We introduce QFARE, a hybrid quantum-classical architecture for MNIST digit classification. Our approach employs a classical variational autoencoder (VAE) to compress 28×28 grayscale images into 64-dimensional latent representations. These compressed features are then loaded into an 8-qubit register. We augment this register with 4 additional ancilla qubits, whose partial mid-circuit measurements and subsequent conditional resets induce nonunitary transformations on the main qubits. This effectively provides a nonlinearity mechanism in an otherwise unitary quantum circuit, analogous to activation functions in classical neural networks. We train the resulting model end-to-end using a reinforcement learning algorithm (TD3) that explores the space of circuit parameters without relying on gradients of the quantum circuit, thus avoiding barren plateaus. Our theoretical framework proves that these measurement-based feedforward operations can simulate broad classes of nonunitary channels, guaranteeing universal classification capability when paired with a classical classifier. On a noiseless simulator, our experiments demonstrate that QFARE achieves around 99% accuracy on MNIST with significantly fewer parameters than purely classical neural network baselines. We also investigate the impact of circuit depth, the number of ancilla qubits, and how these aspects scale. This work shows how feedforward-enabled discrete-qubit designs can yield powerful and parameter-efficient classifiers for standard image recognition tasks.
We introduce QFARE, a hybrid quantum-classical architecture for MNIST digit classification. Our approach employs a classical variational autoencoder (VAE) to compress 28×28 grayscale images into 64-dimensional latent representations. These compressed features are then loaded into an 8-qubit register. We augment this register with 4 additional ancilla qubits, whose partial mid-circuit measurements and subsequent conditional resets induce nonunitary transformations on the main qubits. This effectively provides a nonlinearity mechanism in an otherwise unitary quantum circuit, analogous to activation functions in classical neural networks. We train the resulting model end-to-end using a reinforcement learning algorithm (TD3) that explores the space of circuit parameters without relying on gradients of the quantum circuit, thus avoiding barren plateaus. Our theoretical framework proves that these measurement-based feedforward operations can simulate broad classes of nonunitary channels, guaranteeing universal classification capability when paired with a classical classifier. On a noiseless simulator, our experiments demonstrate that QFARE achieves around 99% accuracy on MNIST with significantly fewer parameters than purely classical neural network baselines. We also investigate the impact of circuit depth, the number of ancilla qubits, and how these aspects scale. This work shows how feedforward-enabled discrete-qubit designs can yield powerful and parameter-efficient classifiers for standard image recognition tasks.
We implement a hybrid quantum-classical model for image classification that compresses MNIST digit images into a low-dimensional feature space and then maps these features onto a 5-qubit quantum state. First, an autoencoder compresses each 28×28 image (784 pixels) into a 64-dimensional latent vector, preserving salient features of the digit with minimal reconstruction error. We further reduce the latent representation to 5 principal components using Principal Component Analysis (PCA), to match the 5 available qubits. These 5 features are encoded as rotation angles in a quantum circuit with 5 qubits. The quantum feature map applies single-qubit rotations (Ry gates) proportional to the feature values, followed by a Hadamard gate and a cascade of entangling CNOT gates to produce a non-product entangled state. Measuring the 5-qubit state yields a 32-dimensional probability distribution over basis outcomes, which serves as a quantum-enhanced feature vector for classification. A classical neural network with a softmax output is then trained on these 32-dimensional quantum feature vectors to predict the digit class. We evaluate the hybrid model on the MNIST dataset and compare it to a purely classical baseline that uses the 64-dimensional autoencoder latent features for classification. The results show that the hybrid model can successfully classify digits, demonstrating the feasibility of integrating quantum computing in the classification pipeline, although its accuracy (about 75\% on test data) currently falls below the classical baseline (about 98\% on the same compressed data).
This research explores quantum machine learning for image classification, comparing classical and quantum models. A classical convolutional neural network (CNN), based on the LeNet architecture, achieved 99.12% accuracy on MNIST, outperforming a quantum CNN, which attained 93.30%. Quantum encoders applied to Fashion-MNIST reached 85.60%, while quantum support vector machine (SVM), implemented for binary classification, obtained 71.34%. The study integrates hybrid quantum-classical models, leveraging quantum circuits for feature extraction. A quantum autoencoder-based classifier was introduced, demonstrating efficient data compression and classification without additional qubits. Feature encoding using RX gates mapped classical data into quantum states, and the impact of parameterized quantum circuit structures on classification accuracy was analyzed. Results indicate that specific ansatz structures yield superior accuracy, highlighting the significance of quantum circuit design. While classical models currently outperform quantum counterparts, quantum approaches reduce trainable parameters and computational complexity. Limitations in current quantum hardware, including noise and scalability, restrict performance. However, advancements in error mitigation, quantum gate efficiency, and scalable quantum architecture could bridge the gap with classical methods. These quantum techniques hold potential in aerospace applications, such as satellite image classification, anomaly detection in remote sensing, and real-time processing of high-dimensional image data. This study underscores the growing role of quantum circuits in machine learning, particularly in feature extraction and classification, suggesting that future quantum hardware could unlock new capabilities in end-to-end learning beyond hybrid approaches.
Deep learning has achieved significant success in pattern recognition, with convolutional neural networks (CNNs) serving as a foundational architecture for extracting spatial features from images. Quantum computing provides an alternative computational framework, a hybrid quantum-classical convolutional neural networks (QCCNNs) leverage high-dimensional Hilbert spaces and entanglement to surpass classical CNNs in image classification accuracy under comparable architectures. Despite performance improvements, QCCNNs typically use fixed quantum layers without incorporating trainable quantum parameters. This limits their ability to capture non-linear quantum representations and separates the model from the potential advantages of expressive quantum learning. In this work, we present a hybrid quantum-classical-quantum convolutional neural network (QCQ-CNN) that incorporates a quantum convolutional filter, a shallow classical CNN, and a trainable variational quantum classifier. This architecture aims to enhance the expressivity of decision boundaries in image classification tasks by introducing tunable quantum parameters into the end-to-end learning process. Through a series of small-sample experiments on MNIST, F-MNIST, and MRI tumor datasets, QCQ-CNN demonstrates competitive accuracy and convergence behavior compared to classical and hybrid baselines. We further analyze the effect of ansatz depth and find that moderate-depth quantum circuits can improve learning stability without introducing excessive complexity. Additionally, simulations incorporating depolarizing noise and finite sampling shots suggest that QCQ-CNN maintains a certain degree of robustness under realistic quantum noise conditions. While our results are currently limited to simulations with small-scale quantum circuits, the proposed approach offers a potentially promising direction for hybrid quantum learning in near-term applications.
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.
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× 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.
We present a hybrid quantum-classical recurrent neural network (QRNN) architecture in which the recurrent core is realized as a parametrized quantum circuit (PQC) controlled by a classical feedforward network. The hidden state is the quantum state of an n-qubit PQC in an exponentially large Hilbert space C2n, which serves as a coherent recurrent quantum memory. The PQC is unitary by construction, making the hidden-state evolution norm-preserving without external constraints. At each timestep, mid-circuit Pauli expectation-value readouts are combined with the input embedding and processed by the feedforward network, which provides explicit classical nonlinearity. The outputs parametrize the PQC, which updates the hidden state via unitary dynamics. The QRNN is compact and physically consistent, and it unifies (i) unitary recurrence as a high-capacity memory, (ii) partial observation via mid-circuit readouts, and (iii) nonlinear classical control for input-conditioned parametrization. We evaluate the model in simulation with up to 14 qubits on sentiment analysis, MNIST, permuted MNIST, copying memory, and language modeling. For sequence-to-sequence learning, we further devise a soft attention mechanism over the mid-circuit readouts and show its effectiveness for machine translation. To our knowledge, this is the first model (RNN or otherwise) grounded in quantum operations to achieve competitive performance against strong classical baselines across a broad class of sequence-learning tasks.