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arXiv:2402.17749

$ζ$-QVAE: A Quantum Variational Autoencoder utilizing Regularized Mixed-state Latent Representations

Gaoyuan Wang, Jonathan Warrell, Prashant S. Emani, Mark Gerstein

Published Feb 27, 2024• 1 citation
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2402.17749

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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.
Variational autoencoders are powerful representation learning models that map complex data into low-dimensional latent spaces, enabling the discovery of interpretable and disentangled factors. Such representations can facilitate the interpretation and controllable generation of data describing complex scientific systems. Understanding how these factors are organized and encoded in latent space is therefore important for developing reliable representation learning models. Recently, quantum variational autoencoders (QVAEs) have been proposed as quantum representation models, demonstrating informative latent representations and improved latent-space occupancy through quantum regularization. However, it remains unclear whether and how QVAEs can learn disentangled and interpretable latent factors. A key challenge in investigating quantum latent factors is that a small number of qubits spans an exponentially large Hilbert space, making the notion of an individual quantum latent dimension nontrivial. Here, we investigate what constitutes an individual quantum latent dimension and whether it can encode a distinct factor. We develop theoretical insights into quantum latent dimensions and support them with empirical studies on representative synthetic problems, including MNIST variants. Across three datasets, we demonstrate that QVAEs can discover factorized and semantically interpretable latent representations, with individual qubits functioning as meaningful latent factors. These results establish a foundation for understanding quantum latent spaces and their potential for structured and interpretable representation learning.
Abstract Variational autoencoders (VAEs) are powerful generative models with the salient ability to perform inference. Here, we introduce a quantum variational autoencoder (QVAE): a VAE whose latent generative process is implemented as a quantum Boltzmann machine (QBM). We show that our model can be trained end-to-end by maximizing a well-defined loss-function: a ‘quantum’ lower-bound to a variational approximation of the log-likelihood. We use quantum Monte Carlo (QMC) simulations to train and evaluate the performance of QVAEs. To achieve the best performance, we first create a VAE platform with discrete latent space generated by a restricted Boltzmann machine. Our model achieves state-of-the-art performance on the MNIST dataset when compared against similar approaches that only involve discrete variables in the generative process. We consider QVAEs with a smaller number of latent units to be able to perform QMC simulations, which are computationally expensive. We show that QVAEs can be trained effectively in regimes where quantum effects are relevant despite training via the quantum bound. Our findings open the way to the use of quantum computers to train QVAEs to achieve competitive performance for generative models. Placing a QBM in the latent space of a VAE leverages the full potential of current and next-generation quantum computers as sampling devices.
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.
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.
Abstract Variational quantum circuits (VQC) lie at the forefront of quantum machine learning research. Still, the use of quantum networks for real data processing remains challenging as the number of available qubits cannot accommodate a large dimensionality of data—if the usual angle encoding scenario is used. To achieve dimensionality reduction, Principal Component Analysis is routinely applied as a pre-processing method before the embedding of the classical features on qubits. In this work, we propose an alternative method which reduces the dimensionality of a given dataset by taking into account the specific quantum embedding that comes after. This method aspires to make quantum machine learning with VQCs more versatile and effective on datasets of high dimension. At a second step, we propose a quantum-inspired classical autoencoder model which can be used to encode information in low latent spaces. The power of our proposed models is exhibited via numerical tests. We show that our targeted dimensionality reduction method considerably boosts VQC’s performance, and we also identify cases for which the second model outperforms classical autoencoders in terms of reconstruction loss.