PaperlayerView exact revision on arXiv

Source-linked AI summary

Hybrid Quantum-Classical Model for Image Classification

Muhammad Adnan Shahzad

arXiv:2509.13353v1cs.CVcs.AIcs.LG

TL;DR

This study addresses limited comparative evidence on hybrid quantum-classical models’ performance, efficiency, and robustness across vision tasks. It benchmarks hybrid models with quantum layers against classical CNNs, finding consistent accuracy and efficiency advantages, with accuracy gains increasing with dataset complexity.

  • Problem

    Comparative evidence on hybrid and classical models across dataset complexities, training dynamics, resource use, and adversarial robustness remains limited.

    Source: §I · p. 1

  • Method

    The study benchmarks hybrid models combining classical CNNs and quantum layers against classical models across MNIST, CIFAR100, and STL10.

    Source: §I · p. 2, B. Implementation Framework · p. 3

  • Results

    Hybrid models consistently achieved higher accuracy, trained faster, and used resources more efficiently; accuracy gains rose from +1.17% on MNIST to +10.29% on STL10.

    Source: §IV · p. 15, §V · p. 16

  • Takeaways & Limitations

    The reported accuracy advantage increased with dataset complexity, reaching +10.29% on STL10.

    Source: §IV · p. 15

    Classical simulation constrains circuit depth, and larger-scale experiments would require actual quantum hardware.

    Source: §IV · p. 15

Abstract

from arXiv · show

This study presents a systematic comparison between hybrid quantum-classical neural networks and purely classical models across three benchmark datasets (MNIST, CIFAR100, and STL10) to evaluate their performance, efficiency, and robustness. The hybrid models integrate parameterized quantum circuits with classical deep learning architectures, while the classical counterparts use conventional convolutional neural networks (CNNs). Experiments were conducted over 50 training epochs for each dataset, with evaluations on validation accuracy, test accuracy, training time, computational resource usage, and adversarial robustness (tested with $\epsilon=0.1$ perturbations).Key findings demonstrate that hybrid models consistently outperform classical models in final accuracy, achieving {99.38\% (MNIST), 41.69\% (CIFAR100), and 74.05\% (STL10) validation accuracy, compared to classical benchmarks of 98.21\%, 32.25\%, and 63.76\%, respectively. Notably, the hybrid advantage scales with dataset complexity, showing the most significant gains on CIFAR100 (+9.44\%) and STL10 (+10.29\%). Hybrid models also train 5--12$\times$ faster (e.g., 21.23s vs. 108.44s per epoch on MNIST) and use 6--32\% fewer parameters} while maintaining superior generalization to unseen test data.Adversarial robustness tests reveal that hybrid models are significantly more resilient on simpler datasets (e.g., 45.27\% robust accuracy on MNIST vs. 10.80\% for classical) but show comparable fragility on complex datasets like CIFAR100 ($\sim$1\% robustness for both). Resource efficiency analyses indicate that hybrid models consume less memory (4--5GB vs. 5--6GB for classical) and lower CPU utilization (9.5\% vs. 23.2\% on average).These results suggest that hybrid quantum-classical architectures offer compelling advantages in accuracy, training efficiency, and parameter scalability, particularly for complex vision tasks.

I. Introduction

Hybrid quantum-classical models combine classical learning with quantum layers, and this study benchmarks them against classical models across vision datasets to address gaps in comparative performance, efficiency, and robustness evidence.

I. Introduction

  • The study motivates hybrid models as a way to combine deep learning’s representational power with potential quantum computational advantages amid concerns about classical models’ scalability and energy efficiency.The introduction also notes recent NISQ advances have enabled practical experimentation with quantum machine-learning algorithms.Source: §I · p. 1
  • Existing comparisons insufficiently characterize performance across problem complexities, training dynamics, resource use, and adversarial robustness.Prior studies also tended to cover single datasets or omit comprehensive computational-efficiency comparisons.Source: §I · pp. 1–2
  • Quantum machine learning may use superposition and entanglement for enhanced feature representation when quantum layers are integrated into classical neural networks.The described architecture embeds classical inputs before parameterized rotation gates and entangling operations.Source: §I · pp. 1–2, Figure 1 · p. 2
  • Table I presents key previous studies in quantum machine learning.Source: Table I · p. 2
  • The study’s contributions include benchmarking hybrid and classical models on MNIST, CIFAR100, and STL10, analyzing resource use and robustness, and reporting accuracy gains that increase with dataset complexity.The reported gains range from +1.17% to +9.44% across datasets.Source: §I · p. 2

A. Mathematical Foundations

The mathematical framework describes quantum states in an n-qubit Hilbert space, outlines classical-data encoding choices, and represents the trainable circuit and quantum measurement operations.

A. Mathematical Foundations

  • The n-qubit Hilbert space has dimension 2^n and computational-basis states corresponding to classical bit strings.Its tensor-product structure represents composite systems as products of individual qubit spaces.Source: A. Mathematical Foundations · pp. 2–3
  • Amplitude encoding places classical data in quantum-state probability amplitudes, while angle encoding maps each data point to qubit rotation angles.The passage presents these as distinct encoding schemes with different storage-density and implementation-complexity trade-offs.Source: A. Mathematical Foundations · pp. 2–3
  • The variational quantum circuit is a layered quantum-neural-network structure with Hermitian-generator rotations and an entangling layer that typically uses CNOT gates.Source: A. Mathematical Foundations · p. 3
  • Quantum expectation values are described as weighted sums of measurement outcomes, with observable eigenvalues as the weights.Source: A. Mathematical Foundations · p. 3

B. Implementation Framework

The implementation combines classical CNNs with quantum layers and configures a four-qubit, two-layer circuit alongside dataset-specific preprocessing and a tracked training and visualization workflow.

B. Implementation Framework

  • The configured quantum circuit uses 4 qubits and 2 layers, and training uses a batch size of 64 for 50 epochs.Source: B. Implementation Framework · p. 3
  • The implementation uses PennyLane, PyTorch, and TorchVision, with preprocessing and augmentation strategies tailored to MNIST, CIFAR-100, and STL-10.Source: B. Implementation Framework · p. 3
  • The hybrid model combines classical CNNs with quantum layers through PennyLane’s TorchLayer.The implementation also includes dataset transforms, resource tracking, and plots of training curves, feature spaces, and quantum circuits.Source: B. Implementation Framework · p. 3

C. Datasets and Experimental Setup

The experiments compare models on three image datasets with different class counts, resolutions, and image types, using a common 50-epoch training protocol and multiple performance and resource measures.

C. Datasets and Experimental Setup

  • The benchmarks are MNIST with 70,000 28×28 grayscale images across 10 classes, CIFAR100 with 60,000 32×32 RGB images across 100 classes, and STL10 with 13,000 96×96 RGB images across 10 classes.Source: C. Datasets and Experimental Setup · pp. 3–4
  • All models were trained for 50 epochs using identical hyperparameters and data-augmentation strategies.Source: C. Datasets and Experimental Setup · p. 4
  • Evaluation covered validation and test accuracy, training time, computational-resource use, and adversarial robustness under ε = 0.1 perturbations.The hybrid models used a 4-qubit circuit with amplitude encoding and basic entangler layers.Source: C. Datasets and Experimental Setup · p. 4

A. MNIST Dataset Analysis

On MNIST, the hybrid model outperformed the classical CNN in test accuracy and showed advantages in convergence, adversarial performance, and feature-space structure. It used comparable memory and lower CPU utilization, but took longer per epoch.

A. MNIST Dataset Analysis

  • The hybrid model converged faster in loss and accuracy, maintained superior F1 scores, and performed better against ϵ = 0.1 attacks.Figure 2 compares training metrics between the models.Source: A. MNIST Dataset Analysis · p. 4, Figure 2 · p. 4
  • Hybrid training took 2.3× longer per epoch, with comparable memory use and lower CPU utilization than the classical model.Figure 3 presents resource-utilization metrics during MNIST training.Source: A. MNIST Dataset Analysis · p. 4, Figure 3 · p. 5
  • 99.38% test accuracy for the hybrid model exceeded the classical CNN’s 98.21%.Figure 4 also compares precision, recall, and F1 scores.Source: A. MNIST Dataset Analysis · p. 4, Figure 4 · p. 5
  • Hybrid features formed tighter clusters, separated difficult digit pairs such as 4/9 better, and produced smoother decision boundaries than classical features.The PCA projections and t-SNE visualizations show these feature-space differences.Source: A. MNIST Dataset Analysis · p. 5
  • The training set was balanced across all 10 digit classes, and the hybrid model made fewer errors on slanted digits than the classical model.The classical model struggled more with unusual stroke patterns.Source: A. MNIST Dataset Analysis · p. 5

B. CIFAR100 Dataset Analysis

On CIFAR100, the hybrid model showed faster convergence, higher validation accuracy, and better adversarial performance than the classical model. Its feature representations also showed tighter clustering and more coherent class regions, although training took longer per epoch.

B. CIFAR100 Dataset Analysis

C. STL10 Dataset Analysis

On STL10, the hybrid model reached higher validation accuracy and showed superior convergence and adversarial performance. It required more training time per epoch and had a higher memory footprint, while its feature space showed compact clusters and smoother class boundaries.

C. STL10 Dataset Analysis

  • Hybrid training took 2.1× more time per epoch, with comparable CPU utilization and 15% higher memory use than the classical model.The authors describe the approach as viable for high-resolution image processing tasks.Source: C. STL10 Dataset Analysis · p. 11
  • The hybrid model showed strong discrimination between visually similar and rare STL10 classes, and better handled subtle class distinctions.Source: C. STL10 Dataset Analysis · p. 11
  • Hybrid features formed more compact clusters and smoother decision boundaries than the classical model’s more fragmented boundaries.Source: C. STL10 Dataset Analysis · p. 11
  • 92.1% validation accuracy for the hybrid model exceeded the classical model’s 88.3%.Figure 24 compares training metrics on STL10.Source: C. STL10 Dataset Analysis · p. 11, Figure 24 · p. 12

IV. Discussion

Hybrid models outperform classical networks across the evaluated datasets, with accuracy gains that grow with dataset complexity. They also show faster training, lower CPU utilization, and dataset-dependent robustness, while simulation constraints limit the approach.

IV. Discussion

  • Hybrid models reached higher validation accuracy faster; classical models showed more overfitting on CIFAR100, while the hybrid lead on STL10 grew after epoch 15.The STL10 pattern was described as indicating better generalization capabilities.Source: §IV · p. 13
  • Hybrid models trained faster across datasets and averaged 9.5% CPU utilization versus 23.2% for classical models.Memory use was typically comparable, at 4–5GB for most experiments.Source: §IV · pp. 13, 15
  • At ϵ = 0.1, hybrid models were 4.2× more robust on MNIST, while robustness remained comparably low for both models on CIFAR100 and STL10.The authors suggest quantum features may be harder to perturb on simpler feature spaces, while complex datasets may need further architectural optimization.Source: §IV · p. 15
  • +1.17% on MNIST, +9.44% on CIFAR100, and +10.29% on STL10 mark growing hybrid accuracy advantages as dataset complexity increases.Hybrid models also achieved higher validation and test accuracy across all datasets despite having fewer parameters.Source: §IV · pp. 13, 15
  • Current limitations include circuit-depth constraints from classical simulation; future work includes other circuit architectures, real quantum processors, and additional data modalities.The paper also calls for improving robustness on complex datasets.Source: §IV · pp. 15–16

V. Conclusion

Across MNIST, CIFAR100, and STL10, hybrid models achieved higher accuracy and faster training than classical counterparts. The authors identify simulation constraints and simple circuit architectures as limitations, while positioning efficiency and accuracy as promising strengths.

V. Conclusion

  • Hybrid models achieved higher accuracy across all three datasets, with the largest improvements on more complex tasks.The authors suggest quantum circuits may capture complex, nonlinear data relationships more efficiently than classical layers.Source: §V · p. 16
  • Hybrid models’ faster training, lower parameter counts, and MNIST robustness advantage support their appeal where efficiency matters, though robustness gains diminished on complex datasets.The paper connects this advantage to resource-constrained environments and large-scale applications.Source: §V · p. 16
  • Restricted qubit counts from simulation constraints and simple quantum circuits limit the current approach; future work includes hardware deployment and applications beyond computer vision.The paper also proposes larger circuits with more sophisticated entanglement patterns.Source: §V · p. 16
  • The authors position hybrid models as promising for efficient, high-accuracy machine learning, particularly when training speed and parameter efficiency are critical.Source: §V · p. 16
Loading 2509.13353v1…