# Quantum Variational Autoencoder

arXiv: https://arxiv.org/abs/1802.05779 · HTML: https://mlsanity.com/paper/1802.05779/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2018.

## Built on by (most cited first, 30 of 41)

- [Recent Advances for Quantum Neural Networks in Generative Learning](https://mlsanity.com/paper/2206.03066/) (2022)
- [On Circuit-based Hybrid Quantum Neural Networks for Remote Sensing Imagery Classification](https://mlsanity.com/paper/2109.09484/) (2021)
- [Generative quantum machine learning via denoising diffusion probabilistic models](https://mlsanity.com/paper/2310.05866/) (2023)
- [projUNN: efficient method for training deep networks with unitary matrices](https://mlsanity.com/paper/2203.05483/) (2022)
- [Adiabatic Quantum Graph Matching with Permutation Matrix Constraints](https://mlsanity.com/paper/2107.04032/) (2021)
- [On the Sample Complexity of Quantum Boltzmann Machine Learning](https://mlsanity.com/paper/2306.14969/) (2023)
- [Variational inference with a quantum computer](https://mlsanity.com/paper/2103.06720/) (2021)
- [A Hybrid Quantum-Classical Algorithm for Robust Fitting](https://mlsanity.com/paper/2201.10110/) (2022)
- [Quantum Annealing Formulation for Binary Neural Networks](https://mlsanity.com/paper/2107.02751/) (2021)
- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Hybrid quantum-classical machine learning for generative chemistry and drug design](https://mlsanity.com/paper/2108.11644/) (2021)
- [Quantum Generative Diffusion Model: A Fully Quantum-Mechanical Model for Generating Quantum State Ensemble](https://mlsanity.com/paper/2401.07039/) (2024)
- [Quantum neural network autoencoder and classifier applied to an industrial case study](https://mlsanity.com/paper/2205.04127/) (2022)
- [Quantum State Generation with Structure-Preserving Diffusion Model](https://mlsanity.com/paper/2404.06336/) (2024)
- [Scalable Variational Quantum Circuits for Autoencoder-based Drug Discovery](https://mlsanity.com/paper/2112.12563/) (2021)
- [CaloDVAE : Discrete Variational Autoencoders for Fast Calorimeter Shower Simulation](https://mlsanity.com/paper/2210.07430/) (2022)
- [Mixed-State Quantum Denoising Diffusion Probabilistic Model](https://mlsanity.com/paper/2411.17608/) (2024)
- [Quantum Generative Models for Image Generation: Insights from MNIST and MedMNIST](https://mlsanity.com/paper/2504.00034/) (2025)
- [The Conceptual VAE](https://mlsanity.com/paper/2203.11216/) (2022)
- [From Conceptual Spaces to Quantum Concepts: Formalising and Learning Structured Conceptual Models](https://mlsanity.com/paper/2401.08585/) (2023)
- [Quantum Generative Adversarial Autoencoders: Learning latent representations for quantum data generation](https://mlsanity.com/paper/2509.16186/) (2025)
- [Assessment of image generation by quantum annealer](https://mlsanity.com/paper/2103.08373/) (2021)
- [Quantum Inception Score](https://mlsanity.com/paper/2311.12163/) (2023)
- [Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning](https://mlsanity.com/paper/2505.05151/) (2025)
- [Physics-inspired Generative AI models via real hardware-based noisy quantum diffusion](https://mlsanity.com/paper/2505.22193/) (2025)
- [Anomaly Detection in Aeronautics Data with Quantum-compatible Discrete Deep Generative Model](https://mlsanity.com/paper/2303.12302/) (2023)
- [PearSAN: A Machine Learning Method for Inverse Design using Pearson Correlated Surrogate Annealing](https://mlsanity.com/paper/2412.19284/) (2024)
- [Quantum Circuit-Based Learning Models: Bridging Quantum Computing and Machine Learning](https://mlsanity.com/paper/2602.00048/) (2026)
- [VConstruct: Filling Gaps in Chl-a Data Using a Variational Autoencoder](https://mlsanity.com/paper/2101.10260/) (2021)
- [Formalising and Learning a Quantum Model of Concepts](https://mlsanity.com/paper/2302.14822/) (2023)

## Abstract (arXiv)

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 (RBM). 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.