Hybrid quantum neural networks are increasingly explored for classification, yet it remains unclear how their performance and quantum behavior scale with circuit depth and qubit count. We present a controlled scaling study of hybrid quantum-classical classifiers along two axes: (1) increasing the number of quantum layers L at fixed qubits Q, and (2) increasing the number of qubits Q at fixed depth L. Across multiple datasets, we evaluate predictive performance using Accuracy, PR-AUC, Precision, Recall, and F1, and track quantum-specific metrics (QCE, EEE, QGN) to characterize how quantum properties evolve under scaling. Our results summarize scaling trends, saturation regimes, and dataset-dependent sensitivity, and further analyze how quantum metrics relate to predictive performance. This study provides practical guidance for selecting (Q,L) in hybrid QNN classifiers and establishes a consistent evaluation protocol for scaling analysis.
Journal reference
2026 International Joint Conference on Neural Networks (IJCNN), Maastricht, Netherlands, 2026, pp. 1-8
Hybrid quantum neural networks are increasingly explored for classification, yet it remains unclear how their performance and quantum behavior scale with circuit depth and qubit count. We present a controlled scaling study of hybrid quantum-classical classifiers along two axes: (1) increasing the number of quantum layers L at fixed qubits Q, and (2) increasing the number of qubits Q at fixed depth L. Across multiple datasets, we evaluate predictive performance using Accuracy, PR-AUC, Precision, Recall, and F1, and track quantum-specific metrics (QCE, EEE, QGN) to characterize how quantum properties evolve under scaling. Our results summarize scaling trends, saturation regimes, and dataset-dependent sensitivity, and further analyze how quantum metrics relate to predictive performance. This study provides practical guidance for selecting (Q,L) in hybrid QNN classifiers and establishes a consistent evaluation protocol for scaling analysis.
Hybrid quantum neural networks (QNNs) pair a classical feature extractor with a variational quantum circuit, and the effective dimension of the circuit's quantum Fisher information matrix (QFIM) is widely used to assess such models. This scalar is often interpreted as an indicator of trainability or accuracy, although these readings are rarely tested under controlled conditions. We therefore investigate what it actually measures. We define the effective dimension as the participation ratio of the QFIM diagonal, which lies between one and the parameter count, and we evaluate it across two image datasets, four frozen backbones including a random-projection control, four circuit depths on eight qubits, and three seeds. During training, the effective dimension remains well below the parameter count, and its correlation with test accuracy ranges from -0.72 to +0.87, changing sign across seeds in half of the configurations. Increasing depth activates a larger share of the circuit directions, from 0.38 to 0.91 of the parameter count, while the initialization gradient variance remains between 1e-5 and 1e-4, so no barren plateau (BP) appears at eight qubits. At a fixed circuit, the four backbones share an initial effective dimension of 6 to 9, even though CIFAR-10 accuracy ranges from 23.14% to 86.44%. These results show that the effective dimension characterizes circuit geometry rather than model quality. We conclude with a practical protocol that assigns each diagnostic to the question it can answer.
Abstract Hybrid quantum-classical neural networks (HQNNs) are a promising paradigm in quantum enhaced machine learning, yet their evaluation remains an open challenge constrained by two key issues: reliance on single metrics (e.g., loss or gradients) and synthetic benchmarks that fail to reflect real-world complexities. This work introduces a multi-metric diagnostic framework, that offers a holistic view of HQNN behavior by analyzing primary axes: quantum trainability (gradient norms), model convergence (loss curves), and quantum utility (via the Quantum Contribution Score, QCS). And secondary axes: expressivity, gradient efficiency and entanglement entropy. Across 16 models over real-world and synthetic data with a classical artificial neural network as baseline. Through this framework empirical phenomena in practical evaluations are developed, including gradient recovery after barren plateaus, data and expressivity dependent QCS trends, relation between gradient behaviour and qubit to layer ratio and model convergence despite barren plateaus.
Given the recent prominence of Noisy Intermediate Scale Quantum (NISQ) devices, hybrid quantum-classical neural networks have recently drawn a lot of excitement as a potential solution to improving learning efficiency. Our current paper describes a Hybrid Quantum-Classical Convolutional Neural Network (HQCNN) which is defined as a pretrained backbone of ResNet-18 and a small quantum-enhanced feature-transformation layer of Qiskit. The convolutional high-dimensional features are reduced to the classical eight-dimensional one, which in turn is encoded into a four-qubit parameterized quantum circuit. The resultant quantum expectation values are combined with the compressed features to come up with a hybridized representation of twelve dimensions, used to classify multi-class dataset. Experimental analysis of CIFAR10 data has shown that the suggested HQCNN achieves a test accuracy of 94.74% and improves class-wise precision, recall, and F1-scores than a number of existing hybrid models while using a significantly smaller number of latent features. More investigation into the quantum module indicates that it is predictable about scalability to batch, resistant to perturbations in features, and efficiently performed by evaluating circuit vectors. These results indicate that compact and expressive representations of images that can be helpful in the NISQ era can be acquired using hybrid architectures, thus providing a practical way to forward the benefits of quantum to modern deep-learning pipelines.
Quantum computing is expected to fundamentally change computer systems in the future. Recently, a new research topic of quantum computing is the hybrid quantum–classical approach for machine learning, in which a parameterized quantum circuit, also called quantum neural network (QNN), is optimized by a classical computer. This hybrid approach can have the benefits of both quantum computing and classical machine learning methods. In this early stage, it is of crucial importance to understand the new characteristics of quantum neural networks for different machine learning tasks. In this paper, we will study quantum neural networks for the task of classifying images, which are high-dimensional spatial data. In contrast to previous evaluations of low-dimensional or scalar data, we will investigate the impacts of practical encoding types, circuit depth, bias term, and readout on classification performance on the popular MNIST image dataset. Various interesting findings on learning behaviors of different QNNs are obtained through experimental results. To the best of our knowledge, this is the first work that considers various QNN aspects for image data.
Quantum neural networks (QNNs) offer a principled pathway for integrating quantum computation with machine learning through superposition- and entanglement-based representations. This chapter proposes an architecture-aware design and evaluation framework for modern QNNs, emphasizing robustness and system feasibility alongside predictive performance. Multiple architecturesvariational QNNs, quantum convolutional neural networks, tensor-network hybrids, and fully quantum models—are assessed under a unified protocol. Experimental analysis shows that the proposed architecture-search–guided QNN achieves 91.8% classification accuracy and an F1-score of 0.914, outperforming fixed-template variational QNNs by approximately 5.6 percentage points. Under depolarizing noise with probability p = 0.10, the proposed model retains 85.3% accuracy, whereas baseline QNNs fall below 80%. Moreover, circuit depth is reduced by nearly 25% relative to standard variational designs, leading to faster convergence (42 epochs vs. 57 epochs).
Quantum neural networks (QNNs) have recently attracted remarkable attention as a potential alternative to classical and deep neural network (NN) models particularly under constraints imposed by noisy intermediate-scale quantum (NISQ) devices, which support only shallow circuits with few quantum bits (qubits) and limited variational depth. However, applying QNNs to natural language processing (NLP) remains challenging because text representations are typically high-dimensional, while NISQ classifiers can only encode a small number of features at a time, requiring classical compression to enable stable training and flexible circuit configuration. In addition, many existing studies integrate QNNs into rich-text representation pipelines, where the quantum circuit is often implemented as a variational quantum circuit (VQC). Here, the VQC acts as an additional component within a larger model, and it remains unclear how the quantum component improves the classification task. Therefore, in this work, we propose a fully reproducible and compact QNN pipeline that provides a controlled setting for studying the contribution of the VQC to text classification. The model is trained end-to-end with a lightweight classical compression layer, and the overall study is supported by systematic ablation analyses of the compression layer, the classifier heads under a shared frozen low-dimensional representation, and quantum circuit structure. Our model uses the term frequency-inverse document frequency (TF-IDF) features with linear compression followed by a shallow four-qubit, two-layer VQC, implemented in PyTorch and PennyLane for end-to-end training. It is evaluated on five benchmark text classification datasets against classical baselines, including logistic regression and multilayer perceptron (MLP) models. Experimental results show that the proposed QNN achieves a competitive performance across all evaluated datasets, yielding the best results on three of the five benchmark datasets.