Recent progress in quantum algorithms and hardware indicates the potential importance of quantum computing in the near future. However, finding suitable application areas remains an active area of research. Quantum machine learning is touted as a potential approach to demonstrate quantum advantage within both the gate-model and the adiabatic schemes. For instance, the Quantum-assisted Variational Autoencoder (QVAE) has been proposed as a quantum enhancement to the discrete VAE. We extend on previous work and study the real-world applicability of a QVAE by presenting a proof-of-concept for similarity search in large-scale high-dimensional datasets. While exact and fast similarity search algorithms are available for low dimensional datasets, scaling to high-dimensional data is non-trivial. We show how to construct a space-efficient search index based on the latent space representation of a QVAE. Our experiments show a correlation between the Hamming distance in the embedded space and the Euclidean distance in the original space on the Moderate Resolution Imaging Spectroradiometer (MODIS) dataset.Further, we find real-world speedups compared to linear search and demonstrate memory-efficient scaling to half a billion data points.
Recent progress in quantum algorithms and hardware indicates the potential importance of quantum computing in the near future. However, finding suitable application areas remains an active area of research. Quantum machine learning is touted as a potential approach to demonstrate quantum advantage within both the gate-model and the adiabatic schemes. For instance, the Quantum-assisted Variational Autoencoder (QVAE) has been proposed as a quantum enhancement to the discrete VAE. We extend on previous work and study the real-world applicability of a QVAE by presenting a proof-of-concept for similarity search in large-scale high-dimensional datasets. While exact and fast similarity search algorithms are available for low dimensional datasets, scaling to high-dimensional data is non-trivial. We show how to construct a space-efficient search index based on the latent space representation of a QVAE. Our experiments show a correlation between the Hamming distance in the embedded space and the Euclidean distance in the original space on the Moderate Resolution Imaging Spectroradiometer (MODIS) dataset.Further, we find real-world speedups compared to linear search and demonstrate memory-efficient scaling to half a billion data points.
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.
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 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.
In recent years, machine learning and deep learning have driven advances in domains such as image classification, speech recognition, and anomaly detection by leveraging multi-layer neural networks to model complex data. Simultaneously, quantum computing (QC) promises to address classically intractable problems via quantum parallelism, motivating research in quantum machine learning (QML). Among QML techniques, quantum autoencoders show promise for compressing high-dimensional quantum and classical data. However, designing effective quantum circuit architectures for quantum autoencoders remains challenging due to the complexity of selecting gates, arranging circuit layers, and tuning parameters.
This paper proposes a neural architecture search (NAS) framework that automates the design of quantum autoencoders using a genetic algorithm (GA). By systematically evolving variational quantum circuit (VQC) configurations, our method seeks to identify high-performing hybrid quantum-classical autoencoders for data reconstruction without becoming trapped in local minima. We demonstrate effectiveness on image datasets, highlighting the potential of quantum autoencoders for efficient feature extraction within a noise-prone, near-term quantum era. Our approach lays a foundation for broader application of genetic algorithms to quantum architecture search, aiming for a robust, automated method that can adapt to varied data and hardware constraints.
The aim of the current study is to propose a Quantum-Assisted Variational Autoencoder (QAVAE) model capable of efficiently identifying anomalies in high-dimensional, time-series data produced by cyber-physical systems. The existing approaches to machine learning have some limitations when recording temporal interactions and take substantial time to run with many attributes. To meet all of these challenges, this study aims at proposing a quantum-assisted approach to anomaly detection using the potential of a Quantum-Assisted Variational Autoencoder (QAVAE). The general goal of this research is to optimize anomaly detection systems using consummate deep learning quantum computing models. According to the QAVAE framework, variational inference is employed for learning latent representations of time series data; besides, quantum circuits are utilized for enhancing the capacity of the model and its generalization capability. This work was accomplished using Python programming language, and the analysis was carried out using TensorFlow Quantum. The QAVAE model demonstrates the highest accuracy of 95.2%, indicating its strong capability in correctly identifying both anomalous and normal instances. So, it can learn well from the data and keep stable in the evaluation process, which will make it suitable for real-time anomaly detection in dynamic environments. In conclusion, the QAVAE model brings a reasonable approach and solution for anomaly detection that is accurate in identifying and scalable too. Utilizing the HAI, the dataset achieved a high detection accuracy of 95.2%. Further research has to be dedicated to its application to quantum computing architecture as well as to modifications that allow for its use on multi-variable actual-life data.
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.