Variational Quantum Attention for Molecular Graph Learning

Yu-Cheng Lin; Yu-Chao Hsu; Tai-Yue Li; Nan-Yow Chen; Samuel Yen-Chi Chen

quant-phOct 3, 2026

Variational Quantum Attention for Molecular Graph Learning

Authors: Yu-Cheng Lin, Yu-Chao Hsu, Tai-Yue Li, Nan-Yow Chen, Samuel Yen-Chi Chen

Organizations: Department of Electrophysics, National Yang Ming Chiao Tung University, Hsinchu 300092, Taiwan. · Department of Internal Medicine, School of Medicine College of Medicine, Taipei Medical University, Taipei, Taiwan · School of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea · National Center for High-Performance Computing , National Institutes of Applied Research (NIAR), Hsinchu 300092, Taiwan · Brookhaven National Laboratory, Upton NY, USA

Abstract

Molecular property prediction is central to computational drug discovery, where graph neural networks learn to weight neighboring atomic environments during message passing. Yet it remains unclear how variational quantum circuits alter learned attention behavior in molecular graphs. We introduce an edge-aware variational quantum attention mechanism for molecular graph learning, in which the receiving atom, neighboring atom, and connecting bond jointly determine the quantum attention state. Across five molecular property and bioactivity prediction tasks, QGAT achieves competitive performance relative to GATv2, with a consistent improvement on BBBP across all six evaluated circuit ansatzes. We further compare how the quantum and classical attention scores weight molecular structure beyond accuracy. In the Verubecestat BACE1 inhibitor series, QGAT achieves a higher Spearman correlation than GATv2 and assigns positive attributions to several structural changes consistent with reported structure-activity relationships (SARs). This case study shows that the two attention mechanisms can exhibit different prediction and attribution behavior across structurally related BACE1 analogues, while broader validation is required to determine how consistently these differences generalize across chemical series and targets. Circuit ablations further show that performance depends on the circuit design. Together, these results show that variational quantum attention can serve as a viable alternative molecular attention parameterization while inducing circuit- and chemistry-dependent behavior distinct from a matched classical scorer.

Figures & tables

Figure 1: Overview of the edge-aware QGAT architecture for molecular property prediction.

Model	Classification		Regression
	BACE	BBBP	FreeSolv	ESOL	ChEMBL-BACE
	AUC $\uparrow$	AUC $\uparrow$	RMSE $\downarrow$	RMSE $\downarrow$	Spearman $\uparrow$	RMSE $\downarrow$
No. of molecules	1,513	2,039	642	1,128	4,580
Avg. no. of atoms	65	46	18	26	59
D-MPNN	$0.7591\pm 0.0305$	$0.6713\pm 0.0230$	$2.5079\pm 0.1136$	$1.0740\pm 0.0813$	$0.6520\pm 0.0266$	$0.9804\pm 0.0261$
AttentiveFP	$0.7872\pm 0.0337$	$0.6469\pm 0.0273$	$1.9674\pm 0.3156$	$0.9672\pm 0.0666$	$0.6455\pm 0.0398$	$0.9970\pm 0.0456$

Table 1: Results on molecular property prediction tasks. Performance is reported as the mean

\pm

standard deviation over five scaffold folds. The best and second best results for each metric are highlighted in red and blue , respectively.

Ansatz	BACE	BBBP	FreeSolv	ESOL	ChEMBL-BACE
	AUC $\uparrow$	AUC $\uparrow$	RMSE $\downarrow$	RMSE $\downarrow$	Spearman $\uparrow$	RMSE $\downarrow$
1	$\mathbf{0.8283\pm 0.0133}$	$0.6920\pm 0.0069$	$\mathbf{1.7400\pm 0.2033}$	$0.9278\pm 0.0564$	$0.7263\pm 0.0083$	$0.8955\pm 0.0140$
2	$0.8136\pm 0.0132$	$0.7023\pm 0.0092$	$1.7435\pm 0.0805$	$0.9962\pm 0.1096$	$0.7228\pm 0.0152$	$0.9041\pm 0.0185$
3	$0.8143\pm 0.0131$	$\mathbf{0.7157\pm 0.0095}$	$1.7942\pm 0.1943$	$0.9806\pm 0.0941$	$0.7227\pm 0.0184$	$0.9041\pm 0.0261$
4	$0.8138\pm 0.0154$	$0.7000\pm 0.0148$	$1.8142\pm 0.1723$	$0.9342\pm 0.0377$	$\mathbf{0.7357\pm 0.0147}$	$\mathbf{0.8800\pm 0.0188}$
5	$0.8063\pm 0.0105$	$0.7058\pm 0.0182$	$1.8783\pm 0.2774$	$0.9288\pm 0.0559$	$0.7185\pm 0.0121$	$0.9070\pm 0.0239$

Table 2: Performance across six variational circuit ansatzes. Results are reported as the mean

\pm

standard deviation across five scaffold folds. The best result for each evaluation metric is highlighted in red . Ansatz 6 results on ChEMBL-BACE are omitted due to the substantially higher computational cost of this configuration under our simulation budget.

Functional groups	GATv2	QGAT
$\mathrm{-OH}$	0.411	0.475
$\mathrm{-NH_{2}}$	0.283	0.120
$\mathrm{-CF_{3}}$	-1.023	-1.092
$\mathrm{-tBu}$	-0.611	-0.523
$\mathrm{-C(=O)N}$	0.267	0.052
$\mathrm{-C(=O)CH_{3}}$	0.275	0.084

Table 3: Representative key functional group attributions produced by GATv2 and QGAT on ESOL.

Figure 2: Attention visualization for Verubecestat. The right panel highlights the structural groups and binding interactions discussed in the text, with dashed lines indicating hydrogen bonds. QGAT attention scores are transformed for visualization to enhance contrast.

Figure 3: Integrated gradients attribution for Verubecestat.

Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Task	No. Tasks	Molecules	Target
BACE	Classification	1	1,513	Binding results for a set of inhibitors of human BACE1
BBBP	Classification	1	2,039	Permeability properties of the BBB penetration
FreeSolv	Regression	1	642	Hydration free energy
ESOL	Regression	1	1,128	Water solubility
ChEMBL-BACE	Regression	1	4,580	Binding results for a set of inhibitors of human BACE1

Appendix

Table 4: Summary for the molecular property and bioactivity datasets used in this study

Figure 4: Examples of molecular scaffolds and compounds sharing the corresponding core structures. Highlighted atoms indicate the Bemis–Murcko scaffold, while peripheral substituents vary among compounds within the same scaffold group.

Entity	Feature Type	Description	Type	Size
Atom	CGCNN	Atomic number, radius, and electronegativity	One-Hot	92
Chemical bond edge	Bond direction	None, beginwedge, begindash, etc.	One-Hot	7
	Bond type	Single, Double, Triple, or Aromatic	One-Hot	4
	Bond length	$r_{ij}$ and $r_{ij}^{2}$	Float	2
	Ring membership	Whether the bond belongs to a ring	One-Hot	2
Charge-distance edge	Partial charges	Atomic charges in molecule	Float	3

Appendix

Table 5: Feature Types used for molecular graph construction

Dataset	Model	Ansatz	Hidden	Heads	Layers	$N_{b}$	Qubits	Batch	Params.
BACE	QGAT	1	16	4	2	1	6	64	13,153
BACE	GATv2	–	16	4	2	–	–	64	13,249
BBBP	QGAT	3	32	4	4	3	7	64	73,385
BBBP	GATv2	–	32	4	4	–	–	64	73,729
FreeSolv	QGAT	1	32	4	4	1	7	64	73,273
FreeSolv	GATv2	–	32	4	4	–	–	64	73,729

Appendix

Table 6: GAT and QGAT hyperparameters for different datasets.

Figure 5: Six ansatzes evaluated in this study. For illustration, the circuits are shown with

n_{q}=4

qubits and

N_{b}=1

block. All ansatzes use shallow hardware-efficient circuits composed of parameterized single-qubit rotations and CNOT entangling gates, while differing in rotation patterns and entangling connectivity.

$\boldsymbol{N_{b}}$	BACE	BBBP	FreeSolv	ESOL	ChEMBL-BACE
	AUC $\uparrow$	AUC $\uparrow$	RMSE $\downarrow$	RMSE $\downarrow$	Spearman $\uparrow$	RMSE $\downarrow$
1	$\mathbf{0.8283\pm 0.0133}$	$0.7019\pm 0.0164$	$\mathbf{1.7400\pm 0.2033}$	$0.9263\pm 0.0275$	$0.7265\pm 0.0198$	$0.9018\pm 0.0130$
2	$0.8023\pm 0.0235$	$0.7125\pm 0.0095$	$1.7697\pm 0.1798$	$\mathbf{0.9103\pm 0.0317}$	$\mathbf{0.7357\pm 0.0147}$	$\mathbf{0.8800\pm 0.0188}$
3	$0.8018\pm 0.0126$	$\mathbf{0.7157\pm 0.0095}$	$1.8498\pm 0.2731$	$0.9218\pm 0.0538$	–	–
4	$0.8119\pm 0.0118$	$0.6919\pm 0.0153$	$1.8816\pm 0.2340$	$0.9377\pm 0.0645$	–	–

Appendix

Table 7: Effect of variational circuit depth on QGAT performance. Results are reported as mean

\pm

standard deviation across five folds. The best result for each task is shown in red . Unreported results are denoted by “–” due to higher computational cost.

Figure 6: Performance of QGAT at inference stage under depolarizing noise. Models are trained under noiseless simulation and evaluated with depolarizing noise injecting into the VQC at different channel strengths. Error bars indicate variation across five scaffold folds.

Figure 7: Performance of QGAT at inference stage under amplitude damping noise. Models are trained under noiseless simulation and evaluated with amplitude damping injecting into the VQC at different channel strengths. Error bars indicate variation across five scaffold folds.

Figure 8: The attributions of different functional groups in the whole BACE dataset. Green colors represent GATv2 model, while blue colors represent QGAT model.

Figure 9: The attributions of different functional groups in the whole BBBP dataset. Green colors represent GATv2 model, while blue colors represent QGAT model.

Figure 10: The attributions of different functional groups in the whole FreeSolv dataset. Green colors represent GATv2 model, while blue colors represent QGAT model.

Figure 11: The attributions of different functional groups in the whole ESOL dataset. Green colors represent GATv2 model, while blue colors represent QGAT model.

Figure 12: The attributions of different functional groups in the whole ChEMBL-BACE dataset. Green colors represent GATv2 model, while blue colors represent QGAT model.

Figure 13: IG attribution maps for the AC pairs identified in the Verubecestat series: compounds 21 – 24 . Attributions are normalized within each molecule for visualization. The figure provides the complete atom level attribution patterns corresponding to the qualitative AC analysis discussed in the main text.

Figure 14: IG attribution maps for the AC pairs identified in the Verubecestat series: compounds 30 – 32 . Attributions are normalized within each molecule for visualization. The figure provides the complete atom level attribution patterns corresponding to the qualitative AC analysis discussed in the main text.

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Graph Neural Networks Variational Quantum Circuits Molecular Property Prediction Quantum Neural Networks

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For low-data and resource-constrained regimes typical of quantum chemistry, parameter-efficient learning is a key objective. Here, we propose a topology-aligned inductive bias in which the model architecture mirrors the molecular bond graph: atoms map to a fixed register of computational units, and bonds determine which pairs interact through shared learnable parameters. This principle is instantiated in two architectures: a variational quantum circuit (Iso-QGNN), and a parameter-matched classical message-passing model (Iso-CGNN). The models are benchmarked on HOMO-LUMO and dipole moment binary classification tasks over the QM9 benchmark. With 64 trainable parameters, the implementations achieve test AUCs of approximately 0.88 (quantum) and 0.91 (classical) on the gap task, and close to 0.78 (both) on the dipole task. The models reach 90% of asymptotic performance within about 250 training molecules and gradient norms remain stable throughout training. These results indicate that the topology-aligned inductive bias is the active ingredient driving parameter efficiency at QM9 scale, with implications for matched-baseline benchmarking in quantum machine learning.

Abstract

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