Exploring the Effects of Entanglement on Quantum Machine Learning of Pathogen Epitope-Receptor Binding

Abstract: Parameterized quantum circuits (PQCs) provide a flexible substrate for hybrid quantum machine learning (QML), but their practical value on Noisy Intermediate-Scale Quantum (NISQ) devices remains an empirical question, especially because training depth and scale can introduce optimization challenges such as barren plateaus. Here we study how the number and topology of two-qubit entangling gates in the feature-map stage influence a fixed hybrid QNN workflow for classifying strong versus weak epitope-receptor binding in Porcine Reproductive and Respiratory Syndrome (PRRS) vaccine design. The dataset consists of docking-derived binding affinities for N=80 9-mer epitopes, labeled as Strong or Weak binding, and partitioned into training, validation, and test subsets using a 40:30:30 split. We compare a classical CNN benchmark with a hybrid Embedding-QNN architecture under four feature-map configurations: a non-entangling Z feature map, an all-to-all high-entanglement ZZ feature map, and two interleaved nearest-neighbour entanglement patterns of low and high depth. Among the configurations tested, the high-entanglement ZZ feature map is seen to provide the strongest evidence of reduced training-set overfit, with a lower training area under the accuracy curve (AUAC) and the highest test/training AUAC ratio, while preserving competitive test-set accuracy. These results do not establish a general QML advantage, but they suggest that feature-map entanglement topology is a meaningful design variable for sparse biological screening tasks and warrants further evaluation with additional metrics, larger datasets, and noise-aware or hardware-based experiments.

• The paper demonstrates that feature-map entanglement topology in PQCs crucially influences QML performance in classifying epitope-receptor binding.
• It employs a hybrid Embedding-QNN architecture with four entanglement configurations, showing that all-to-all ZZ mapping best mitigates overfitting compared to a CNN baseline.
• The findings imply that carefully designed entanglement layouts can enhance generalization in quantum models, aiding vaccine antigen triage in sparse data regimes.

Effects of Entanglement Topology in Quantum Machine Learning for Pathogen Epitope-Receptor Binding

Introduction

This study investigates the influence of feature-map entanglement topology within parameterized quantum circuits (PQCs) on the performance of quantum machine learning (QML) systems for classifying binding affinities between viral epitopes and host receptor molecules. The biological context is vaccine antigen discovery for Porcine Reproductive and Respiratory Syndrome (PRRS), employing a dataset of 80 epitope candidates derived from computational molecular docking experiments. The work is situated in the Noisy Intermediate-Scale Quantum (NISQ) regime, focusing on whether quantum entanglement structure in the circuit feature map contributes meaningfully to predictive success under severe data limitations, in direct comparison with a classical convolutional neural network (CNN) baseline.

Methods

A hybrid Embedding-QNN architecture was adopted, comprising a classical learned embedding that reduces one-hot-encoded 9-mer epitopes (20×9 input dimensionality) to a compact feature vector, which is then mapped into a PQC. Four feature-map entanglement configurations were evaluated:

1. Z feature map: Non-entangling baseline, encoding features by single-qubit phase rotations.
2. ZZ feature map: All-to-all high-entanglement configuration, introducing pairwise two-qubit phase interactions.
3. Low-depth interleaved: Z feature map augmented with a single pass of nearest-neighbor entangling gates.
4. High-depth interleaved: Z feature map with repeated nearest-neighbor entangling gates to match the two-qubit gate count of the all-to-all configuration.

Circuit simulations were noiseless (statevector-based), holding quantum convolutional/pooling and RealAmplitudes ansatz stages constant across all experiments. Both CNN and QNN models were trained using the Adam optimizer and stratified data splits into train/validation/test subsets with a 40/30/30 ratio, reflecting the nearly balanced strong/weak binding class distribution.

Results

Unfiltered Performance and Overfitting

Initial QNN runs without validation filtering yielded accuracies near chance (53–54% test set), in sharp contrast to the CNN benchmark's typical 70–75% test performance. This result reflects both the training fragility and the landscape flatness associated with PQCs in small-data regimes.

Validation-Gated Run Filtering

Application of a validation threshold filter (requiring ≥85% validation accuracy during training) dramatically improved retained QNN runs, resulting in test-set accuracies on par with the CNN baseline (70–75%) across entanglement configurations. The high-entanglement all-to-all ZZ feature map demonstrated the most pronounced regularization: it yielded the lowest normalized area under the accuracy curve (AUAC) for training, the highest test/training AUAC ratio (0.792), and the smallest number of retained high-performing runs. This suggests that entanglement topology—particularly complete pairwise connectivity—more effectively suppresses overfitting relative to depth-matched nearest-neighbor approaches, even when total two-qubit gate counts are similar.

Graph-Theoretic Characterization

Graph-theoretic quantification underscored the distinctions between feature-map entanglement layouts. The all-to-all ZZ map uniquely achieved maximum connectivity (diameter 1, average node degree 4.0, 36 unique qubit pairs), whereas high-depth interleaved maps achieved comparable gate counts but lower connectivity and increased step multiplicity. This reinforces that not only entanglement quantity but also topological distribution impacts model behavior.

Discussion

The empirical findings highlight the nuanced role of entanglement topology: the structure and connectivity of feature-map entangling gates can materially affect model generalization in QML systems, at least for small, sparse biological datasets. The all-to-all ZZ configuration's favorable generalization profile—competitive test accuracy and superior test/training AUAC ratio—contraindicates the assumption that circuit depth or raw two-qubit gate count alone suffice for optimal PQC design. The observed regularization effect may stem from enhanced expressivity or more favorable gradient landscapes associated with global entanglement, though these conjectures require further theoretical development.

However, these results do not claim a general QML advantage over classical models; performance parity is only achieved for a small subset of QNN initializations selected by stringent validation, and all runs are conducted in a noise-free simulation regime. In real-world hardware, decoherence and readout error could alter these dynamics substantively, potentially diminishing or inverting observed trends.

The results are consistent with recent theoretical work showing that model/data interaction, circuit architecture, and the structure of the quantum feature map jointly determine the learning regime and generalization properties [Caro et al., 2022; Gil-Fuster et al., 2024]. Furthermore, they echo calls for QML benchmarking to emphasize model design choices—such as entanglement topology—over undifferentiated comparisons to classical baselines.

Implications and Future Directions

From a practical standpoint, QML approaches with well-chosen entanglement topology could become valuable for triaging vaccine antigen candidates where extensive labeled data is unavailable and each high-fidelity experimental assay is costly. The current findings advocate for future explorations that:

• Increase dataset size and diversity for enhanced statistical power.
• Extend the survey of feature-map entanglement families (e.g., alternative graph topologies, variational feature maps, and deeper repetition).
• Incorporate hardware noise and simulated decoherence using realistic quantum error models.
• Adopt additional metrics (ROC-AUC, precision-recall, calibration, uncertainty quantification) to fully delineate model performance.
• Systematically examine alternative classical and hybrid optimizers to address QML training fragility.

Theoretical analyses illuminating the connection between feature-map entanglement topology, gradient landscape geometry, and expressivity in QNNs are needed to solidify architectural guidelines.

Conclusion

This work demonstrates that the topology of feature-map entanglement in PQC-based QML architectures serves as a critical design parameter, influencing generalization and overfitting in the context of sparse biological binding classification. All-to-all high-entanglement (ZZ) maps produced the most robust generalization among configurations tested, despite statevector simulation limitations and the need for a strong validation filter. While not establishing broad QML superiority, these results identify feature-map topology as an actionable lever for enhancing quantum and hybrid model performance on data-scarce, resource-constrained biomedical applications. Future research should systematically map the entanglement–generalization landscape using larger datasets and analysis on real quantum devices.