Embedding-Aware Quantum-Classical SVMs for Scalable Quantum Machine Learning

Main Findings:

We demonstrate the first systematic evidence that quantum kernel advantage depends critically on embedding choice, revealing fundamental synergy between transformer attention and quantum feature spaces.

ViT embeddings uniquely enable quantum advantage, achieving up to 8.02% accuracy improvements on Fashion-MNIST
CNN features show consistent performance degradation in quantum kernels
16-qubit tensor network simulation provides scalable quantum machine learning pathway

This summary was automatically generated by Google's NotebookLM

Hybrid Quantum-Classical Pipeline

Complete pipeline overview showing the sequential steps from data extraction to QSVM evaluation

Embedding-Aware QSVM Framework.

The pipeline combines class-balanced k-means distillation with pretrained embeddings, followed by PCA compression and quantum kernel classification using tensor network simulation. This approach reduces complexity from O(70000²) to O(1600²) kernel evaluations while preserving essential dataset characteristics.

Abstract

Quantum Support Vector Machines face scalability challenges due to high-dimensional quantum states and hardware limitations. We propose an embedding-aware quantum-classical pipeline combining class-balanced k-means distillation with pretrained Vision Transformer embeddings.

Our key finding: ViT embeddings uniquely enable quantum advantage, achieving up to 8.02% accuracy improvements over classical SVMs on Fashion-MNIST and 4.42% on MNIST, while CNN features show performance degradation. Using 16-qubit tensor network simulation via cuTensorNet, we provide the first systematic evidence that quantum kernel advantage depends critically on embedding choice.

This reveals fundamental synergy between transformer attention and quantum feature spaces, providing a practical pathway for scalable quantum machine learning that leverages modern neural architectures. The framework demonstrates that achieving quantum advantage requires careful algorithm-representation co-design rather than naive application of quantum methods.

Quantum Circuit Architecture

Quantum circuit diagram showing the 4-qubit parameterized circuit with Hadamard gates, RZ and RY rotations, and CNOT entanglement gates

Data Re-uploading Quantum Feature Map.

Each qubit is initialized with Hadamard gates, followed by parameterized RZ and RY rotations for data encoding. CNOT gates create entanglement between adjacent qubits, forming an embedding-aware quantum feature map that leverages the exponentially large Hilbert space dimension 2^n.

Quantum Advantage with Modern Embeddings

Quantum vs Classical SVM Performance Comparison

Dataset	Embedding Type	Classic SVM Acc	Quantum SVM Acc	Quantum Advantage
MNIST	Raw Pixels	0.945	0.887	-6.14%
	EffNet-512	0.969	0.935	-3.55%
	EffNet-1536	0.973	0.948	-2.58%
	ViT-B/32-512	0.948	0.990	+4.42%
	ViT-B/16-512	0.954	0.995	+4.25%
	ViT-L/14	0.983	0.990	+0.76%
	ViT-L/14@336-768	0.984	0.993	+0.94%
Fashion-MNIST	Raw Pixels	0.783	0.730	-6.71%
	EffNet-512	0.917	0.887	-3.29%
	EffNet-1536	0.916	0.877	-4.26%
	ViT-B/32-512	0.848	0.900	+6.18%
	ViT-L/14	0.871	0.897	+3.01%
	ViT-L/14@336-768	0.865	0.900	+4.02%

Quantum advantage emerges specifically with transformer-based representations, revealing fundamental synergy between quantum kernels and modern neural embeddings.

Comprehensive Cross-Validation Results

Violin plots showing test accuracy distributions for MNIST across K-fold cross-validation

Violin plots showing test accuracy distributions for Fashion-MNIST across K-fold cross-validation

Stable and Robust Quantum Advantage.

ViT-based quantum models show consistently higher accuracies and lower variance compared to baselines and EfficientNet-based QSVMs. The narrow, high-accuracy distributions confirm that quantum advantage is stable and reproducible across different data splits.

Detailed Cross-Validation Performance (Best Models)

Dataset	Model	Test Acc	Precision	F1	AUC	Time (s)	Memory (MB)
MNIST	Baseline	0.882 ± 0.010	0.887 ± 0.010	0.882 ± 0.011	0.990 ± 0.004	4492.196 ± 39.285	44116.842 ± 25.978
	Baseline+	0.884 ± 0.018	0.888 ± 0.019	0.884 ± 0.018	0.991 ± 0.004	3812.316 ± 42.187	43537.845 ± 22.515
	QSVM: EffNet-512	0.889 ± 0.018	0.893 ± 0.015	0.889 ± 0.017	0.992 ± 0.003	3910.851 ± 25.007	43506.193 ± 21.365
	QSVM: EffNet-1536	0.904 ± 0.020	0.906 ± 0.019	0.904 ± 0.020	0.994 ± 0.003	3819.504 ± 23.488	43566.972 ± 22.614
	QSVM: ViT-B/32-512	0.962 ± 0.008	0.963 ± 0.007	0.962 ± 0.008	0.999 ± 0.000	3900.742 ± 24.954	43510.314 ± 21.536
	QSVM: ViT-B/16-512	0.973 ± 0.003	0.974 ± 0.003	0.973 ± 0.003	0.999 ± 0.000	3763.170 ± 25.646	43513.467 ± 20.800
	QSVM: ViT-L/14	0.969 ± 0.009	0.970 ± 0.008	0.969 ± 0.008	0.999 ± 0.001	3816.003 ± 31.957	43520.979 ± 18.243
	QSVM: ViT-L/14@336-768	0.976 ± 0.010	0.977 ± 0.010	0.975 ± 0.010	0.999 ± 0.001	3939.404 ± 24.480	43520.375 ± 22.726
FashionMNIST	Baseline	0.725 ± 0.048	0.723 ± 0.041	0.716 ± 0.044	0.963 ± 0.003	4456.288 ± 32.991	44086.054 ± 22.615
	Baseline+	0.734 ± 0.028	0.727 ± 0.029	0.723 ± 0.027	0.963 ± 0.004	3803.786 ± 27.142	43510.356 ± 19.410
	QSVM: EffNet-512	0.823 ± 0.016	0.823 ± 0.019	0.818 ± 0.016	0.980 ± 0.002	3797.365 ± 29.575	43256.111 ± 21.782
	QSVM: EffNet-1536	0.809 ± 0.022	0.808 ± 0.020	0.805 ± 0.020	0.980 ± 0.004	3887.396 ± 26.549	43301.836 ± 17.939
	QSVM: ViT-B/32-512	0.818 ± 0.015	0.821 ± 0.014	0.816 ± 0.015	0.981 ± 0.002	3773.245 ± 25.367	43250.348 ± 24.488
	QSVM: ViT-B/16-512	0.829 ± 0.008	0.831 ± 0.009	0.827 ± 0.009	0.982 ± 0.004	3853.586 ± 38.180	43258.243 ± 23.672
	QSVM: ViT-L/14	0.831 ± 0.021	0.831 ± 0.022	0.829 ± 0.022	0.981 ± 0.003	3766.821 ± 21.742	43266.337 ± 20.614
	QSVM: ViT-L/14@336-768	0.841 ± 0.019	0.841 ± 0.020	0.840 ± 0.020	0.983 ± 0.002	3859.313 ± 20.656	43265.254 ± 20.394

Computational Efficiency Analysis

Runtime vs accuracy comparison for MNIST showing optimal balance between performance and efficiency

Runtime vs accuracy comparison for Fashion-MNIST showing trade-offs between computational cost and classification performance

Optimal Performance-Efficiency Trade-off.

ViT-B/16-512 offers the best balance, achieving 97.3% accuracy with fastest runtime (3,763 seconds). Memory usage remains consistent around 43GB across all configurations, demonstrating scalable quantum simulation capabilities.

Model Generalization

Strong Cross-Validation to Test Set Alignment.

Clear diagonal structure with minimal off-diagonal errors confirms robust generalization. The alignment between cross-validation and held-out test results demonstrates that high accuracy reflects true performance across all classes, not overfitting to specific categories.

BibTeX

@article{ordonez2025embedding,
  title={Embedding-Aware Quantum-Classical SVMs for Scalable Quantum Machine Learning},
  author={Ord{\'o}{\~n}ez, Sebasti{\'a}n Andr{\'e}s Cajas and Torres, Luis Fernando Torres and Bifulco, Mario and Duran, Carlos Andres and Bosch, Cristian and Carbajo, Ricardo Simon},
  journal={arXiv preprint arXiv:2508.00024},
  year={2025}
}

Embedding-Aware Quantum-Classical SVMs for Scalable Quantum Machine Learning

Main Findings:

Hybrid Quantum-Classical Pipeline

Embedding-Aware QSVM Framework.

Abstract

Key Features

⚛️ Quantum-Classical Hybrid

🎯 Embedding-Aware Design

📈 Proven Quantum Advantage