Learning Disentangled Representations with Quantum Variational Autoencoders
Authors: Gaoyuan Wang, Jerry Tan, Mark Gerstein
Organizations: Program in Computational Biology and Bioinformatics, Yale University, New Haven, Connecticut 06520, USA · Department of Molecular Biophysics and Biochemistry, Yale University, New Haven, Connecticut 06520, USA · Department of Computer Science, Yale University, New Haven, Connecticut 06520, USA · Department of Statistics & Data Science, Yale University, New Haven, Connecticut 06520, USA · Department of Biomedical Informatics & Data Science, Yale University, New Haven, Connecticut 06520, USA
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.
Figures & tables
Figure 1: Latent representation distributions. At β=0.2 , ζ -QVAE encodes the majority of class information in qubit 0, demonstrating successful disentanglement of latent factors.
Figure 2: The multi-class classification accuracy of a simple predictive neural network quantifies the amount of class information encoded in each qubit. Qubits 1 and 2 perform at near–random-guess levels, while qubit 0 encodes the majority of the class information. Shaded areas indicate the error range.
Figure 3: Latent distributions for rotated digits. At β=0.2 , qubit 0 aligns with rotation angles. Qubit 1 shows no correlation, indicating disentanglement of latent factors.
Figure 4: The MSE of simple predictive neural networks quantify the amount of rotation-angle information encoded in each qubit. Qubit 0 encodes the majority of the information, while qubit 1 performs near random. Shaded areas indicate the error range.
Figure 5: MSE of a simple classical neural-network predictor used to quantify the amount of generative-factor information encoded in each subsystem. Qubit 0 predominantly encodes position information, whereas qubits 1 and 2 primarily encode width information. Shaded regions indicate the error range across runs.
Figure 6: Latent distributions for spectral lines. Qubit 0 aligns with the position factor while showing a much weaker association with the width factor, indicating successful disentanglement of the latent variables. At β=0.2 , the latent distribution becomes significantly more structured compared to β=0 , reflecting the effect of regularization on the learned representation.
Department of Electrical Engineering, KAIST, Daejeon, South Korea · Center for Theoretical Physics of Complex Systems, Institute for Basic Science (IBS), Daejeon - 34126, Korea · Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 121 16 Praha 2, Czech Republic
German University in Cairo, Cairo, Egypt · University of Melbourne, Melbourne, Australia · High Performance Computing Lab, Electronics Research Institute, Cairo, Egypt