# A Framework for Demonstrating Practical Quantum Advantage: Racing Quantum against Classical Generative Models

arXiv: https://arxiv.org/abs/2303.15626 · HTML: https://mlsanity.com/paper/2303.15626/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 76 references that are in the map.
- First posted on arXiv 27 Mar 2023.

## Builds on (most cited first, 30 of 34)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [NIPS 2016 Tutorial: Generative Adversarial Networks](https://mlsanity.com/paper/1701.00160/) (2016)
- [A Critical Review of Recurrent Neural Networks for Sequence Learning](https://mlsanity.com/paper/1506.00019/) (2015)
- [Deep Learning: A Critical Appraisal](https://mlsanity.com/paper/1801.00631/) (2018)
- [How Faithful is your Synthetic Data? Sample-level Metrics for Evaluating and Auditing Generative Models](https://mlsanity.com/paper/2102.08921/) (2021)
- [Cyclical Annealing Schedule: A Simple Approach to Mitigating KL Vanishing](https://mlsanity.com/paper/1903.10145/) (2019)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Discrete Variational Autoencoders](https://mlsanity.com/paper/1609.02200/) (2016)
- [Sample-Efficient Optimization in the Latent Space of Deep Generative Models via Weighted Retraining](https://mlsanity.com/paper/2006.09191/) (2020)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [Unsupervised Generative Modeling Using Matrix Product States](https://mlsanity.com/paper/1709.01662/) (2017)
- [Bias and Generalization in Deep Generative Models: An Empirical Study](https://mlsanity.com/paper/1811.03259/) (2018)
- [The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine](https://mlsanity.com/paper/1904.02214/) (2019)
- [Continuously Differentiable Exponential Linear Units](https://mlsanity.com/paper/1704.07483/) (2017)
- [On the Quantum versus Classical Learnability of Discrete Distributions](https://mlsanity.com/paper/2007.14451/) (2020)
- [Do Quantum Circuit Born Machines Generalize?](https://mlsanity.com/paper/2207.13645/) (2022)
- [Mutual Information Scaling and Expressive Power of Sequence Models](https://mlsanity.com/paper/1905.04271/) (2019)
- [A review of Generative Adversarial Networks (GANs) and its applications in a wide variety of disciplines -- From Medical to Remote Sensing](https://mlsanity.com/paper/2110.01442/) (2021)

## Built on by (most cited first, 16 of 16)

- [Quantum-Noise-Driven Generative Diffusion Models](https://mlsanity.com/paper/2308.12013/) (2023)
- [Generative quantum advantage for classical and quantum problems](https://mlsanity.com/paper/2509.09033/) (2025)
- [In Search of Quantum Advantage: Estimating the Number of Shots in Quantum Kernel Methods](https://mlsanity.com/paper/2407.15776/) (2024)
- [Tensor tree learns hidden relational structures in data to construct generative models](https://mlsanity.com/paper/2408.10669/) (2024)
- [Physics-inspired Generative AI models via real hardware-based noisy quantum diffusion](https://mlsanity.com/paper/2505.22193/) (2025)
- [QGAN-based data augmentation for hybrid quantum-classical neural networks](https://mlsanity.com/paper/2505.24780/) (2025)
- [Trainability of IQP Quantum Circuit Born Machines Under Gaussian Initialization](https://mlsanity.com/paper/2606.10179/) (2026)
- [Evaluating quantum generative models via imbalanced data classification benchmarks](https://mlsanity.com/paper/2308.10847/) (2023)
- [Hybrid Classical-Quantum architecture for vectorised image classification of hand-written sketches](https://mlsanity.com/paper/2407.06416/) (2024)
- [Supervised Quantum Machine Learning: A Future Outlook from Qubits to Enterprise Applications](https://mlsanity.com/paper/2505.24765/) (2025)
- [Quantum-Enhanced Generative Models for Rare Event Prediction](https://mlsanity.com/paper/2511.02042/) (2025)
- [Quantum Generative Models for Computational Fluid Dynamics: A First Exploration of Latent Space Learning in Lattice Boltzmann Simulations](https://mlsanity.com/paper/2512.22672/) (2025)
- [Quantum Scrambling Born Machine](https://mlsanity.com/paper/2602.17281/) (2026)
- [Adversarial Effects on Expressibility and Trainability in Distributed Variational Quantum Algorithms](https://mlsanity.com/paper/2605.03629/) (2026)
- [Quantum Diffusion Models for Medical Image Analysis](https://mlsanity.com/paper/2609.31070/) (2026)
- [Generative Quantum Machine Learning Methods for Cancer Detection using Augmented Datasets](https://mlsanity.com/paper/2610.15110/) (2026)

## Abstract (arXiv)

Generative modeling has seen a rising interest in both classical and quantum machine learning, and it represents a promising candidate to obtain a practical quantum advantage in the near term. In this study, we build over a proposed framework for evaluating the generalization performance of generative models, and we establish the first quantitative comparative race towards practical quantum advantage (PQA) between classical and quantum generative models, namely Quantum Circuit Born Machines (QCBMs), Transformers (TFs), Recurrent Neural Networks (RNNs), Variational Autoencoders (VAEs), and Wasserstein Generative Adversarial Networks (WGANs). After defining four types of PQAs scenarios, we focus on what we refer to as potential PQA, aiming to compare quantum models with the best-known classical algorithms for the task at hand. We let the models race on a well-defined and application-relevant competition setting, where we illustrate and demonstrate our framework on 20 variables (qubits) generative modeling task. Our results suggest that QCBMs are more efficient in the data-limited regime than the other state-of-the-art classical generative models. Such a feature is highly desirable in a wide range of real-world applications where the available data is scarce.