Hybrid Quantum-Classical Encoding for Accurate Residue-Level pKa Prediction

Van Le; Tan Le

physics.chem-phMar 9, 2026

Hybrid Quantum-Classical Encoding for Accurate Residue-Level pKa Prediction

Authors: Van Le, Tan Le

Organizations: the Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA · the School of Engineering, Architecture and Aviation, Hampton University, Hampton, VA 23669, USA

Abstract

Accurate prediction of residue-level pKa values is essential for understanding protein function, stability, and reactivity. While existing resources such as DeepKaDB and CpHMD-derived datasets provide valuable training data, their descriptors remain primarily classical and often struggle to generalize across diverse biochemical environments. We introduce a reproducible hybrid quantum-classical framework that enriches residue-level representations with a Gaussian kernel-based quantum-inspired feature mapping. These quantum-enhanced descriptors are combined with normalized structural features to form a unified hybrid encoding processed by a Deep Quantum Neural Network (DQNN). This architecture captures nonlinear relationships in residue microenvironments that are not accessible to classical models. Benchmarking across multiple curated descriptor sets demonstrates that the DQNN achieves improved cross-context generalization relative to classical baselines. External evaluation on the PKAD-R experimental benchmark and an A $β$ 40 case study further highlights the robustness and transferability of the quantum-inspired representation. By integrating quantum-inspired feature transformations with classical biochemical descriptors, this work establishes a scalable and experimentally transferable approach for residue-level pKa prediction and broader applications in protein electrostatics.

Figures & tables

Fig. 1: Schematic overview contrasting dataset origins and methodological innovations in residue‑level p K a prediction. (Left) DeepKaDB: descriptor‑driven resource derived from soluble proteins in PDBbind, providing curated feature sets for classical machine learning models. (Center) PHMD549: simulation‑driven dataset generated via GPU‑accelerated CpHMD, expanding PHMD279 to 26,552 residues across 549 proteins. (Right) DQNN framework: hybrid quantum–classical pipeline that integrates curated descriptors with quantum‑inspired feature transformations.

Model	RMSE		MAE		MaxErr		R		Slope (m)
Model	Train	Test	Train	Test	Train	Test	Train	Test	Train	Test
DQNN	0.393	0.886	0.270	0.645	2.582	6.384	0.973	0.886	0.911	0.799
GradientBoosting	0.001	1.288	0.001	0.964	0.011	6.356	1.000	0.807	1.000	0.935
GPR_SE	0.923	1.856	0.507	1.253	7.870	7.208	0.839	0.385	0.718	0.139
kNN_k5	1.116	1.941	0.319	1.276	9.440	8.440	0.799	0.443	0.802	0.366

TABLE I: Performance comparison across models using RMSE, MAE, MaxErr, Pearson correlation (R), and regression slope (m) for both training and testing sets. Best test-set values are highlighted in bold.

Fig. 2: Comparison of A $\beta$ 40 histidine pKa predictions using experimental measurements, DeepKa, and the proposed DQNN model. Error bars indicate reported standard deviations for DeepKa and replicate variability for DQNN.

Residue	Experiment	$DeepKa_{\text{mean}}$	$DeepKa_{\text{SD}}$	$DQNN_{\text{mean}}$	$DQNN_{\text{SD}}$	$DeepKa_{\text{Error}}$	$DQNN_{\text{Error}}$	Error Reduction
His13	6.7	6.0	0.10	6.527	0.069	0.700	0.173	0.527
His14	6.4	5.9	0.10	6.501	0.061	0.500	0.101	0.399
His6	6.7	6.8	0.30	6.479	0.104	0.100	0.221	-0.121

TABLE II: Summary of A

\beta

40 histidine pKa predictions comparing DeepKa and DQNN against experimental values. Errors are reported as absolute deviations from experiment, and error reduction is defined as the difference between DeepKa and DQNN errors.

Molecular Property Prediction

Molecular property prediction estimates chemical, physical, and biological properties from molecular structure and context.

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Jun 10, 2026J/K move · Enter open · S save

Comprehensive pKa Data Augmentation from Limited Real Data through an Engineered Models-Quantum Framework

Wang Rui, Liu Dinghao

Department of Chemistry, Tsinghua University, Beijing 100084, P. R. China · Department of Chemical Engineering, Tsinghua University, Beijing 100084, P. R. China · School of Science, China Pharmaceutical University, Nanjing 211198, P. R. China

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Proton dissociation constants (pKa) are critical for functional molecule discovery and molecular modeling. Building on iBonD, the largest experimental pKa database established, we and other researchers have developed several methods including machine-learning-based empirical prediction and high-accuracy energy calculations. Despite this foundation, the rapid augmentation of high-quality pKa data remains fundamentally constrained. As part of this work, we performed large-scale regression-based pKa prediction on unlabeled molecular datasets using a collection of extensively optimized machine-learning models. The results indicate that, since the feature distributions of unlabeled molecular datasets, the pKa data distribution approximates normality, with extreme scarcity of tail-region samples. Although such augmentation is highly valuable for improving overall data availability and predictive modeling, it remains insufficient for efficiently discovering molecules with broad-spectrum pKa properties. To address this, we explore the targeted generation of molecules with sparse pKa properties from the vast chemical space. Given that traditional continuous latent space VAE-RNN methods for molecular generation suffer from insufficient stability and fail to demonstrate clear advantages in complementing sparse data, we design and implement a quantum-assisted sparse-pKa molecular generation. Feasibility is validated on a simulated quantum annealer, and superior extreme-value sampling is further achieved on physical coherent Ising machines (CIMs). (to be continued)

Abstract

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