# Limits of quantum generative models with classical sampling hardness

arXiv: https://arxiv.org/abs/2512.24801 · HTML: https://mlsanity.com/paper/2512.24801/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 65 references that are in the map.
- First posted on arXiv 31 Dec 2025.

## Builds on (most cited first, 15 of 15)

- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [The Pitfalls of Simplicity Bias in Neural Networks](https://mlsanity.com/paper/2006.07710/) (2020)
- [Power of data in quantum machine learning](https://mlsanity.com/paper/2011.01938/) (2020)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [Does provable absence of barren plateaus imply classical simulability?](https://mlsanity.com/paper/2312.09121/) (2023)
- [The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine](https://mlsanity.com/paper/1904.02214/) (2019)
- [On the Quantum versus Classical Learnability of Discrete Distributions](https://mlsanity.com/paper/2007.14451/) (2020)
- [Classical surrogates for quantum learning models](https://mlsanity.com/paper/2206.11740/) (2022)
- [Trainability barriers and opportunities in quantum generative modeling](https://mlsanity.com/paper/2305.02881/) (2023)
- [Shadows of quantum machine learning](https://mlsanity.com/paper/2306.00061/) (2023)
- [On the relation between trainability and dequantization of variational quantum learning models](https://mlsanity.com/paper/2406.07072/) (2024)
- [Query lower bounds for log-concave sampling](https://mlsanity.com/paper/2304.02599/) (2023)
- [Protocols for classically training quantum generative models on probability distributions](https://mlsanity.com/paper/2210.13442/) (2022)
- [Provable quantum speedups for computing persistence in topological data analysis](https://mlsanity.com/paper/2410.21258/) (2024)

## Built on by (most cited first, 1 of 1)

- [Characterizing Trainability of Instantaneous Quantum Polynomial Circuit Born Machines](https://mlsanity.com/paper/2602.11042/) (2026)

## Abstract (arXiv)

Sampling tasks have been successful in establishing quantum advantages both in theory and experiments. This has fueled the use of quantum computers for generative modeling to create samples following the probability distribution underlying a given dataset. In particular, the potential to build generative models on classically hard distributions would immediately preclude classical simulability, due to theoretical separations. In this work, we study quantum generative models from the perspective of output distributions, showing that models that anticoncentrate are not trainable on average, including those exhibiting quantum advantage. In contrast, models outputting data from sparse distributions can be trained. We consider special cases to enhance trainability, and observe that this opens the path for classical algorithms for surrogate sampling. This observed trade-off is linked to verification of quantum processes. We conclude that quantum advantage can still be found in generative models, although its source must be distinct from anticoncentration.