This work presents an implementation-grounded quantum convolutional neural network (QCNN) pipeline in which classical images are amplitude-encoded with the quantum signal-induced heap transform (QsiHT), transformed by a 2-D quantum Fourier transform (2-D QFT), and classified by a two-stage QCNN. Each convolution stage applies shared single-qubit rotations and ring CNOT entanglement, pooling is unitary-only, and prediction is obtained from the final readout qubit probability via thresholding. Training uses parameter-shift gradients with Adam-style updates and includes practical regularization through random-affine data augmentation, ℓ2 weight decay, and class-balanced subset sampling. Experiments in IBM Qiskit on a binary MNIST task (classes (0, 1)) evaluate 4-qubit (4 × 4) and 6-qubit (8 × 8) models under finite-shot simulation (256 shots), yielding final validation accuracies of 91.41% and 99.80%, respectively. These results indicate that the QsiHT+QFT front-end integrates effectively with shallow QCNN layers and benefits from increased qubit resolution in this setting.
This work presents an implementation-grounded quantum convolutional neural network (QCNN) pipeline in which classical images are amplitude-encoded with the quantum signal-induced heap transform (QsiHT), transformed by a 2-D quantum Fourier transform (2-D QFT), and classified by a two-stage QCNN. Each convolution stage applies shared single-qubit rotations and ring CNOT entanglement, pooling is unitary-only, and prediction is obtained from the final readout qubit probability via thresholding. Training uses parameter-shift gradients with Adam-style updates and includes practical regularization through random-affine data augmentation, ℓ2 weight decay, and class-balanced subset sampling. Experiments in IBM Qiskit on a binary MNIST task (classes (0, 1)) evaluate 4-qubit (4 × 4) and 6-qubit (8 × 8) models under finite-shot simulation (256 shots), yielding final validation accuracies of 91.41% and 99.80%, respectively. These results indicate that the QsiHT+QFT front-end integrates effectively with shallow QCNN layers and benefits from increased qubit resolution in this setting.
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.
Classical convolutional neural networks (CNNs) have achieved notable success in image classification but face challenges in scalability, interpretability, and computational cost. With the growing availability of Noisy Intermediate-Scale Quantum (NISQ) devices, hybrid quantum-classical models offer a promising alternative by leveraging quantum parallelism and entanglement. In this work, we present a hybrid Quantum Convolutional Neural Network (QCNN) that integrates quantum convolutional layers into classical image classification pipeline for the MNIST dataset. Our architecture features a modular, low-depth Quantum Kernel Convolution (QKC) design suitable for near-term hardware. We implement the system using Qiskit and evaluate in terms of classification accuracy, circuit efficiency, and integration feasibility. Our results demonstrate that (i) the hybrid QCNN achieves similar accuracy to classical models while reducing the number of classical parameters, and (ii) quantum layers can successfully perform dimensionality reduction through entanglement-based pooling. This study highlights the potential of hybrid QCNN as a practical quantum-enhanced model for real-world image recognition tasks.
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.
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.
Convolutional neural networks owe much of their success to hard-coding translation equivariance. Quantum convolutional neural networks (QCNNs) have been proposed as near-term quantum analogues, but the relevant notion of translation depends on the data encoding. For address/amplitude encodings such as FRQI, a pixel shift acts as modular addition on an index register, whereas many MERA-inspired QCNNs are equivariant only under cyclic permutations of physical qubits. We formalize this mismatch and construct QCNN layers that commute exactly with the pixel cyclic shift (PCS) symmetry induced by the encoding. Our main technical result is a constructive characterization of all PCS-equivariant unitaries: conjugation by the quantum Fourier transform (QFT) diagonalizes translations, so any PCS-equivariant layer is a Fourier-mode multiplexer followed by an inverse QFT (IQFT). Building on this characterization, we introduce a deep PCS-QCNN with measurement-induced pooling, deferred conditioning, and inter-layer QFT cancellation. We also analyze trainability at random initialization and prove a lower bound on the expected squared gradient norm that remains constant in a depth-scaling regime, ruling out a depth-induced barren plateau in that sense.
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.