Variational Autoencoders (VAEs) are fundamental for generative modeling and image reconstruction, yet their performance often struggles to maintain high fidelity in reconstructions. This study introduces a hybrid model, Quantum Variational Autoencoder (Q-VAE), which integrates quantum encoding within the encoder while utilizing fully connected layers to extract meaningful representations. The decoder uses transposed convolution layers for up-sampling. The Q-VAE is evaluated against the classical VAE and the classical direct-passing VAE, which utilizes windowed pooling filters. Results on the MNIST and USPS datasets demonstrate that Q-VAE consistently outperforms classical approaches, achieving lower Fréchet Inception Distance scores, thereby indicating superior image fidelity and enhanced reconstruction quality. These findings highlight the potential of Q-VAE for high-quality synthetic data generation and improved image reconstruction in generative models.
Variational Autoencoders (VAEs) are fundamental for generative modeling and image reconstruction, yet their performance often struggles to maintain high fidelity in reconstructions. This study introduces a hybrid model, Quantum Variational Autoencoder (Q-VAE), which integrates quantum encoding within the encoder while utilizing fully connected layers to extract meaningful representations. The decoder uses transposed convolution layers for up-sampling. The Q-VAE is evaluated against the classical VAE and the classical direct-passing VAE, which utilizes windowed pooling filters. Results on the MNIST and USPS datasets demonstrate that Q-VAE consistently outperforms classical approaches, achieving lower Fréchet Inception Distance scores, thereby indicating superior image fidelity and enhanced reconstruction quality. These findings highlight the potential of Q-VAE for high-quality synthetic data generation and improved image reconstruction in generative models.
We propose a quantum implicit neural representation (QINR)-based autoencoder (AE) and variational autoencoder (VAE) for image reconstruction and generation tasks. Our purpose is to demonstrate that the QINR in VAEs and AEs can transform information from the latent space into highly rich, periodic, and high-frequency features. Additionally, we aim to show that the QINR-VAE can be more stable than various quantum generative adversarial network (QGAN) models in image generation because it can address the low diversity problem. Our quantum-classical hybrid models consist of a classical convolutional neural network (CNN) encoder and a quantum-based QINR decoder. We train the QINR-AE/VAE with binary cross-entropy with logits (BCEWithLogits) as the reconstruction loss. For the QINR-VAE, we additionally employ Kullback-Leibler divergence for latent regularization with beta/capacity scheduling to prevent posterior collapse. We introduce learnable angle-scaling in data reuploading to address optimization challenges. We test our models on the MNIST, E-MNIST, and Fashion MNIST datasets to reconstruct and generate images. Our results demonstrate that the QINR structure in VAE can produce a wider variety of images with a small amount of data than various generative models that have been studied. We observe that the generated/reconstructed images from the QINR-VAE/AE are clear with sharp boundaries and details. Overall, we find that the addition of QINR-based quantum layers into the AE/VAE frameworks shows improved performance of reconstruction/generation under the constrained experimental setting relative to the specific baselines.
Abstract Recent proposals for quantum generative adversarial networks (GANs) suffer from the issue of mode collapse, analogous to classical GANs, wherein the distribution learnt by the GAN fails to capture the high mode complexities of the target distribution. Mode collapse can arise due to the use of uninformed prior distributions in the generative learning task. To alleviate the issue of mode collapse for quantum GANs, this work presents a novel hybrid quantum-classical generative model, the VAE-QWGAN, which combines the strengths of a classical variational autoencoder (VAE) with a hybrid quantum Wasserstein GAN (QWGAN). The VAE-QWGAN fuses the VAE decoder and QWGAN generator into a single quantum model and utilizes the VAE encoder for data-dependent latent vector sampling during training. This, in turn, enhances the diversity and quality of generated images. To generate new data from the trained model at inference, we sample from a Gaussian mixture model (GMM) prior that is learnt on the latent vectors generated during training. We conduct extensive experiments for image generation QGANs on MNIST/Fashion-MNIST datasets and compute a range of metrics that measure the diversity and quality of generated samples. We show that VAE-QWGAN demonstrates significant improvement over existing QGAN approaches.
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.
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.
ζ-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, ζ-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 ζ-QVAE, we demonstrate its performance on genomics and synthetic data. Our results indicate that ζ-QVAE learns representations that better utilize the capacity of the latent space and exhibits similar or better performance compared to matched classical models.
Neural topic models enable scalable semantic discovery, but their integration with quantum hardware remains largely unexplored. We present a proof-of-concept hybrid classical-quantum variational autoencoder (VAE) for topic modeling, embedding parameterized quantum circuits within the VAE inference network while retaining a classical topic-word decoder. To address the resource constraints of quantum hardware, we propose a modified Gaussian Softmax posterior that decouples latent space dimensionality from the number of topics to be extracted, enabling the model to operate with a low-resource 10-qubit quantum device. On the AgNews dataset, the hybrid VAE outperforms state-of-the-art neural topic models (NTMs), reaching a Cv coherence score of 0.71 and an NPMI score of 0.20 while preserving high topic diversity. For comparison, we also construct a fully classical variant, which also outperforms state-of-the-art models on AgNews and exhibits clear class separation in the latent space. These results demonstrate that hybrid VAEs are computationally viable even on NISQ-era devices and represent a promising direction for quantum-enhanced topic modeling.