Hybrid Variational Quantum-Classical Framework with Adaptive Weighting and Efficiency Assessment

Dilli Hang Rai

quant-phAug 30, 2026

Hybrid Variational Quantum-Classical Framework with Adaptive Weighting and Efficiency Assessment

Authors: Dilli Hang Rai

Organizations: Institute of Science and Technology Tribhuvan University, Kritipur, Nepal

Abstract

Hybrid quantum-classical neural networks have emerged as a promising approach for leveraging quantum computing in machine learning while mitigating current hardware limitations. This paper presents Sim-HVQC, a hybrid Deep Quantum Neural Network that couples an adaptive, parameter-free SimAM weighting module with classical feature extraction to preserve class-discriminative information prior to encoding into a Variational Quantum Circuit (VQC). Previous studies are restricted to binary classification [1] [2] [3] [4] [5]. In contrast, the proposed framework is trained and evaluated on various multi-class datasets(MNIST, KMNIST, Fashion-MNIST, and EMNIST). The framework further demonstrates reproducibility, parameter efficiency, and interpretability through multi-seed evaluation, parameter analysis, and latent/quantum feature inspection. The source code is publicly available at https://github.com/Dilli822/ SimAM-HVQC

Figures & tables

Fig. 1: Occlusion-based qubit sensitivity maps for a sample input. The varying sensitivity patterns across qubits indicate that different quantum measurements capture complementary information from the compressed latent representation

Fig. 2: Architecture of the proposed SimAM-enhanced hybrid variational quantum-classical neural network (SIMAM-HVQC). The input image is first processed by the parameter-free SIMAM attention module to enhance informative feature responses. The refined feature map is flattened and passed through a classical fully connected feature extractor, reducing the original $784$ -dimensional representation to $256$ , $128$ , and finally $Q$ quantum-compatible features. The resulting features are scaled using $\boldsymbol{\theta}=\pi\tanh(\mathbf{F})$ and encoded into the quantum register through $R_{Y}$ -based AngleEmbedding. The variational quantum component consists of $Q$ qubits and $L$ trainable Strongly Entangling Layers, followed by Pauli- $Z$ expectation-value measurements to produce $Q$ quantum features. These measurements are subsequently processed by a classical fully connected classifier $Q\rightarrow H\rightarrow C$ , where $H$ denotes the hidden-layer dimension and $C$ the number of target classes, producing the final class prediction $\hat{Y}$ . The lower panel provides the corresponding gate-level representation of the variational quantum circuit, illustrating the trainable single-qubit rotations and entangling operations.

Dataset
Parameter	Value
Dataset used	MNIST, KMNIST, EMNIST, FashionMNIST
Input image dimension	$28\times 28$ (grayscale)
Flattened input size	784
Number of classes	10, 47
Layer Dimensions (In $\rightarrow$ Out)

TABLE I: Model Configuration, Dataset, and Hyperparameter Summary

Study	Method	Qubits	Dataset	Classes	Loss	Acc. (%)
[ 1 ]	MPS-VQC	4	MNIST	2	0.3183	99.44
			MNIST	4	-	85.14
[ 12 ]	QCNN	12 qubits	MNIST	4	-	90.03
	(Hybrid VQC)		F-MNIST	4	-	85.93
[ 13 ]	HQNN	16	MNIST	10	-	89.06
[ 8 ]	HQNN	5	MNIST	2	0.0274	99.21

TABLE II: Comparison of Proposed Method Performance with the Existing Methods Performance

Dataset	KMNIST		F-MNIST		MNIST		EMNIST
Utilized	Acc.(%)	Loss	Acc.(%)	Loss	Acc.(%)	Loss	Acc.(%)	Loss
10%	75.09	0.5083	83.07	0.5838	94.46	0.2874	83.66	0.6001
20%	80.54	0.4943	83.68	0.5730	95.00	0.2769	85.12	0.5421
30%	83.72	0.3934	85.28	0.4551	96.10	0.2590	85.44	0.4420
40%	85.50	0.4347	86.28	0.4768	96.12	0.2382	86.86	0.4530
50%	86.47	0.4356	86.75	0.3926	96.35	0.2347	86.47	0.3949

TABLE III: Performance at Different Dataset Utilization Levels

Fig. 3: PCA of latent representations across the hybrid quantum-classical network. Each panel projects a layer’s feature space onto its top two principal components (variance explained on axes), colored by digit label. Class separability increases with depth, with the quantum layer and final classifier layer achieving the clearest separation despite low dimensionality.

Metric	SIM-HVQC
Parameters	236,258
Qubits	8
Quantum Layers	6
Quantum Parameters	144
Test Samples	2,000
Inference Time (s)	1.6249

TABLE IV: Efficiency Assessment of the Proposed SIM-HVQC on CPU

Fig. 4: Shows that the eight quantum measurements progressively develop distinct response patterns across the six variational layers, indicating specialization of quantum features and formation of a discriminative quantum representation for classification.

Dataset	SIM-HVQC		No SIM-HVQC
	Accuracy (%)	Loss	Accuracy (%)	Loss
MNIST	97.57 $\pm$ 0.05	0.1437 $\pm$ 0.0139	97.48 $\pm$ 0.18	0.1638 $\pm$ 0.0054
Fashion-MNIST	87.98 $\pm$ 0.08	0.3345 $\pm$ 0.0132	87.51 $\pm$ 0.11	0.4424 $\pm$ 0.0218
EMNIST	80.16 $\pm$ 0.17	0.7212 $\pm$ 0.0236	78.99 $\pm$ 0.06	0.8921 $\pm$ 0.0302
KMNIST	88.20 $\pm$ 0.63	0.3544 $\pm$ 0.0283	88.23 $\pm$ 0.57	0.9284 $\pm$ 0.0593

TABLE V: Ablation Study of Sim-HVQC With and Without SimAM

Fig. 5: Top Figure: Attention, saliency, and occlusion maps illustrate feature importance for a sample input. Bottom Figure: The dataset-level comparison for ’n=200’ sample test-dataset shows improved accuracy and significantly higher prediction confidence when SimAM is enabled (Wilcoxon $p=4.54\times 10^{-25}$ , Cohen’s $d=0.349$ ).

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Oct 2, 2026J/K move · Enter open · S save

Evolving Hybrid Quantum-Classical Architectures for Image Classification

Devroop Kar, Daniel Krutz, Travis Desell

Rochester Institute of Technology Rochester, NY 14623, USA

Hybrid Quantum-Classical ML Variational Quantum Circuits Image Classification

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Hybrid quantum classical neural networks integrate parameterized quantum circuits (PQCs) with established deep learning architectures, but their performance depends strongly on the choice of quantum circuit architecture, a choice that remains largely manual. Most existing approaches rely on hand-designed or fixed circuit ansätze, requiring circuit structure, gate composition, and qubit connectivity to be specified in advance with no guarantee that they suit the task. This limitation is especially acute in image classification, where quantum circuits must transform features extracted by classical networks while remaining compact enough for practical training, requirements that generic, task-agnostic ansätze are unlikely to satisfy simultaneously. We extend EXAQC, an evolutionary framework for automated quantum circuit discovery, to image classification. EXAQC evolves PQCs as intermediate processing modules while retaining classical feature-extraction and prediction layers. On MNIST, Fashion-MNIST, and CIFAR-10, EXAQC achieves 98.42%, 90.62%, and 85.47% accuracy, respectively, while using comparable gate counts to other quantum architecture-search methods. Against classical networks, evolved hybrid models maintain comparable accuracy with substantially fewer trainable parameters, reaching 85.68% on CIFAR-10 with over 25

\times

fewer parameters than a 10-layer CNN. Encoding choice also matters: rotation-based encodings (RX, RY, U3) outperform amplitude encoding by 22-25 points on CIFAR-10. These results demonstrate that automated circuit discovery yields compact quantum modules that can replace larger classical components in vision architectures while retaining competitive accuracy.

Abstract

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