MolPaQ: Modular Quantum-Classical Patch Learning for Interpretable Molecular Generation

Syed Rameez Naqvi; Lu Peng

cs.LGMar 27, 2026

MolPaQ: Modular Quantum-Classical Patch Learning for Interpretable Molecular Generation

Authors: Syed Rameez Naqvi, Lu Peng

Organizations: Department of Computer Science, Tulane University, New Orleans, LA, USA.

Abstract

Molecular generative models must jointly ensure validity, diversity, and property control, yet existing approaches typically trade off among these objectives. We present MOLPAQ, a modular quantum-classical generator that assembles molecules from quantum-generated latent patches. A \b{eta}-VAE pretrained on QM9 learns a chemically aligned latent manifold; a reduced conditioner maps molecular descriptors into this space; and a parameter-efficient quantum patch generator produces entangled node embeddings that a valence-aware aggregator reconstructs into valid molecular graphs. Adversarial fine-tuning with a latent critic and chemistry-shaped reward yields 100% RDKit validity, 99.75% novelty, and 0.905 diversity. Beyond aggregate metrics, the pretrained quantum generator, steered by the conditioner, improves mean QED by approx. 2.3% and increases aromatic motif incidence by approx. 10-12% relative to a parameter-matched classical generator, highlighting its role as a compact topology-shaping operator.

Figures & tables

Figure 1: Overview of the MolPaQ Pipeline

Figure 2: Parameterized RY–CNOT circuit used in M3. Latent angles control initial rotations, followed by two Strongly Entangling Layers (SEL) with ring-connectivity CNOTs. The measured expectations $\langle Z_{i}\rangle$ form quantum-generated node embeddings.

Validity	Uniqueness	Novelty	QED $\uparrow$	SA $\downarrow$	logP $\downarrow$	Diversity $\uparrow$	Good@chem
100%	100.00%	99.75%	0.499	4.630	3.404	0.905	3,537

Table 1: Core quality on QM9 (10,908 generated molecules).

	Gen (all)	Gen (Good)	QM9
$\%$ $\geq$ 1 AR	34.0	64.6	17.8
Mean AR / mol	0.750	1.258	0.207
Mean T rings / mol	1.282	1.620	1.741

Table 2: Aromaticity and ring statistics (aggregator audit).

Setup	FCD (ECFP $\rightarrow$ PCA)
QM9 vs. QM9 (split)	0.126
Generated vs. Generated (split)	0.264
QM9 vs. Generated ( $k{=}100$ )	3.405
QM9 vs. Generated (shrink)	3.387
QM9 vs. Generated ( Good region)	3.744

Table 3: Fréchet distance between QM9 and generated distributions using ECFP4

\rightarrow

PCA. Lower is better. PCA uses

k{=}100

components (EVR

0.585

); sample sizes matched at

n{=}5000

Figure 3: Pareto analysis for traversal dimension 2. Scatter of QED versus logP, with points colored by SA (lower is better).

Figure 4: Relationship between QED and logP over 50k generated molecules. The shaded region denotes the preferred logP range $[-0.5,5.0]$ , covering $\sim$ 75% of samples.

SMILES (truncated)	QED $\uparrow$	logP	SA $\downarrow$
CC(C)(C)OC(=O)Nc1ccc(OC)cc1	0.800	3.62	5.01
COc1ccc(NC(=O)OC(C)(C)C)cc1	0.760	3.72	5.08

Table 4: Top molecules on the chemistry-constrained Pareto front (dim 2), demonstrating realistic QED–SA–logP balance.

Lipinski	Veber	Egan	PAINS/Brenk	hERG	CYP3A4
91.9	99.4	97.4	65.9	57.8	8.3
Scored	Good@chem	Pareto	Great	Border	Top200	Top50
10,908	3,537	1,199	516	58	200	50

Table 5: ADMET fast-pass summary. Percentages over all scored molecules; shortlist counts denote unique SMILES.

Method	Model Type	Valid (%)	Uni. $\times$ Val. (%)	Nov. $\times$ Val. (%)	Diversity	Time (s)
QVAE-Mole ( Wu et al., 2024 )	VAE	78.13	27.39	57.38	0.64	0.08
SQ-VAE ( Li and Ghosh, 2022 )	VAE	44.23	7.24	16.32	0.58	0.15
QGAN-HG ( Li et al., 2021 )	GAN	66.64	8.08	18.48	0.72	0.04
P2-QGAN-HG ( Li et al., 2021 )	GAN	17.64	12.38	9.54	0.55	0.02
MolPaQ (ours)	GAN	100.0	100.0	99.75	0.905	0.036

Table 6: Comparison on QM9 (10K generated molecules). “Time (s)” denotes the average inference time per molecule.

Appendix figures & tables29 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 5: t-SNE to visualize generated properties & QM9 alignment

Set	$n$	BertzCT (median [IQR])	Unique BM scaffolds
Generated	10,908	450.7 [224.9]	2,906
QM9 (Reference)	133,798	158.8 [62.6]	15,851

Appendix

Table 7: BertzCT and Bemis–Murcko Scaffold Diversity

Panel of Figure 6 — Figure 6: Topological complexity and scaffold diversity analysis. (Left) Distribution of Bertz topological complexity (BertzCT) for generated molecules vs. QM9 reference. Generated molecules show significantly higher median complexity (451 vs. 159), consistent with enriched aromatic and ring systems. (Right) Bemis–Murcko scaffold diversity (non-empty scaffolds only). The generated set spans $\sim$ 2,900 unique scaffolds compared to 15,851 in QM9, indicating broad but non-redundant scaffold coverage.

	Gen (all)	Gen ( Good )	QM9
% with $\geq$ 1 AR	34.0	64.6	17.8
Mean AR / mol	0.750	1.258	0.207
Mean TR / mol	1.282	1.620	1.741
Mean AA / mol	2.7	5.4	1.0

Appendix

Table 8: Ring and aromaticity statistics. The Good@chem subset concentrates aromatic motifs while preserving total ring counts comparable to QM9. Legend: AR: aromatic rings, TR: total rings, AA: aromatic atoms.

Panel of Figure 7 — Figure 7: Distributions of (left) total atom count and (right) aromatic atom count for QM9, all generated molecules, and the Good@chem subset. Generated molecules exhibit broader atom-count variation (10–25 atoms) relative to QM9 (centered near 9–10), while the Good@chem subset increases aromatic atom frequency, reflecting enrichment of conjugated motifs.

Panel of Figure 8 — Figure 8: Distributions of (left) total rings and (right) aromatic rings per molecule. While total ring counts remain similar to QM9, the Good@chem subset shows a higher fraction of aromatic rings (peaking at 1–2 rings per molecule), indicating that the aggregator captures ring-forming tendencies typical of drug-like compounds.

Panel of Figure 9 — Figure 9: Property alignment between QM9, generated, and Good@chem molecules for (left) QED, (center) SA, and (right) $\log P$ . The Good@chem subset shifts toward higher QED and moderate $\log P$ , with lower SA scores than the full generated distribution, demonstrating that MolPaQ ’s conditioning and aggregation modules effectively steer generation toward chemically desirable regions of property space.

Target quantiles (QED, logP)	QED	logP	SA
(25%, 25%)	0.53 $\pm$ 0.10	2.99 $\pm$ 0.83	4.49 $\pm$ 1.09
(50%, 50%)	0.53 $\pm$ 0.11	3.23 $\pm$ 0.93	4.54 $\pm$ 1.13
(75%, 75%)	0.56 $\pm$ 0.09	2.98 $\pm$ 0.87	4.62 $\pm$ 1.17

Appendix

Table 9: Descriptor-only steering on interquartile QED

\times

logP targets (median

\pm

IQR over generated valid molecules,

n\!\approx\!200

per cell).

Figure 10: LogP calibration curve (achieved vs. target). The near-flat response highlights the model’s bias toward moderate lipophilicity.

Property	$\rho$	$p$ -value	$n$
QED	$-0.052$	$0.18$	669
SA	$-0.032$	$0.40$	669
logP	$-0.008$	$0.84$	669

Appendix

Table 10: Latent–property correlations for the traversed dimension (dim 2). Spearman

\rho

and two-sided

p

-values;

n{=}669

Panel of Figure 12 — Figure 12: Property values vs latent value for dim 2 with least-squares guide line. No visible trend is observed.

Figure 13: Expanded view of the top-36 generated molecule for improved readability

Figure 14: Front-only view highlighting the efficient set for traversal dimension 2. Only two molecules satisfy all chemistry constraints, corresponding to the red circled points in Fig. 3 .

#	SMILES	QED	logP	SA
1	CC(C)(C)OC(=O)Nc1ccc(OC)cc1	0.800	3.62	5.01
2	COc1ccc(NC(=O)OC(C)(C)C)cc1	0.760	3.72	5.08

Appendix

Table 11: Full chemistry-constrained Pareto front for traversal dimension 2. Both candidates show desirable QED and logP within bounds, and moderate SA, confirming chemically realistic outputs.

Panel of Figure 15 — Figure 15: Mode-collapse stress test over 50k samples.

Figure 16: validity vs. samples. Both diversity tracks grow steadily; validity stabilizes near 0.787.

Metric	Value	Notes
Samples generated	50,000	random latent draws
Validity (final)	0.787	RDKit sanitization pass fraction
Unique SMILES	35,036	cumulative at 50k
Unique scaffolds	9,180	Murcko scaffolds at 50k
Rolling mean Tanimoto	0.094	Morgan ( $r=2$ , 2048), window $W=512$

Appendix

Table 12: Summary metrics at the end of the 50k-sample mode-collapse stress test.

Panel of Figure 17 — Figure 17: Histograms of QED and logP for 50k generated molecules. The logP histogram shows most samples within the recommended range of $[-0.5,5.0]$ .

Panel of Figure 18 — Figure 18: Empirical cumulative distribution functions (ECDFs) of QED and logP. The cumulative profiles mirror realistic drug-like distributions.

Property	Mean / Median	Comment
Validity	0.787	Fraction of RDKit-sanitized molecules
QED	0.499 / 0.507	Centered around typical drug-likeness range
logP	3.120 / 3.064	74.9% within $[-0.5,5.0]$
SA	N/A	(SA computation disabled during this run)

Appendix

Table 13: Summary statistics for physicochemical properties of 50k generated molecules.

	Count	Fraction of Good@chem
Great-ADMET (Strict)	516	14.6%
Borderline	58	1.6%
Unique scaffolds (Strict)	337	–
Unique scaffolds (Top-200)	159	–
Unique scaffolds (Top-50)	46	–

Appendix

Table 14: Summary of ADMET filtering and shortlist composition.

Figure 19: Distributions of ADMET-relevant descriptors and rule-based passes over 10,908 generated molecules. Each panel shows the empirical frequency of molecular properties (e.g., MW, TPSA, logP, f_sp 3 , solubility, permeability) and filter outcomes (Lipinski, Veber, Egan, PAINS/Brenk, hERG, CYP3A4). Vertical lines indicate common medicinal-chemistry thresholds. The bulk of MolPaQ ’s generated compounds fall within drug-like regions, with most violating fewer than one rule, demonstrating effective property steering.

Panel of Figure 20 — Figure 20: Distribution of physicochemical and ADMET-related properties for generated candidates.

Metric	Median (Gen)	Median (Ref)	KS $p$	MWU $p$	$n_{\text{gen}}$	$n_{\text{ref}}$
QED	0.510	0.473	$<\!10^{-300}$	$8.27\times 10^{-277}$	11,331	133,798
SA	4.646	4.264	$1.83\times 10^{-265}$	$1.38\times 10^{-283}$	11,331	133,798
logP	3.328	0.282	$<\!10^{-300}$	$<\!10^{-300}$	11,331	133,798

Appendix

Table 15: Distributional tests between Generated and QM9 (Reference). Medians reported; two-sided Kolmogorov–Smirnov (KS) and Mann–Whitney U (MWU) p-values. Extremely small p-values are shown as

<\!10^{-300}

due to underflow.

Figure 21: Docking score distributions for DHFR (6XG5). Left: protein-only receptor; right: holo receptor including NADPH. Dashed lines mark the co-crystal ligand ( $-7.70$ kcal/mol). Many generated molecules achieve comparable or better binding energies, illustrating implicit pharmacophore consistency.

Figure 22: Docking score distribution for DNA gyrase (2XCT). The co-crystal ligand ciprofloxacin (CPF, $-8.99$ kcal/mol) is shown by the dashed line. Generated molecules cluster between $-8.5$ and $-6.0$ kcal/mol, with several outperforming CPF.

Target	Co-crystal	Mean Gen.	Median Gen.	% Better
6XG5 (DHFR)	$-7.70$	$-7.25$	$-7.35$	41.5%
2XCT (DNA gyrase)	$-8.99$	$-7.35$	$-7.40$	11.0%

Appendix

Table 16: Summary of docking results for enzyme targets. Generated ligands show competitive binding relative to co-crystal references, despite being trained without docking supervision.

Metric	Quantum	MLP
Novelty (%)	99.75	99.47
QED (avg)	0.499	0.488
logP (avg)	3.404	3.209
SA (avg)	4.630	4.596
Diversity	0.905	0.904
Good@chem (#)	3,535	3,624

Appendix

Table 17: Ablation between quantum and classical (MLP) patch generators. Means over full generated sets; aromatic and ring metrics computed over all valid molecules.

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