Quantum convolutional neural networks (QCNNs) offer a promising architecture for near-term quantum machine learning by combining hierarchical feature extraction with modest parameter growth. However, any QCNN operating on classical data must rely on an encoding scheme to embed inputs into quantum states, and this choice can dominate both performance and resource requirements. This work presents an implementation-level comparison of three representative encodings -- Angle, Amplitude, and a Hybrid phase/angle scheme -- for QCNNs under depolarizing noise. We develop a fully differentiable PyTorch--Qiskit pipeline with a custom autograd bridge, batched parameter-shift gradients, and shot scheduling, and use it to train QCNNs on downsampled binary variants of MNIST and Fashion-MNIST at $4\times 4$ and $8\times 8$ resolutions.
Our experiments reveal regime-dependent trade-offs. On aggressively downsampled $4\times 4$ inputs, Angle encoding attains higher accuracy and remains comparatively robust as noise increases, while the Hybrid encoder trails and exhibits non-monotonic trends. At $8\times 8$, the Hybrid scheme can overtake Angle under moderate noise, suggesting that mixed phase/angle encoders benefit from additional feature bandwidth. Amplitude-encoded QCNNs are sparsely represented in the downsampled grids but achieve strong performance in lightweight and full-resolution configurations, where training dynamics closely resemble classical convergence. Taken together, these results provide practical guidance for choosing QCNN encoders under joint constraints of resolution, noise strength, and simulation budget.
Comments
9 pages, 9 figures. Implementation-level comparison under depolarizing noise
Quantum convolutional neural networks (QCNNs) offer a promising architecture for near-term quantum machine learning by combining hierarchical feature extraction with modest parameter growth. However, any QCNN operating on classical data must rely on an encoding scheme to embed inputs into quantum states, and this choice can dominate both performance and resource requirements. This work presents an implementation-level comparison of three representative encodings -- Angle, Amplitude, and a Hybrid phase/angle scheme -- for QCNNs under depolarizing noise. We develop a fully differentiable PyTorch--Qiskit pipeline with a custom autograd bridge, batched parameter-shift gradients, and shot scheduling, and use it to train QCNNs on downsampled binary variants of MNIST and Fashion-MNIST at 4×4 and 8×8 resolutions.
Our experiments reveal regime-dependent trade-offs. On aggressively downsampled 4×4 inputs, Angle encoding attains higher accuracy and remains comparatively robust as noise increases, while the Hybrid encoder trails and exhibits non-monotonic trends. At 8×8, the Hybrid scheme can overtake Angle under moderate noise, suggesting that mixed phase/angle encoders benefit from additional feature bandwidth. Amplitude-encoded QCNNs are sparsely represented in the downsampled grids but achieve strong performance in lightweight and full-resolution configurations, where training dynamics closely resemble classical convergence. Taken together, these results provide practical guidance for choosing QCNN encoders under joint constraints of resolution, noise strength, and simulation budget.
Quantum machine learning is one of the most exciting new avenues in the world of artificial intelligence, especially because of the enormous computational power of quantum computers and the promise of the development of near error-free quantum computers in the not-so-distant future. For quantum algorithms to be used in real-life applications, quantum computers must be able to work with classical data. One of the key steps in quantum algorithms dealing with classical data is the encoding of classical data points to quantum states, which can then be processed by quantum gates. It is known that the type of encoding technique that works best for a particular network is dependent on the dataset being used. In this paper, a new parallel structure is proposed utilizing two encoding techniques, namely amplitude encoding and angle encoding, for effective classical data classification via quantum neural network. The paper further proposes a maximally expressible and entangled ansatz used to design a simple Quantum Convolutional Neural Network (QCNN) with only 32 parameters, that is used in the latter stages of the network and is kept the same across all encoding instances so that a comparison between the different encoding methods is possible. Extensive experimentation is carried out on two publicly available image datasets, namely MNIST and Fashion MNIST. The results show that the proposed method achieves better results than any of the encoding techniques deployed alone for binary classification.
Quantum Machine Learning (QML) has recently emerged as a highly promising research frontier. Within this domain, Quantum Neural Networks (QNNs),characterized by Variational Quantum Circuits (VQCs) at their core and featuring layers of quantum gates optimized by classical algorithms, have garnered significant attention. However, a rigorous and exhaustive evaluation of their practical performance remains largely incomplete. In this study, we conduct a comprehensive comparative analysis of three prominent hybrid classical-quantum architectures: Quantum Convolutional Neural Networks (QCNN), Quantum Recurrent Neural Networks (QRNN), and Quantum Vision Transformers (QViT), focusing on the critical dimensions of generalization, accuracy, and robustness. Our findings provide novel insights that address previous evaluative gaps. Notably, while these models exhibit exceptional performance on low-feature datasets such as MNIST, their learning efficacy degrades significantly when transitioned to high-feature datasets. Furthermore, convolutional-based models like QCNN appear less effective on high-dimensional data than other machine learning architectures. Additionally, while all models are susceptible to adversarial noise, traditional architectures, such as recurrent and convolutional networks, demonstrate superior resilience. Conversely, in the presence of quantum noise, the transformer-based architecture proves its strength by maintaining high robustness against measurement noise, channel noise, and finite-shot effects, whereas other architectures suffer marked performance declines. These results provide a granular perspective on the current state of the field and underscore the critical importance of tailoring model selection to the constraints of contemporary Noisy Intermediate-Scale Quantum (NISQ) environments.
Quantum convolutional neural networks (QCNNs) typically consist of quantum encoding, convolution, and pooling layers. However, existing QCNNs for image classification still face two major limitations. Most encoding layers rely on single-parameter angle encoding, which limits their ability to represent complex image features. Many circuit architectures are relatively deep, increasing cir cuit complexity and noise accumulation and thus hindering implementation on noisy intermediate-scale quantum devices. To address these issues, this paper proposes a low-depth three-parameter encoding quantum convolutional neural network (LTP-QCNN) for image classification. The model employs a three parameter angle encoding layer that maps compressed image features onto the rotation angles of single-qubit gates. A first low-depth quantum convolutional layer is employed to extract local features, followed by a quantum pooling layer for quantum-state dimensionality reduction and information fusion. The pooled quantum states are then processed by a second quantum convolutional layer to extract discriminative features. Finally, the measured quantum feature vector is input into a classical classification layer to produce the final prediction. Simulation experiments were conducted on the Fashion-MNIST, MNIST, and KMNIST benchmark datasets. On Fashion-MNIST, LTP-QCNN achieved an accuracy of 99.85% on binary classification, while the accuracies for five-class and six class tasks reached 90.98% and 89.48%, respectively. The results demonstrate that LTP-QCNN achieves effective and stable image classification under limited quantum resources.
Quantum machine learning is a promising paradigm for learning from limited data, a central bottleneck in domains such as medical imaging, clinical trials, and rare diseases. Quantum convolutional neural networks (QCNNs) are particularly attractive in this setting, combining a hierarchical architecture with strong inductive bias and a parameter count that grows only logarithmically with system size. Their appeal rests on the generalization bounds of Caro et al. (2022), which show that the generalization error of a quantum model scales with the number of trainable parameters rather than with the Hilbert-space dimension, placing QCNNs in a potentially sample-efficient regime. We develop a hardware-compatible QCNN with mid-circuit measurement and classical feed-forward, and show on a binary handwritten-digit task that strong test performance is achievable from as few as 10 training samples, with the generalization error decreasing as the training set grows. At a matched 45-parameter budget the QCNN learns where an equally small classical convolutional network stays at chance, although an unconstrained classical baseline with roughly 25,000 parameters remains strongest when data are plentiful. Transpiling amplitude and angle encoded circuits across image resolutions from 2x2 to 512x512 pixels then exposes the dominant scaling bottleneck: amplitude encoding stays qubit-efficient but grows extremely deep, whereas angle encoding stays shallow but becomes qubit-prohibitive. On the medically motivated BreastMNIST benchmark the QCNN does not surpass the unconstrained classical network, yet it learns consistently above chance using orders of magnitude fewer parameters. Our results indicate that for QCNNs, learning from few samples is attainable in practice, whereas scaling to realistic image data is constrained less by optimization than by data encoding and hardware execution.
Quantum machine learning is emerging as a promising frontier at the intersection of quantum computing and Artificial Intelligence, offering potential gains in speed, efficiency, and robustness. In this paper, a hybrid Quantum Convolutional Neural Network (QCNN) architecture is presented for visual pattern recognition tasks, leveraging quantum superposition and entanglement for enhanced feature extraction. Unlike previous studies that focus on small-scale or simplified datasets, this study systematically evaluates QCNNs across multiple benchmark datasets and provides a direct comparison with classical CNNs, highlighting practical quantum advantages such as parameter efficiency and noise-resilience. The proposed approach encodes classical image data from benchmark datasets, including70K28×28grayscale images from MNIST and FashionMNIST, and60Kdownsampled grayscale CIFAR-10 images, into quantum states using amplitude encoding, followed by hierarchical quantum convolution and pooling layers implemented via parametrised quantum circuits (PQCs). The model culminates in a classical dense layer for final classification. Experimental results demonstrate that the QCNN achieves competitive performance on low-dimensional grayscale datasets with 93.2 % accuracy on MNIST and 88.5% on Fashion MNIST, though it underperforms on more complex datasets like CIFAR-10 with 67.8 % accuracy due to current quantum hardware limitations. While not yet surpassing classical CNNs in raw accuracy, the proposed QCNN exhibits notable parameter efficiency, noise resilience, and theoretical potential for energy-efficient computation, highlighting its promise for future applications as quantum technologies mature.
Abstract With the significant enhancement of quantum computing capabilities and their expanding applications in various fields, quantum image processing combined with quantum computing has become a key area of research in quantum computing, holding important theoretical value. In the face of the challenges posed by the digital information era, image classification technology demands higher standards from machine learning algorithms in terms of accuracy, computational speed, generalization capability, and complexity. This paper studies a series of quantum data encoding methods and parametric quantum circuit architectures, and proposes the application of Hybrid Hierarchical Encoding (HHE) and Hybrid Quantum Convolutional Neural Network (HQCNN). The new encoding method HHE integrates the benefits of angle encoding and enhances the hybrid amplitude encoding design to achieve optimal classification performance without compromising the depth of quantum circuits.HQCNN demonstrates outstanding classification performance and remarkable control over model complexity by leveraging the data processing capabilities of classical convolution and the complex computational power of quantum convolution. Experimental results show that HHE and HQCNN achieve better classification accuracy on the MNIST and Fashion-MNIST datasets compared to traditional classical CNN models, particularly when the number of parameters is significantly reduced.