# Trainability of IQP Quantum Circuit Born Machines Under Gaussian Initialization

arXiv: https://arxiv.org/abs/2606.10179 · HTML: https://mlsanity.com/paper/2606.10179/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 22 references that are in the map.
- First posted on arXiv 8 Jun 2026.

## Builds on (most cited first, 13 of 13)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Differentiable Learning of Quantum Circuit Born Machine](https://mlsanity.com/paper/1804.04168/) (2018)
- [Exponential concentration in quantum kernel methods](https://mlsanity.com/paper/2208.11060/) (2022)
- [The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine](https://mlsanity.com/paper/1904.02214/) (2019)
- [On weight initialization in deep neural networks](https://mlsanity.com/paper/1704.08863/) (2017)
- [Escaping from the Barren Plateau via Gaussian Initializations in Deep Variational Quantum Circuits](https://mlsanity.com/paper/2203.09376/) (2022)
- [Do Quantum Circuit Born Machines Generalize?](https://mlsanity.com/paper/2207.13645/) (2022)
- [A Framework for Demonstrating Practical Quantum Advantage: Racing Quantum against Classical Generative Models](https://mlsanity.com/paper/2303.15626/) (2023)
- [Generalization Metrics for Practical Quantum Advantage in Generative Models](https://mlsanity.com/paper/2201.08770/) (2022)
- [IQP Born Machines under Data-dependent and Agnostic Initialization Strategies](https://mlsanity.com/paper/2603.14576/) (2026)
- [Characterizing Trainability of Instantaneous Quantum Polynomial Circuit Born Machines](https://mlsanity.com/paper/2602.11042/) (2026)

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

- [Generative Quantum Machine Learning Methods for Cancer Detection using Augmented Datasets](https://mlsanity.com/paper/2610.15110/) (2026)

## Abstract (arXiv)

Quantum Circuit Born Machines (QCBMs) offer a natural approach to generative machine learning by leveraging the Born rule. Recent work has provided a method to classically train QCBMs with Instantaneous Quantum Polynomial (IQP) circuits via the Maximum Mean Discrepancy (MMD) loss. Despite the assumed intractability of sampling from IQP circuits classically, their expectation values can be computed classically, enabling training of these IQP QCBMs. However, quantum machine learning (QML) models have various other challenges, including trainability issues caused by exponential concentration or barren plateaus. While these issues have been explored for parameters sampled from a uniform distribution, little work has been done to rigorously treat the use of arbitrary Gaussian initialization schemes. This work leverages Stein's lemma and Lipschitz concentration bounds for Gaussian random variables to provide an analytical lower bound of the variance of the gradient and a probabilistic concentration bound of the deviation of the gradient from its mean. It discusses strategies to either avoid or encourage exponential concentration, as well as the conditions under which barren plateaus are more likely to occur.