6/ Huge thanks to my amazing supervisors Stefan Woerner and @zoufalc.bsky.social from @ibm-research.bsky.social Zürich, as well as @mvscerezo.bsky.social and @qzoeholmes.bsky.social for their expertise & feedback along the way :)

5/ Empirical validation:
- We train a qGAN to learn a challenging 2D Gaussian mixture.
- We observe that global contributions to gradients, while initially small, become significant over training. This challenges the notion that only local observables are viable for training.

4/ In particular, our results enable us to prove that qGANs -- quantum generators trained with classical discriminators -- avoid barren plateaus, even for arbitrarily deep discriminators. This insight suggests qGANs as a scalable and promising approach for distribution learning.

3/ Our work provides significantly tighter upper & lower gradient bounds for VQAs, compatible with realistic circuit assumptions & efficiently evaluable with classical resources. This clarifies when & why barren plateaus occur and offers practical tools to design scalable VQAs.

2/ VQAs are one of the most promising near-term approaches to solving problems in quantum chemistry and black-box optimization, including machine learning. But they often fail to scale because of *barren plateaus*, aka gradients that vanish exponentially in the system size.