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Image Reconstruction Through Adaptive Quantum Feature Representation Using Variational Autoencoders

Dina A. Amer, Asmaa Fawzy

Published Sep 30, 2026• 0 citations
Publisher

Abstract

Image reconstruction and generation have become fundamental tasks in computer vision and quantum-inspired machine learning. Existing quantum-inspired variational autoencoders have demonstrated promising capabilities; however, they often suffer from limited local feature representation, unstable optimization, and performance degradation under noisy environments. This paper proposes quantum-inspired feature-preserving reconstruction variational autoencoder (QFR-VAE), which integrates adaptive handcrafted feature extraction with quantum-inspired latent representation learning. First, it extracts informative local descriptors from overlapping image patches. Then, it employs a differentiable soft gating mechanism before quantum-inspired single-qubit encoding, retaining the full spatial resolution of the input. The encoded representation is then learned using a convolutional variational autoencoder optimized with a composite objective. The proposed model was assessed on the MNIST and Fashion-MNIST datasets under both ideal and depolarizing noisy environments using FID, SSIM, PSNR, and LPIPS. Under ideal environments, it obtained an FID of 24.03, an SSIM of 0.9568, a PSNR of 22.74 dB, and an LPIPS of 0.0539 on MNIST. Whereas for Fashion-MNIST, it achieved an FID of 38.06, an SSIM of 0.8501, a PSNR value 20.66 dB, and an LPIPS of 0.1431. A component study isolating each element of the proposed framework was introduced to show that the single-qubit readout performs comparably to a classical mapping that matches its parameter account.

DOI
10.3390/info17100957

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Image reconstruction and generation have become fundamental tasks in computer vision and quantum-inspired machine learning. Existing quantum-inspired variational autoencoders have demonstrated promising capabilities; however, they often suffer from limited local feature representation, unstable optimization, and performance degradation under noisy environments. This paper proposes quantum-inspired feature-preserving reconstruction variational autoencoder (QFR-VAE), which integrates adaptive handcrafted feature extraction with quantum-inspired latent representation learning. First, it extracts informative local descriptors from overlapping image patches. Then, it employs a differentiable soft gating mechanism before quantum-inspired single-qubit encoding, retaining the full spatial resolution of the input. The encoded representation is then learned using a convolutional variational autoencoder optimized with a composite objective. The proposed model was assessed on the MNIST and Fashion-MNIST datasets under both ideal and depolarizing noisy environments using FID, SSIM, PSNR, and LPIPS. Under ideal environments, it obtained an FID of 24.03, an SSIM of 0.9568, a PSNR of 22.74 dB, and an LPIPS of 0.0539 on MNIST. Whereas for Fashion-MNIST, it achieved an FID of 38.06, an SSIM of 0.8501, a PSNR value 20.66 dB, and an LPIPS of 0.1431. A component study isolating each element of the proposed framework was introduced to show that the single-qubit readout performs comparably to a classical mapping that matches its parameter account.
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ζζζ-QVAE: A Quantum Variational Autoencoder utilizing Regularized Mixed-state Latent Representations
A major challenge in quantum computing is its application to large real-world datasets due to scarce quantum hardware resources. One approach to enabling tractable quantum models for such datasets involves finding low-dimensional representations that preserve essential information for downstream analysis. In classical machine learning, variational autoencoders (VAEs) facilitate efficient data compression, representation learning for subsequent tasks, and novel data generation. However, no quantum model has been proposed that captures these features for direct application to quantum data on quantum computers. Some existing quantum models for data compression lack regularization of latent representations. Others are hybrid models with only some internal quantum components, impeding direct training on quantum data. To address this, we present a fully quantum framework, ζζζ-QVAE, which encompasses all the capabilities of classical VAEs and can be directly applied to map both classical and quantum data to a lower-dimensional space, while effectively reconstructing much of the original state from it. Our model utilizes regularized mixed states to attain optimal latent representations. It accommodates various divergences for reconstruction and regularization. Furthermore, by accommodating mixed states at every stage, it can utilize the full-data density matrix and allow for a training objective defined on probabilistic mixtures of input data. Doing so, in turn, makes efficient optimization possible and has potential implications for private and federated learning. In addition to exploring the theoretical properties of ζζζ-QVAE, we demonstrate its performance on genomics and synthetic data. Our results indicate that ζζζ-QVAE learns representations that better utilize the capacity of the latent space and exhibits similar or better performance compared to matched classical models.
A major challenge in near-term quantum computing is its application to large real-world datasets due to scarce quantum hardware resources. One approach to enabling tractable quantum models for such datasets involves finding low-dimensional representations that preserve essential information for downstream analysis. In classical machine learning, variational autoencoders (VAEs) facilitate efficient data compression, representation learning for subsequent tasks, and novel data generation. However, no quantum model has been proposed that exactly captures all of these features for direct application to quantum data on quantum computers. Some existing quantum models for data compression lack regularization of latent representations, thus preventing direct use for generation and control of generalization. Others are hybrid models with only some internal quantum components, impeding direct training on quantum data. To address this, we present a fully quantum framework, $\ensuremath{\zeta}$-QVAE, which encompasses all the capabilities of classical VAEs and can be directly applied to map both classical and quantum data to a lower-dimensional space, while effectively reconstructing much of the original state from it. Our model utilizes regularized mixed states to attain optimal latent representations. It accommodates various divergences for reconstruction and regularization. Furthermore, by accommodating mixed states at every stage, it can utilize the full data density matrix and allow for a training objective defined on probabilistic mixtures of input data. Doing so, in turn, makes efficient optimization possible and has potential implications for private and federated learning. In addition to exploring the theoretical properties of $\ensuremath{\zeta}$-QVAE, we demonstrate its performance on representative genomics and synthetic data. Our results indicate that $\ensuremath{\zeta}$-QVAE consistently learns representations that better utilize the capacity of the latent space and exhibits similar or better performance compared with matched classical models.
Quantum convolutional neural networks (QCNNs) have become increasingly popular in quantum machine learning (QML) due to their efficient parameterization and hierarchical representation of quantum information. Anomaly detection is an important machine learning task with applications across a wide range of domains, including scientific data analysis. In this work, we adapt a QCNN architecture into a quantum autoencoder (QAE) framework for reconstruction-based anomaly detection. The models are trained in a semi-supervised manner on normal samples to reconstruct feature-extracted and dimensionally reduced time-series data, with reconstruction error used as an anomaly score. We investigate two quantum convolutional autoencoder architectures that differ in their treatment of latent information: a hierarchical architecture in which information remains distributed across the circuit and a bottleneck-based architecture in which information is explicitly compressed and reconstructed using additional decoder qubits. The size of the quantum latent space is varied to study its influence on reconstruction accuracy and anomaly detection performance. The approaches are benchmarked against both a variational quantum circuit and a comparable classical baseline using a real-world exoplanet anomaly-detection dataset. Results indicate a trade-off between latent-space size and model capacity, while also suggesting that explicit latent-space compression through a quantum bottleneck can improve anomaly detection performance relative to architectures that retain information throughout the circuit.
Abstract Image denoising is essential for removing noise in images caused by electric device malfunctions or other factors during image acquisition. It ensures the preservation of image quality and accurate interpretation. Many convolutional autoencoder algorithms have proven effective in image denoising. Owing to their promising efficiency, quantum computers have gained popularity. This paper proposes a method, the quantum convolutional autoencoder (QCAE), which enhances traditional convolutional autoencoders by replacing their latent space with a quantum counterpart implemented via a quantum approximate optimization algorithm (QAOA)-inspired ansatz circuit. To enhance efficiency, we leveraged the advantages of the QAOA-incorporated parameter-shift rule to identify an optimized cost function, facilitating effective learning from data and gradient computation on an actual quantum computer. The proposed QCAE method outperformed its classical counterpart as it exhibited lower training loss and a higher structural similarity index (SSIM) value. QCAE also outperformed its classical counterpart in denoising the MNIST dataset by up to 40% in terms of SSIM value, confirming its enhanced capabilities in real-world applications. Evaluation of QAOA performance across different circuit configurations and layer variations showed that our technique outperformed other circuit designs by 25% on average.