# Generative quantum advantage for classical and quantum problems

arXiv: https://arxiv.org/abs/2509.09033 · HTML: https://mlsanity.com/paper/2509.09033/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 89 references that are in the map.
- First posted on arXiv 10 Sep 2025.

## Builds on (most cited first, 30 of 32)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Spurious Local Minima are Common in Two-Layer ReLU Neural Networks](https://mlsanity.com/paper/1712.08968/) (2017)
- [Information-theoretic bounds on quantum advantage in machine learning](https://mlsanity.com/paper/2101.02464/) (2021)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine](https://mlsanity.com/paper/1904.02214/) (2019)
- [TensorFlow Quantum: A Software Framework for Quantum Machine Learning](https://mlsanity.com/paper/2003.02989/) (2020)
- [Globally Optimal Gradient Descent for a ConvNet with Gaussian Inputs](https://mlsanity.com/paper/1702.07966/) (2017)
- [On the Quantum versus Classical Learnability of Discrete Distributions](https://mlsanity.com/paper/2007.14451/) (2020)
- [Exponential separations between learning with and without quantum memory](https://mlsanity.com/paper/2111.05881/) (2021)
- [Out-of-distribution generalization for learning quantum dynamics](https://mlsanity.com/paper/2204.10268/) (2022)
- [Enhancing Generative Models via Quantum Correlations](https://mlsanity.com/paper/2101.08354/) (2021)
- [Trainability barriers and opportunities in quantum generative modeling](https://mlsanity.com/paper/2305.02881/) (2023)
- [Learning to predict arbitrary quantum processes](https://mlsanity.com/paper/2210.14894/) (2022)
- [Optimal Quantum Sample Complexity of Learning Algorithms](https://mlsanity.com/paper/1607.00932/) (2016)
- [On quantum backpropagation, information reuse, and cheating measurement collapse](https://mlsanity.com/paper/2305.13362/) (2023)
- [Learning many-body Hamiltonians with Heisenberg-limited scaling](https://mlsanity.com/paper/2210.03030/) (2022)
- [Quantum statistical query learning](https://mlsanity.com/paper/2002.08240/) (2020)
- [Efficient estimation of Pauli observables by derandomization](https://mlsanity.com/paper/2103.07510/) (2021)
- [Learning shallow quantum circuits](https://mlsanity.com/paper/2401.10095/) (2024)
- [Hardness of Learning Neural Networks under the Manifold Hypothesis](https://mlsanity.com/paper/2406.01461/) (2024)
- [A Framework for Demonstrating Practical Quantum Advantage: Racing Quantum against Classical Generative Models](https://mlsanity.com/paper/2303.15626/) (2023)
- [Hardness of Learning Neural Networks with Natural Weights](https://mlsanity.com/paper/2006.03177/) (2020)
- [Learning quantum states prepared by shallow circuits in polynomial time](https://mlsanity.com/paper/2410.23618/) (2024)

## Built on by (most cited first, 11 of 11)

- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Exponential quantum advantage in processing massive classical data](https://mlsanity.com/paper/2604.07639/) (2026)
- [Gated QKAN-FWP: Scalable Quantum-inspired Sequence Learning](https://mlsanity.com/paper/2605.06734/) (2026)
- [A PAC-Bayesian approach to generalization for quantum models](https://mlsanity.com/paper/2603.22964/) (2026)
- [Learning and Generating Mixed States Prepared by Shallow Channel Circuits](https://mlsanity.com/paper/2604.01197/) (2026)
- [Scaling Quantum Machine Learning without Tricks: Full-Resolution and Diverse Image Generation](https://mlsanity.com/paper/2603.00233/) (2026)
- [Minimizing classical resources in variational measurement-based quantum computation for generative modeling](https://mlsanity.com/paper/2604.11578/) (2026)
- [Lie Group Diffusion Models for Hardware-Aware Quantum Circuit Synthesis](https://mlsanity.com/paper/2606.29636/) (2026)
- [Toward Generative Quantum Utility via Correlation-Complexity Map](https://mlsanity.com/paper/2603.06440/) (2026)
- [Adversarial Effects on Expressibility and Trainability in Distributed Variational Quantum Algorithms](https://mlsanity.com/paper/2605.03629/) (2026)
- [Verifiable Sampling for Delegated Generative Quantum Machine Learning](https://mlsanity.com/paper/2610.13211/) (2026)

## Abstract (arXiv)

Recent breakthroughs in generative machine learning, powered by massive computational resources, have demonstrated unprecedented human-like capabilities. While beyond-classical quantum experiments can generate samples from classically intractable distributions, their complexity has thwarted all efforts toward efficient learning. This challenge has hindered demonstrations of generative quantum advantage: the ability of quantum computers to learn and generate desired outputs substantially better than classical computers. We resolve this challenge by introducing families of generative quantum models that are hard to simulate classically, are efficiently trainable, exhibit no barren plateaus or proliferating local minima, and can learn to generate distributions beyond the reach of classical computers. Using a 68-qubit superconducting quantum processor, we demonstrate these capabilities in two scenarios: learning classically intractable probability distributions and learning quantum circuits for accelerated physical simulation. Our results establish that both learning and sampling can be performed efficiently in the beyond-classical regime, opening new possibilities for quantum-enhanced generative models with provable advantage.