an embedded subsystem where single-reference CCSD is known to fail, such as the stretched hydrogen ring at R = 1.3 Å or a bond-breaking transition-metal complex, and compare against DMET-FCI; if the energy error grows several-fold beyond the roughly 1 kcal/mol seen here, the claim that SQD is a reliable DMET solver fails.","supporting_citations":[{"cited_title":"Knizia and G","cited_arxiv_id":null,"evidence_quote":"Introduces DMET and the Schmidt-decomposition construction of the embedding Hamiltonian."},{"cited_title":"Knizia and G","cited_arxiv_id":null,"evidence_quote":"Derives the DMET subsystem Hamiltonian and its active-space form used in Eq. (1)."},{"cited_title":"Wouters, C","cited_arxiv_id":null,"evidence_quote":"Provides the practical one-shot DMET formulation with global chemical potential that the paper follows."},{"cited_title":"Motta, K","cited_arxiv_id":null,"evidence_quote":"Defines the LUCJ ansatz whose CCSD-parametrized circuit in Eq. (2) generates the sampled configurations."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the heat-bath configuration interaction method used as the classical reference for the hydrogen ring energies."},{"cited_title":"Hachmann, W","cited_arxiv_id":null,"evidence_quote":"Establishes the hydrogen ring as a benchmark for strongly correlated methods, motivating the H18 test."}],"review_version":1}