Convolution operations are foundational to classical image processing and modern deep learning architectures, yet their extension into the quantum domain has remained algorithmically and physically costly due to inefficient data encoding and prohibitive circuit complexity. In this work, we present a resource-efficient quantum algorithm that reformulates the convolution product as a structured matrix multiplication via a novel sparse reshaping formalism. Leveraging the observation that localized convolutions can be encoded as doubly block-Toeplitz matrix multiplications, we construct a quantum framework wherein sparse input patches are prepared using optimized key-value QRAM state encoding, while convolutional filters are represented as quantum states in superposition. The convolution outputs are computed through inner product estimation using a low-depth SWAP test circuit, which yields probabilistic amplitude information with reduced sampling overhead. Our architecture supports batched convolution across multiple filters using a generalized SWAP circuit. Compared to prior quantum convolutional approaches, our method eliminates redundant preparation costs, scales logarithmically with input size under sparsity, and enables direct integration into hybrid quantum-classical machine learning pipelines. This work provides a scalable and physically realizable pathway toward quantum-enhanced feature extraction, opening up new possibilities for quantum convolutional neural networks and data-driven quantum inference.
Convolution operations are foundational to classical image processing and modern deep learning architectures, yet their extension into the quantum domain has remained algorithmically and physically costly due to inefficient data encoding and prohibitive circuit complexity. In this work, we present a resource-efficient quantum algorithm that reformulates the convolution product as a structured matrix multiplication via a novel sparse reshaping formalism. Leveraging the observation that localized convolutions can be encoded as doubly block-Toeplitz matrix multiplications, we construct a quantum framework wherein sparse input patches are prepared using optimized key-value QRAM state encoding, while convolutional filters are represented as quantum states in superposition. The convolution outputs are computed through inner product estimation using a low-depth SWAP test circuit, which yields probabilistic amplitude information with reduced sampling overhead. Our architecture supports batched convolution across multiple filters using a generalized SWAP circuit. Compared to prior quantum convolutional approaches, our method eliminates redundant preparation costs, scales logarithmically with input size under sparsity, and enables direct integration into hybrid quantum-classical machine learning pipelines. This work provides a scalable and physically realizable pathway toward quantum-enhanced feature extraction, opening up new possibilities for quantum convolutional neural networks and data-driven quantum inference.
Quantum computing is rapidly reshaping the landscape of image recognition by offering enhanced computational capabilities. Classical deep learning architectures such as Convolutional Neural Networks (CNNs) struggle with scalability and efficiency when handling high-dimensional quantum image data. Quantum-enhanced Dilated Convolutional Networks (Q-DCNs) have emerged as a novel solution to this problem. Traditional CNNs, even with dilation, are computationally intensive on large-scale or entangled quantum image datasets. These models fail to exploit quantum parallelism and often suffer from vanishing gradients and redundant parameterization. There is a need for an optimized hybrid quantum-classical model that combines the generalization capacity of dilation with the processing power of quantum circuits. We propose a Quantum-Enhanced Dilated Convolutional Network (Q-DCN), wherein dilated convolutional layers are hybridized with quantum variational circuits (QVCs). The model includes a dilated feature extractor that feeds into a parameterized quantum layer for entanglement-preserving transformation. The quantum circuit acts as a regularizer and nonlinear encoder, effectively reducing model complexity and enhancing feature discrimination. The Q-DCN was evaluated on a simulated quantum image dataset and compared against five existing methods: Classical CNN, Dilated CNN, Quantum CNN (QCNN), Variational Quantum Classifier (VQC), and Quantum Kernel Estimator (QKE). Q-DCN achieved superior accuracy (94.3%), reduced inference time by 23%, and utilized 35% fewer parameters. These results indicate that Q-DCN offers a scalable, efficient, and accurate solution for quantum image recognition.
Image classification plays a vital role in large-scale data analysis, especially in object recognition tasks using advanced Deep Learning (DL) frameworks. However, the growing complexity and computational demands of modern DL models have introduced challenges related to scalability and efficiency. Quantum Computing (QC) has emerged as a promising alternative, capable of addressing these limitations by leveraging the principles of Quantum Machine Learning (QML). However, many existing QML models require a large number of qubits, which poses limitations within the current Noisy Intermediate-Scale Quantum (NISQ) era. This work introduces a novel Adaptive Quantum Convolutional Neural Network (AQCNN) designed for efficient and scalable image classification within the constraints of NISQ devices. Addressing the limitations of existing QML approaches, particularly the high qubit requirements, AQCNN incorporates a resource-efficient quantum convolutional layer that performs localized quantum filtering using parameterized quantum circuits. A classical preprocessing layer encodes input features to reduce qubit load, followed by quantum embedding and hybrid quantum-classical layers that optimize feature extraction and classification performance. The model leverages an adaptive quantum convolution strategy, minimizing quantum gate depth and circuit complexity while preserving critical spatial hierarchies in image data. Evaluated on benchmark datasets, AQCNN achieved 95.88% accuracy on MNIST and 95.68% on FMNIST, outperforming comparable QML architectures. Additionally, the model supports scalable execution through parallel quantum circuit arrays, enabling practical deployment on current quantum hardware. This architecture demonstrates a significant advance in quantum-assisted image classification, balancing performance with qubit and gate efficiency. The integration of adaptive quantum convolution and hybrid processing not only enhances classification accuracy but also provides a viable path forward for deploying QML solutions under realistic hardware constraints.
Convolutional Neural Network (CNN) is a breakthrough learning model that shows outstanding performance in computer vision and deep learning applications. However, it is a relatively burdened model in terms of learning speed and resource usage compared to other learning models when the learning scale becomes large. Quantum Convolutional Neural Network (QCNN) is a novel model as a potential solution using quantum computers to handle this problem. Quantum computers with a limited number of usable qubits needs a resource-efficient method to process large-scale data at once. In addition, Quantum Random Access Memory (QRAM) can store the large data to qubits logarithmically using superposition and entanglement. The QRAM algorithm can design a new QCNN model that can efficiently process in massive data. This paper proposes a more resource and depth efficient model for larger-sized input data and the number of output channels using the QRAM algorithm and efficiently extracting features.
Matrix multiplication is a fundamental operation in compute-intensive tasks and a key component of modern quantum acceleration frameworks. Here we present a quantum matrix multiplication algorithm based on quantum kernels (QKMM), achieving an elementary gate complexity of O(N2log2N), with amplitude encoding overhead explicitly included and without assuming a QRAM oracle. This scaling is asymptotically lower than that of the best-known classical matrix multiplication algorithm O(N2.371339). Building upon QKMM, we establish a family of quantum linear algebra operators, including Quantum Vector Inner Product (V2V), Quantum Vector-Matrix Multiplication (V2M), QKMM (M2M), Quantum One-to-Many Matrix Multiplication(O2M) and Quantum Sequential Matrix Multiplication (SMM), providing a unified framework from vector operations to parallel and sequential matrix transformations. Through noiseless simulations, realistic noise modelling and experiments on a superconducting quantum processor, we systematically characterize the numerical accuracy, resource requirements and hardware execution limits of this operator framework. Furthermore, we integrate SMM into deep neural-network inference, enabling intermediate features to propagate coherently across layers without repeated measurement and re-encoding. These results establish a pathway from quantum circuit-level algorithm design to end-to-end coherent computation, providing a quantum computing framework for matrix-centric compute-intensive applications.
As image datasets grow in scale and complexity, classical convolutional neural networks (CNNs) increasingly face limitations in computational efficiency, scalability, and generalisation in low-data regimes. Quantum machine learning (QML) offers a promising alternative, with quantum convolutional neural networks (QCNNs) exploiting quantum parallelism and entanglement for feature extraction. This paper introduces the Novel Quantum Convolutional Neural Network (No-QCNN), which differs from recent hybrid QCNN/QCQ-CNN architectures by employing an end-to-end quantum convolution-pooling pipeline without inserting an intermediate classical CNN block. No-QCNN is a hybrid quantum-classical model that employs a variational quantum classifier (VQC) optimised via the COBYLA algorithm and is designed for binary and multiclass classification of low-resolution colour images on near-term quantum devices. A key innovation is a problem-specific quantum feature map that pre-processes each image into a structured three-dimensional block-matrix representation, jointly encoding pixel colour (R, G, B) and spatial position before mapping this information into a hierarchical ZZFeatureMap. This encoding captures spatial-chromatic correlations at shallow circuit depth, making it compatible with noisy intermediate-scale quantum (NISQ) constraints. The model is implemented using IBM-Qiskit on a local quantum simulator and benchmarked against a classical CNN. For a six-class classification task on a 50-image dataset, No-QCNN achieves a validation accuracy of 82.05%, substantially outperforming the classical CNN's 40.00%, indicating improved generalisation and reduced overfitting in low-data, multiclass settings. Conversely, for a simpler binary classification task, the classical CNN achieves perfect validation accuracy of 100%, surpassing the No-QCNN's 89.7%. We further observe that No-QCNN performance declines with increasing dataset size and training time due to limited circuit expressibility, data-encoding overhead, and finite-sampling noise inherent to NISQ models. Overall, these results position No-QCNN as a complementary framework best suited to low-data, correlation-rich classification tasks, defining a realistic niche for quantum-enhanced artificial vision and quantum perception in the NISQ era.
This paper proposes and evaluate Hybrid Quantum Convolutional Neural Networks (HQCNNs) that integrate Structured Variational Quantum Circuits (SVQCs) into classical convolutional networks for image classification. Prior quanvolutional architectures often rely on unstructured variational circuits, leading to barren-plateau training landscapes, unpredictable convergence, and poor scaling of expressivity as qubit count grows. Moreover, simplistic data-encoding schemes can either fail to capture spatial correlations or demand impractically deep circuits, while arbitrary entanglement patterns obscure the relationship between circuit design and learning capacity. To address these challenges, we design four HQCNN architectures with progressively increased quantum encoding precision, entanglement topology, and classical post-processing depth. Each HQCNN replaces the convolutional layer with a quanvolutional layer: local image patches are encoded into small qubit registers via an Enhanced Novel Enhanced Quantum Representation (ENEQR), then processed by the SVQCs, and then measured to produce quantum feature maps. The four versions vary in quantum structure: Version 1 uses a simple linear 5-qubit chain (q=2), Version 2 adds wrap-around entanglement (closed-loop topology), Version 3 augments the classical head with a deeper batch-normalized multilayer perceptron, and Version 4 increases encoding fidelity to q=4 (7 qubits per patch). All models end-to-end using the Adam optimizer and cross-entropy loss on the MNIST dataset for 10 epochs using a PennyLane simulator. Version 4 achieves the best test accuracy (96% on MNIST). Fourier spectrum analysis reveals that richer entanglement and higher-fidelity encoding broaden the circuits’ harmonic spectrum, correlating with enhanced representational capacity and improved classification performance. These results confirm that carefully structured quantum layers and enhanced encoding can enrich feature representations and boost accuracy, albeit with increased simulation overhead and training complexity.