Quantum Computing Based Design of Multivariate Porous Materials

Jihan Kim; Shinyoung Kang; Younghun Kim

REVIEW 3 major objections 6 minor 38 references

Quantum Computing Based Design of Multivariate Porous Materials

T0 review · 3 major / 6 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read A three-term cost Hamiltonian, minimized by a variational quantum algorithm, reproduces the experimentally observed linker arrangements in four multivariate porous materials.

desk verdict 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. read the letter →

arxiv 2502.06339 v2 pith:7FC5YWBL submitted 2025-02-10 quant-ph

Shinyoung Kang , Younghun Kim , Jihan Kim This is my paper · ORCID

classification quant-ph

keywords multivariateporousmaterialsquantumcomputingvariationaleigensolverHamiltonianmodelmetal-organicframeworkscovalentorganiccombinatorialoptimizationqubitencoding

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

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.

What carries the argument

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.

What would settle it

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.

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Extended reading notes

Core claim

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.

Load-bearing premise

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.

Editorial extensions

If this is right

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.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

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.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the 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.

What 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.

Where 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.

That 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.

Who 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.

Referee Report

3 major / 6 minor

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.

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 (3)

[Note S1, Table S1, Eq. (8)] 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.
[Results, 'Reproducibility' and Eq. (10)] 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.
[Results, hardware VQE (Fig. 6)] 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'.

minor comments (6)

[Throughout] 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.
[Fig. 2 caption] The caption says 'Cu-THB-HHTP' but the compound is Cu-THQ-HHTP; please correct the typo.
[Eq. (2) and Eq. (5)] 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.
[Table S1 and Table S3] 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.
[Fig. 5C] 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.
[Discussion] 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.

Circularity Check

2 steps flagged · score 7.0 of 10

Validation of ground-state reproduction is partly circular: per-structure α is chosen to make the experimentally known configuration the most probable lowest-Hamiltonian state, and characteristic linker lengths are measured from those same target structures.

fitted input called prediction [Materials and Methods: 'Sampling VQE Calculations with Classical Simulator'; also Results text around Eq. 1; Table S1.]
"To determine the optimal α values for each simulated structure, the comparative analysis was conducted using four different settings, with α set to 0.01, 0.1, 0.25, and 0.5 (table S1). The α value was chosen based on the condition that maximizes the occurrences of the lowest Hamiltonian solution with the highest probability (table S1)."

The paper's validation claim is that the Hamiltonian's ground state 'correctly reproduced the experimental configurations' for the four materials. For the three materials with spatial-adjacency edges, the weight w_ij = d_ij^α in Eq. 1 directly enters the balance term (Eq. 8), and α is selected per structure by the criterion that the known experimental configuration is the lowest-Hamiltonian state with the highest probability. The reported 'reproduction' is therefore not a parameter-free prediction; it is a per-structure fit to the validation target. Only SIOC-COF2 (α=1 on all edges) avoids this particular per-structure tuning.
fitted input called prediction [Note S1; Table S2; Eqs. 5-8 (balance cost term).]
"The characteristic lengths of candidate linkers, 𝑡𝑡𝑞𝑞, were measured by visualizing structures using Atomic Simulation Environment (ASE) (37) (table S2)."

The balance cost term, H_balance = Σ w_ij (L(q,G) − L̄)^2, is the only term that distinguishes among arrangements satisfying the ratio and occupancy constraints. The edge lengths L(q,G) in Eq. 5 are sums of characteristic lengths t_t, and these t_t are measured from the same experimentally known structures that the model is claimed to reproduce. The mean edge length L̄ in Eq. 7 is likewise derived from those measured lengths. Thus the objective function is partly constructed from the ground-truth targets, so the four successful reproductions do not independently test the balance-cost premise that minimal edge-length spread equals experimental stability.

full rationale

The Hamiltonian construction itself is not circular: the ratio and occupancy terms are ordinary constraint penalties, and the balance term is an explicitly acknowledged coarse-grained ansatz motivated by experimental observations rather than derived from first principles. No load-bearing self-citation or imported uniqueness theorem is present. The circularity is confined to the validation section but is central to the paper's strongest claim. Because α is tuned per structure to maximize the probability of the known experimental configuration (Table S1), and because the characteristic lengths entering Eq. 8 are measured from the target structures (Note S1, Table S2), the reported reproduction of Cu-THQ-HHTP, Py-MV-DBA-COF, and MUF-7 is substantially a fitting exercise. SIOC-COF2, with α fixed at 1 for all edges, and the VQE/hardware execution provide some independent algorithmic content, so the paper is not wholly circular. A held-out material or a fixed, pre-specified α protocol would be needed to turn the demonstration into a genuinely predictive test.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The ledger shows that the model rests on several heuristic premises and on parameters measured from or tuned to the very structures used for validation. The free parameters are numerous, and the central validation relies on per-structure alpha selection.

free parameters (4)

alpha (connection sensitivity) = Cu-THQ-HHTP: 0.01; Py-MV-DBA-COF: 0.1; MUF-7: 0.1; SIOC-COF2: 1 (by construction)
Chosen from {0.01, 0.1, 0.25, 0.5} to maximize the number of runs in which the experimental configuration is the most probable lowest-Hamiltonian state (Table S1, Note S1).
C_ratio and C_occ (cost weights) = C_ratio = 200, C_occ = 300
Hand-selected constants to enforce ratio and occupancy constraints ahead of the balance term (Note S1).
Unit cell size N_s = 8 for hcb, 6 for kgm and ith-d topologies
Chosen to keep qubit count under 20 for simulation; the paper states 'under specific assumptions regarding the unit cell size' (Results).
Characteristic linker lengths t_t = THQ 2.42 Å, HHTP 4.87 Å, BDC 2.869 Å, BPDC 5.025 Å, BPDA 4.6 Å, TPDA 6.89 Å, DBA[12] 8.027 Å, DBA[18] 10.516 Å
Measured from the experimental structures using ASE (Table S2); these inputs embed knowledge of the target configurations.

assumptions (4)

ad hoc to paper The experimentally observed configuration is the ground state of the proposed Hamiltonian.
The validation checks whether the model's ground state matches known experimental structures; this equivalence is assumed, not derived (Results, Fig. 5).
domain assumption Minimizing edge-length deviation from the mean (balance term) is a valid proxy for structural stability.
Justified by citing experimental studies that well-ordered linker distributions stabilize frameworks (Results, balance cost section).
domain assumption A graph with first-nearest-neighbor and second-nearest-neighbor connections suffices to capture relevant interactions.
Stated in Eq. 1: spatial adjacency is limited to second-closest edges to balance computational cost.
standard math The Hamiltonian is diagonal in the computational basis, so Sampling VQE can evaluate it by measurement.
Stated in Results: the Hamiltonian involves only classical binary variables, so eigenvalues correspond to measurement outcomes.

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Cite this review

Pith. "Pith review of Quantum Computing Based Design of Multivariate Porous Materials." pith.science (2026). https://pith.science/paper/7FC5YWBL

@misc{pith2026250206339,
  author       = {Pith},
  title        = {Pith review of: Quantum Computing Based Design of Multivariate Porous Materials},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7FC5YWBL}},
  note         = {Machine review of arXiv:2502.06339}
}

read the original abstract

Multivariate (MTV) porous materials exhibit unique structural complexities based on diverse spatial arrangements of multiple building block combinations. These materials possess potential synergistic functionalities that exceed the sum of their individual components. However, the exponentially increasing design complexity of these materials poses challenges for accurate ground-state configuration prediction and design. To address this, a Hamiltonian model was developed for quantum computing that integrates compositional, structural, and balance constraints, enabling efficient optimization of the MTV configurations. The model employs a graph-based representation to encode linkers as qubits. To validate our model, a variational quantum circuit was constructed and executed using the Sampling VQE algorithm. Simulations on experimentally known MTV porous materials successfully reproduced their ground-state configurations, demonstrating the validity of our model. Furthermore, VQE calculations were performed on real quantum hardware for validation purposes, signaling a first step toward a practical quantum algorithm for the rational design of porous materials.

Figures

Figures reproduced from arXiv: 2502.06339 by the authors.

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Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

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