{"id":"9b7283df-b31f-4ed1-a355-0655f643c785","arxiv_id":"2502.06339","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"A graph-based Hamiltonian with ratio, occupancy, and balance costs maps MTV porous material design to a QUBO solved by VQE; simulations reproduce four known structures only after per-structure parameter tuning.","lead":"The authors encode the spatial arrangements of linkers in multivariate porous materials as qubits and define a Hamiltonian whose ground state gives the preferred configuration, then solve it with a variational quantum algorithm. It is a proof-of-principle that quantum computing can be pointed at materials design problems, though the validation is on small, hand-tuned examples.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Validation is weakened by per-structure tuning of alpha and by deriving characteristic lengths from the target structures themselves; the claimed reproduction may be a fitting exercise rather than a predictive test.","rationale":"The reader's weakest_assumption identifies the same core issue: the balance-cost premise is inferred from experiments and alpha is fitted per structure. My stress-test adds two observations that strengthen it: the characteristic linker lengths are measured from the same target structures, and the hardware demonstration only shows energy convergence, not configuration recovery. The paper is honest about the tuning procedure (Table S1 and Note S1), which is why this is a validation gap rather than an internal inconsistency. The conditional verdict already captures the appropriate level of confidence; no change in verdict is needed, but the proposed fixed-alpha and enumeration check should be a prerequisite before the reproduction claim is accepted as predictive.","tokens_in":17598,"tokens_out":3482,"duration_ms":33109,"concrete_test":"A decisive check is to fix the Hamiltonian form and set alpha to a single value for all four structures (e.g., alpha = 0.1, or alpha selected by leave-one-out cross-validation on three structures), then enumerate all ratio- and occupancy-valid configurations classically and record the rank of the experimental configuration by H(q). If the experimental configuration is not the unique lowest-energy state for all four under the fixed or cross-validated alpha, the per-structure alpha selection in Table S1 is load-bearing and the reproduction is an artifact of tuning. Running the same enumeration for each row of Table S1 would also show how sensitive the ranking is.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the Hamiltonian correctly reproduces experimental ground-state configurations of MTV materials. The validation is not parameter-free: (i) Table S1 and Note S1 report that alpha is selected per structure as the value that most often gives the lowest-Hamiltonian configuration the highest probability; the text explicitly says a comparative analysis is needed to select alpha. (ii) The characteristic linker lengths l_t in Table S2 are measured from the same experimentally known structures using ASE, so the geometric input is not independent of the targets. Thus the balance term in Eq. 8, weighted by w_ij = d_ij^alpha, is fitted to the very configurations it is asked to predict. A model with free parameters per material can usually rank the training example first; the four successes therefore do not establish that the balance-cost premise (minimal edge-length spread equals experimental stability) is predictive. In addition, because the valid configurations are few (e.g., 70 for Cu-THQ-HHTP), the paper provides no comparison against classical exhaustive search, and Fig. 6 only shows energy convergence, not that the measured bitstring matches the experimental arrangement. The concern is not that the model is wrong; it is that the evidence presented is insufficient to support the stated validation claim.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a graph-based Hamiltonian model for multivariate (MTV) porous materials, encoding linker identities as qubits and combining ratio, occupancy, and balance cost terms. The model is tested on four experimentally known MTV materials (Cu-THQ-HHTP, Py-MV-DBA-COF, MUF-7, SIOC-COF2) using Sampling VQE in Qiskit, claiming that the experimental configurations are recovered as the most probable low-energy states. A hardware run on ibm_kyiv for SIOC-COF2 shows a decreasing expectation value over 50 optimization iterations. The authors also discuss extensibility to larger, more complex MTV systems, arguing that the quantum approach can overcome the exponential classical search space.","tokens_in":17838,"tokens_out":4467,"duration_ms":39531,"significance":"If the validation were sound, this would be a useful proof-of-principle that a simple qubit Hamiltonian can encode structural design rules for porous materials and that variational quantum algorithms can identify good configurations. The paper is clearly written, provides code via a public GitHub repository, and uses reproducible Qiskit-based workflows, which are strengths. However, the central validation claim is currently undermined by circular parameter selection: the sensitivity parameter α and the characteristic linker lengths are derived from the very experimental structures the model is asked to predict. As a result, the four 'successful reproductions' do not yet demonstrate predictive accuracy, and the hardware experiment only shows energy convergence, not configuration recovery. The claim therefore needs either a substantially reworked validation or a more modest interpretation.","major_comments":[{"comment":"The validation is not independent of the targets: the sensitivity parameter α is selected per material as the value that maximizes the frequency with which the known experimental configuration is the most probable outcome (Note S1, Table S1), and the characteristic linker lengths t_t in Table S2 are measured with ASE from the same experimental structures. Consequently, the balance cost in Eq. (8) is effectively fitted to the very configurations it is asked to predict, so the four 'reproductions' in Fig. 5 do not provide evidence that the balance-cost premise (minimal edge-length spread equals stability) is predictive. Please either run the entire validation with a fixed α (e.g., α=0.1) and fixed t_t values, or use a leave-one-out scheme where α and t_t are determined without the target structure, and report the resulting rankings.","section":"Note S1, Table S1, Eq. (8)"},{"comment":"For all four systems the Hamiltonian is diagonal and the valid configuration space is tiny (e.g., 70 states for Cu-THQ-HHTP, as the paper itself notes), so classical exact enumeration is trivial. The paper never compares the VQE outcome with an exact enumeration of the Hamiltonian's ground states, which would reveal whether the experimental configuration is the unique lowest-energy state, one of several degenerate minima, or merely the most probable among many low-lying states. Without this baseline, the probability distributions in Fig. 5 cannot be interpreted as evidence that the Hamiltonian encodes the correct design rules. Please add for each material the ground-state degeneracy, the energy gap to the first excited state, and the rank of the experimental configuration among all valid configurations under the adopted parameters.","section":"Results, 'Reproducibility' and Eq. (10)"},{"comment":"The hardware run on ibm_kyiv demonstrates only that the expectation value decreases with the optimization iterations; the final hardware value (-1284.6) is far from the optimal value (-4385.9) quoted by the authors, and no measurement-outcome distribution from the hardware circuit is reported. Therefore Fig. 6 does not show that the hardware run identified or even approached the experimental configuration, and the sentence 'This result further validates the reliability of our Hamiltonian model in estimating the ground-state configuration' is not supported. Please report the probabilities of the lowest-Hamiltonian states measured on the hardware, or restrict the claim to 'the hardware run converges towards the classically simulated expectation value'.","section":"Results, hardware VQE (Fig. 6)"}],"minor_comments":[{"comment":"The material name is inconsistent: 'Py-MV-DPA-COF' appears in the Results and in Fig. 5D, while 'Py-MV-DBA-COF' is used elsewhere and in Table S2; please harmonize the name.","section":"Throughout"},{"comment":"The caption says 'Cu-THB-HHTP' but the compound is Cu-THQ-HHTP; please correct the typo.","section":"Fig. 2 caption"},{"comment":"The typesetting of the Hamiltonian in Eq. (2) is garbled, especially the balance term with its subscripts and parentheses; the double sums in Eq. (5) are also hard to parse. Please rewrite these equations with clear index conventions so the reader can verify that L(q,G) is a sum of characteristic lengths on the edge endpoints.","section":"Eq. (2) and Eq. (5)"},{"comment":"The reported α values in Table S3 do not transparently follow the criterion stated in Note S1: for Cu-THQ-HHTP, α=0.01 and α=0.5 give almost identical counts in Table S1 (86 vs 85), and for Py-MV-DBA-COF the counts at α=0.1 (34) and α=0.5 (31) are close; please state the selection rule explicitly and show the full sensitivity analysis.","section":"Table S1 and Table S3"},{"comment":"The ground-state Hamiltonian value for MUF-7 is reported as 0.00; please explain how the sum of the three positive cost terms can be exactly zero for that configuration, or correct the value if it is a rounding artifact.","section":"Fig. 5C"},{"comment":"The novelty claim that 'no one has devised a quantum computing algorithm to identify ground-state chemical configurations for porous materials' is stated without qualifying the earlier cited works on protein models and mRNA optimization; please soften or contextualize this claim.","section":"Discussion"}],"recommendation":"major_revision","confidential_remarks":"The circularity concern is the central issue: Table S1 and Note S1 openly describe per-structure tuning of α, and Table S2 derives characteristic lengths from the experimental targets. This makes the four-case validation a fitting exercise rather than a predictive test. The paper is still a reasonable demonstration of a quantum optimization workflow, but the validation claim needs to be substantially reworked (e.g., fixed parameters, leave-one-out, classical enumeration baseline) or the claims must be scaled back. The code availability and clarity of the quantum-circuit description are positives. If the authors can provide a non-circular test, the paper could become acceptable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know two things about this paper. First, it genuinely is the first mapping of multivariate porous material linker arrangement to a QUBO, and it shows VQE finding the experimental configurations for four known structures. Second, the validation is weaker than the abstract claims: the sensitivity parameter alpha is chosen per structure (Table S1) to maximize the chance that the lowest-energy state matches experiment, and the characteristic linker lengths are measured from the same experimental structures (Note S1, Table S2). So the four successes are partly a fitting exercise, not a clean predictive test.\n\nWhat is new and good: the graph-based encoding with ratio, occupancy, and balance terms is a sensible coarse-grained Hamiltonian for this problem class. The authors are honest that the Hamiltonian is not the physical Schrodinger Hamiltonian. They also include a real hardware run on ibm_kyiv, and they point to a GitHub repository with code. Those are real contributions.\n\nWhere it goes soft: the balance cost assumes that minimizing edge-length spread equals experimental stability. That premise comes from the same experimental examples, and the free parameter alpha is tuned per material. For small systems like Cu-THQ-HHTP, where the ratio constraint leaves only 70 valid configurations, a classical exhaustive search would be trivial and would provide a much stronger baseline. The paper does not compare against any classical solver. The hardware experiment only shows energy convergence, not that the measured bitstring matches the experimental arrangement. And the claim that quantum computing is needed because classical methods become intractable is overstated for these demonstrated sizes; it is a hope for scalability, not something shown here.\n\nThat said, I do not think the central idea is wrong. The model is a reasonable heuristic for ranking linker configurations, and the paper would be a useful starting point for anyone interested in applying quantum optimization to reticular materials. The main fix is validation: hold out at least one material, fix alpha without per-structure tuning, or at minimum report how sensitive the ranking is to alpha and to the measured linker lengths.\n\nWho is this for? Materials chemists curious about QUBO formulations for design problems, and quantum algorithm people looking for small test cases. It deserves a serious referee, but the referee should push for a proper classical baseline and a less sweeping validation claim. My recommendation: send it to peer review, not desk reject, with a request for major revision on the validation section.","headline":"A first QUBO mapping for MTV porous material design, with a validation that is partly fitted to the known structures; worth refereeing but needs independent tests.","tokens_in":18346,"tokens_out":1371,"would_cite":false,"duration_ms":14845,"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":"A three-term cost Hamiltonian, minimized by a variational quantum algorithm, reproduces the experimentally observed linker arrangements in four multivariate porous materials.","keywords":["multivariate porous materials","quantum computing","variational quantum eigensolver","Hamiltonian model","metal-organic frameworks","covalent organic frameworks","combinatorial optimization","qubit encoding"],"falsifier":"Fix one $\\alpha$ rule ahead of time (for example, $\\alpha=0.25$ for all second-nearest-neighbor edges), apply the Hamiltonian to an MTV material whose experimental linker arrangement was not used to build or calibrate the model, and check whether Sampling VQE assigns the highest probability to that measured arrangement; a mismatch would show the balance heuristic does not generalize without per-structure tuning.","tokens_in":17392,"feed_emoji":"⚛️","tokens_out":11029,"duration_ms":93267,"temperature":0.7,"pith_summary":"Multivariate porous materials—metal-organic and covalent organic frameworks built from several different linkers—can arrange their building blocks in astronomically many ways, and only some of those arrangements are stable enough to make. This paper tries to turn the search for the stable arrangement into a quantum optimization problem: each linker choice at each lattice site is encoded as a qubit, and a deliberately simple Hamiltonian, acting as a cost function rather than a full electronic-structure Hamiltonian, is built from ratio, occupancy, and balance constraints. The paper reports that the ground state of this Hamiltonian, found with a sampling variational quantum eigensolver, reproduces the experimentally known arrangements of Cu-THQ-HHTP, Py-MV-DBA-COF, MUF-7, and SIOC-COF2 with the highest probability. A run on real quantum hardware for one of the materials converges toward the classically simulated result. If the claim is right, it gives a route for proposing feasible MTV porous materials before synthesis, using qubits that scale linearly while the number of candidate structures grows exponentially.","feed_headline":"Quantum algorithm matches four real porous-material structures","feed_subtitle":"A graph-based Hamiltonian turns the exponentially hard search over linker arrangements into a ground-state problem for quantum computers.","key_machinery":"The load-bearing object is the cost Hamiltonian $H(q) = H_{\\text{ratio}}(q) + H_{\\text{occupancy}}(q) + H_{\\text{balance}}(q)$ defined on binary linker qubits $q_i^t$, coupled with the graph representation $G(i,j,w_{i,j})$ of the reticular framework. The ratio term enforces the counts $c_t$ of each linker type, the occupancy term enforces exactly one linker per site, and the balance term compares each edge's linker-dependent length $L(q,G)$ with the mean edge length $\\bar{L}$, weighted by connection strength $w_{i,j}=d_{i,j}^{\\alpha}$. This machinery converts the chemical stability question into a diagonal QUBO/Ising cost landscape that a variational quantum circuit can sample; finding the experimental configuration is therefore equivalent to finding the ground state of that landscape.","core_discovery":"The central claim is that a graph-based, three-term model Hamiltonian has, as its lowest-energy configuration, exactly the linker arrangement experiments find for multivariate reticular frameworks. In the model, each linker site of a chosen topology is a node in a graph, each linker type at each site is a qubit, and edges are weighted by $w_{i,j}=d_{i,j}^{\\alpha}$, where $d_{i,j}$ is the spatial distance and $\\alpha$ distinguishes direct topological bonds from weaker spatial adjacencies. The ratio term fixes the user-specified linker counts, the occupancy term forbids vacant or doubly occupied sites, and the balance term $\\sum_{(i,j)} w_{i,j}(L(q,G)-\\bar{L})^2$ penalizes arrangements whose edge lengths deviate from the mean edge length, encoding the observation that well-ordered, non-segregated arrangements are structurally stable. Because the Hamiltonian is diagonal in the computational basis, the paper argues that its ground state can be located by Sampling VQE, and it demonstrates the correspondence for the four experimental structures plus a hardware run on one of them. In the authors' framing, this is a first step toward treating reticular chemistry design as a combinatorial optimization problem solvable with quantum computing.","pith_inferences":["Editor's inference: a decisive test the paper leaves implicit is to freeze a single $\\alpha$ selection rule, apply the model to a newly characterized MTV material not used in calibration, and ask whether Sampling VQE still puts the measured arrangement on top; the balance term's generality is otherwise not independently tested.","Editor's inference: because the Hamiltonian is diagonal and reduces to a QUBO problem, the small validated instances could also be minimized classically; the practical divide between quantum and classical search would show up only on larger, classically hard instances that current hardware cannot yet run.","Editor's inference: the same one-qubit-per-linker-per-site encoding could be reused for other design decisions in ordered materials—metal-node ordering, mixed functional groups, or defect patterning—wherever a balance-type heuristic can be written as a pairwise cost.","Editor's inference: a natural next experiment is to synthesize one of the model's predicted arrangements for an as-yet-uncharacterized MTV composition and compare the measured structure with the predicted ground state, which would test the encoding outside the set of structures used to build it."],"forward_implications":["If the central claim is correct, the stable arrangement of a mixed-linker framework is encoded as the ground state of a cost Hamiltonian, so improving quantum optimizers directly improves the complexity of MTV materials that can be designed.","The scaling argument puts a 72-linker-site, four-linker hcb framework at roughly $7.45\\times10^{34}$ possible configurations while needing 288 qubits, a regime in which exhaustive classical evaluation is impossible.","The four reproduced structures span hcb, ith-d, and kgm topologies, suggesting the graph encoding transfers across framework types by re-building $G(i,j,w_{i,j})$ and the linkers' characteristic lengths.","The hardware run on the 12-qubit SIOC-COF2 system shows the model can be evaluated on noisy near-term devices rather than only in exact simulation; the paper expects more iterations would approach the optimal value."],"supporting_citations":[{"why":"It supplies the experimentally characterized Cu-THQ-HHTP dual-linker MOF whose observed linker arrangement is the benchmark ground state for the hcb topology case.","marker":"[14]"},{"why":"It supplies the MUF-7 series of quaternary MTV-MOFs, the experimental benchmark for the 3D ith-d topology case.","marker":"[13]"},{"why":"It supplies the SIOC-COF2 mixed-linker COF and the stabilizing principle that ordered, balanced linker arrangements are favorable.","marker":"[15]"},{"why":"It supplies the Py-MV-DBA-COF experimental structure used as the second 2D hcb topology benchmark.","marker":"[32]"},{"why":"It supplies the open quantum computing framework used to implement the Sampling VQE circuits, the classical simulator, and the hardware execution.","marker":"[26]"},{"why":"It supplies the top-down structure generation method used to build the hypothetical MTV framework configurations from topology and building-block data.","marker":"[18]"}],"fun_headline_variants":["Quantum algorithm matches four known porous-material structures","Ground-state Hamiltonian design for multivariate porous materials","VQE reproduces experimental linker arrangements in porous crystals","Quantum computing solves porous material linker optimization","Porous-material design via quantum ground-state search"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that minimizing how far each edge length deviates from the mean edge length identifies the experimentally stable arrangement; this rule was inferred from the same experimental structures used for validation, and the sensitivity parameter $\\alpha$ is selected per material in Table S1 so that the known configuration scores highest.","fun_headline_variants_meta":{"raw":{"variants":["Quantum algorithm matches four known porous-material structures","Ground-state Hamiltonian design for multivariate porous materials","VQE reproduces experimental linker arrangements in porous crystals","Quantum computing solves porous material linker optimization","Porous-material design via quantum ground-state search"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000549,"raw_usage":{"total_tokens":2616,"prompt_tokens":935,"completion_tokens":1681,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":551,"completion_tokens_details":{"reasoning_tokens":1623}},"tokens_in":551,"tokens_out":1681,"duration_ms":15368,"temperature":1.0,"reasoning_tokens":1623,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T15:45:36.553880+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Fix one $\\alpha$ rule ahead of time (for example, $\\alpha=0.25$ for all second-nearest-neighbor edges), apply the Hamiltonian to an MTV material whose experimental linker arrangement was not used to build or calibrate the model, and check whether Sampling VQE assigns the highest probability to that measured arrangement; a mismatch would show the balance heuristic does not generalize without per-structure tuning.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It supplies the experimentally characterized Cu-THQ-HHTP dual-linker MOF whose observed linker arrangement is the benchmark ground state for the hcb topology case."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It supplies the MUF-7 series of quaternary MTV-MOFs, the experimental benchmark for the 3D ith-d topology case."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It supplies the SIOC-COF2 mixed-linker COF and the stabilizing principle that ordered, balanced linker arrangements are favorable."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It supplies the Py-MV-DBA-COF experimental structure used as the second 2D hcb topology benchmark."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"It supplies the top-down structure generation method used to build the hypothetical MTV framework configurations from topology and building-block data."}],"review_version":1}